ISSN (Print): 2224-9893 ISSN (Online): 2226-1869 | ||
The use of optimization techniques for definition of the thermomechanical behavior characteristics of vitrifying polymers BOYARSHINOVA I.N. Received: 19.02.2012 Published: 19.02.2012 ![]() Abstract:
The problem of determining the thermomechanical properties of polymers is considered. The methodology supposed solution to the optimization problem. As the criterion function is selected the sum of squared deviations of the calculated stresses from the known experimental values. Restrictions formulated as a quasi-static boundary value problem of thermoviscoelasticity which solution is spent by the method of finite elements. The criterion function minimization is carried out by the Nelder-Mead method. The uniqueness of the solutions is checked by the descent of several initial approximations. Keywords: optimization, criterion function, the boundary value problem of thermoviscoelasticity, vitrifying polymer. Authors:
Boyarshinova Irina Nikolaevna (Perm, Russian Federation) – Ph.D. in Technical Science, Ass.Professor, Department of Computational Mathematics and Mechanics, State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: vmm@cpl.pstu.ac.ru). References: 1. Matveenko V.P., Smetannikov O.Yu., Trufanov N.A., Shardakov I.N. Thermomechanics of polymer materials in a relaxation transition [Termomekhanika polimernykh materialov v usloviyakh relaksatsionnogo perekhoda]. Fizicheskaya mezomekhanika – Physical Mesomechanics, 1999, Vol. 2, No. 4, pp. 23–29. 2. Smetannikov O.Yu., Trufanov N.A., Shardakov I.N. Defining relations for thermo-mechanical behavior of polymeric materials in the glass transition and softening [Opredelyayushchie sootnosheniya termomekhanicheskogo povedeniya polimernykh materialov v usloviyakh steklovaniya i razmyagcheniya]. Izvestiya Rossiyskoy akademii nauk. Mekhanika tverdogo tela – Mechanics of Solids, 1997, No. 3, pp. 106–114. 3. Samarskiy A.A. Introduction to the theory of difference schemes [Vvedenie v teoriyu raznostnykh skhem]. Moscow: Nauka, 1983, 552 p. 4. Zenkevich O. The finite element method in engineering [Metod konechnykh elementov v tekhnike]: Transl. from eng. Moscow: Mir, 1975, 541 p. 5. Lesin V.V., Lisovets Yu.P. Fundamentals of optimization methods [Osnovy metodov optimizatsii]. Moscow, MAI Publ., 1995, 344 p. Numerical analysis of solidifying blade deflected mode development DUBROVSKAYA A.S., DONGAUSER K.A. Received: 19.02.2012 Published: 19.02.2012 ![]() Abstract:
In this article the primary damages, incipient in manufacturing of gas turbine engine blades are described. For casting material behavioral models examination the range of problems was selected. Research was performed by finite-elemental software ProCAST. Results of numerical calculation have been compared to analytical and software Ansys calculation dates. Block blade solidification process research was performed and the mechanism to avoidance of distortions and cracks was founded. Keywords: solidification, casting, blade, gas turbine engine, consumable pattern. Authors:
Alexandra Sergeevna Dubrovskaya (Perm, Russian Federation) – postgraduate student of Applied Mathematics and Mechanics State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: ivanov@ivanov.com). Konstantin Alexandrovich Dongauser (Perm, Russian Federation) – Aviadvigatel OJSC (614990, 93, Komsomolsky prospect, Perm, Russian Federation, e-mail: office@avid.ru). References: 1. Kablov E.N. Blades casting of gas turbine engine (alloys, technology, claddings) [Litye lopatki gazoturbinnykh dvigateley (splavy, tekhnologiya, pokrytiya)]. Moscow, MISIS, 2001, 632 p. 2. Camobell J. Castings. Butterworth-Heinemann Oxford, 2nd ed., 2003, 335 p. 3. Stepanov Yu.A., Balandin G.F., Rybkin V.A. Foundry engineering technology [Tekhnologiya liteynogo proizvodstva]. Moscow: Mashinostroenie, 1983, P. 5. 4. Zhigankova O.O., Dongauzer K.A. Numerical optimization the process of manufacturing single-crystal turbin blade [Chislennaya optimizatsiya protsessa izgotovleniya soplovoy monokristallicheskoy lopatki turbiny gazoturbinnogo dvigatelya]. Vestnik PGTU. Prikladnaya matematika i mekhanika – Journal of PSTU. Applied Mathematics and Mechanics, 2011, No. 9, P. 103. 5. Dantzig J.A., Rappaz M. Solidification. EPFL Press, 2009, 479 p. The numerical analysis of the contact tension of basic parts axisymmetric case KAMENSKIKH A.A. Received: 19.02.2012 Published: 19.02.2012 ![]() Abstract:
The axisymmetric contact tension of a design of basic parts with a spherical segment of flying structures of bridges is considered. Results of research of practical convergence applied finite element algorithm are resulted. Distribution of contact areas is revealed, the distribution character of normal and tangents stresses on contact interaction surfaces of a design is considered, and also distribution of district stress in a layer. Keywords: a tension, contact interaction, elastoplastic, àxisymmetric problem. Authors:
Anna Kamenskikh (Perm, Russian Federation) – engineer of the Department of Computational Mathematics and Mechanics State National Research Polytechnical University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: anna_kamenskih@mail.ru). References: 1. Aleksandrov V.M., Chebakov M.I. Introduction to contact mechanics [Vvedenie v mekhaniku kontaktnykh vzaimodeystviy]. Rostov-na-Donu, Publ. OOO «TsVVR», 2007, 114 p. 2. Ayzikovich S.M., Aleksandrov V.M., Belokon A.V., Krenev L.I., Trubchik I.S. Contact of a problem of the theory of elasticity for non-uniform environments [Kontaktnye zadachi teorii uprugosti dlya neodnorodnykh sred]. Moscow: Fizmatlit, 2006, 237 p. 3. Bogdanov G.I., Tkachenko S.S., Shulman S.A. Basic parts of bridges. P.1 [Opornye chasti mostov. Ch. 1]. St. Petersburg: Peterburgskiy Gos. Univ. putey soobshcheniya, 2006, P. 32. 4. Goryacheva I.G. Mechanics of frictional interaction [Mekhanika friktsionnogo vzaimodeystviya]. Moscow: Nauka, 2001, 479 p. 5. Malinin N.N. The applied theory of plasticity and creep [Prikladnaya teoriya plastichnosti i polzuchesti]. Moscow: Mashinostroenie, 1975, 400 p. 6. Mechanics of contact interactions [Mekhanika kontaktnykh vzaimodeystviy]. Moscow: Nauka, 1966, 708 p. 7. Timoshenko S.P., Guder Dzh. Theory of Elasticity [Teoriya uprugosti]: Transl. from eng. Under. ed. Shapiro G.S. Moscow: Nauka, 1979, 560 p. Deformability of metals at determination of technological residual stresses in pipes KOLMOGOROV G.L., KUZNETSOVA E.V., POLETAEVA A.J. Received: 10.02.2012 Published: 10.02.2012 ![]() Abstract:
The methods of determination of technological residual stresses tensions are considered in this work, including based on power approach, including of technological residual stresses in analytical dependence on mechanical properties of material, parameters of technology, geometry of pipe purveyance and deformability material. The method of determination of complex parameter of deformability is presented, for a case, when circuitous remaining tensions are experimentally certain on the external surface of pipe procurement. Keywords: residual stresses, metals, steel, deformability, degree of plastic deformation, dragging of pipes, technological parameters. Authors:
Kolmogorov German Leonidovich (Perm, Russian Federation) – Doctor of Technical Sciences, Head of Department of Dynamic and strength of mechanism, State National Research Polytechnical University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: dpm@pstu). Kuznetcova Elena Vladimirivna (Perm, Russian Federation) – Ph.D. in Technical Sciences, Associate professor, Deputy dean, Department of Dynamic and strength of mechanism, State National Research Polytechnical University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: mellen75@mail.ru). Poletaeva Alla Yurevna (Perm, Russian Federation) – Student of Department of Dynamic and strength of mechanism, State National Research Polytechnical University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: Alla281@ya.ru). References: 1. Kuznetsova E.V. Residual stresses and technological strength of the axisymmetric metal obtained by plastic deformation: dis. work [Ostatochnye napryazheniya i tekhnologicheskaya prochnost osesimmetrichnykh metalloizdeliy, poluchennykh plasticheskim deformirovaniem: avtoref. dis.]. Perm: PGTU, 2002, 152 ð. 2. Fogel L.M. Improving the properties of reinforcing wire with four-sided profile by improving themode of drawing and profiling: dis. work [Povyshenie svoystv armaturnoy provoloki s chetyrekhstoronnim profilem na osnove sovershenstvovaniya rezhimov volocheniya i profilirovaniya: avtoref. dis.]. Magnitogorsk, 1991, 147 ð. 3. Patent na izobretenie ¹ 2276779 Russian Federation po tematike «Sposob opredeleniya pokazatelya deformativnosti materiala» [Method for determining the deformability index of the material], zayavka ¹2004128707 ot 27.09.2004, Byul.¹14 ot 20.05.2006, patentoobladatel i zayavitel Perm.GTU, avtory Kolmogorov G.L., Melnikova T.E., Kuznetsova E.V. 4. Sokolov I.A., Uralskiy V.I. Residual stress and quality of metal [Ostatochnye napryazheniya i kachestvo metalloproduktsii]. Moscow: Metallurgiya, 1981, 96 p. 5. Patent na izobretenie ¹ 2366912 Russian Federation po tematike «Sposob opredeleniya ostatochnykh napryazheniy» [The method for determining residual stress] zayavka ¹2008111436/28 ot 23.03.2008, Byul.¹25 ot 10.09.2009, patentoobladatel i zayavitel Perm.GTU, avtory Kolmogorov G.L., Kuznetsova E.V. The influence of operational modes and technological residual stresses on corrosion cracking of zirconium covers are used in atomic engineering KUZNETSOVA E.V., ARTASHOVA A.A. Received: 19.02.2012 Published: 19.02.2012 ![]() Abstract:
Kinds of defects in zirconium tubes are applied in atomic power engineering and also theoretical bases of definition of limiting modes of operation with the account possible residual stresses are considered in the article. Ranges of breaking pressure with the account viscosity factor are calculated. Keyword: zirconium covers, surface defects, technological processes, residual stresses, viscosity of destruction, crack resistance, limiting modes of operation. Authors:
Kuznetsova Elena Vladimirovna (Perm, Russian Federation) – Ph.D(tech.), Àssociate professor, Deputy dean, Department Dynamic and strength of mechanism, State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: mellen75@mail.ru). Artashova Aleksandra Anatolyevna (Perm, Russian Federation) – student of Department Dynamic and strength of mechanism, State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: skylse@mail.ru). References: 1. Nikulin S.A. Zirconium alloys for nuclear reactors [Tsirkonievye splavy dlya yadernykh energeticheskikh reaktorov]. Moscow: Ucheba, 2007, 92 p. 2. Nikulin S.A., Khanzhin V.G., Rozhnov A.B., Belov V.A. Behavior of atomic reactor zirconium cladding fuel rod tubes under extreme operating conditions [Povedenie tsirkonievykh trub tvelov atomnykh reaktorov v ekstremalnykh ekspluatatsionnykh usloviyakh]. Metal Science and Heat Treatment – MiTOM, 2009. ¹ 5, – Ñ. 32–39. 3. Kolmogorov G.L., Kuznetsova E.V. Technical residual stresses and the strength of the axisymmetric hollow articles [Tekhnicheskie ostatochnye napryazheniya i prochnost' osesimmetrichnykh polykh izdeliy] Nauchnye issledovaniya i innovatsii. Nauchnyy zhurnal, Perm, 2008, No 4, pp. 43–51. 4. Pestrikov V.M., Morozov E.V. Fracture mechanics of solids: lectures [Mekhanika razrusheniya tverdykh tel: kurs lektsiy]. St. Petersburg: Professiya, 2002, 302 p. 5. Murakami Yu. Handbook of stress intensity factor: in 2 vol. [Spravochnik po koeffitsientam intensivnosti napryazheniy: v 2 t.]. Moscow: Mir, 1990, vol. 1–2. 6. Timoshenko S.P., Guder Dzh. Theory of Elasticity [Teoriya uprugosti]: Transl. from eng. Under. ed. Shapiro G.S. Moscow: Nauka, 1975, 576 p. 7. Sinelnikov L.P., Averin S.A., Panchenko V.L., Evseev M.V. [Issledovanie sostoyaniya tsirkonievoy truby i perekhodnikov kanala SUZ RBMK-1000 posle 26 let ekspluatatsii] Sb. dokladov sedmoy rossiyskoy konferentsii po reaktornomu materialovedeniyu g. Dimitrovgrad, 8–12 sentyabrya 2003 g. (Proceedings of the Seventh Russian Conference on Reactor Material Science, Dimitrovgrad, 8-12 September 2003). Dimitrovgrad, 2004, pp. 125–129. 8. Belov V.A. Fracture resistance of zirconium-modified alloy cladding tubes for nuclear reactors: abstract. thesis. for obtaining the academic. step. Candidate of Technical.Sciences. [Soprotivlenie razrusheniyu modifitsirovannykh tsirkonievykh splavov dlya obolochechnykh trub atomnykh reaktorov: avtoref. dis… kand. tekhn. nauk]. Moscow, 2011, 23 p. On the question of definition of crystallizing polymer media deformed state accounting big deformations KULIKOV R.G., KULIKOVA T.G. Received: 19.02.2012 Published: 19.02.2012 ![]() Abstract:
The problem on cooling of infinite constant thickness plate made of low pressure polyethylene is considered. Evolution of deformed state caused by temperature and shrink deformations arouse in course of cooling and crystallization process is explored. Constitutional relations accounting big deformations were used to solve boundary thermomechanical problem. Key words: crystallization, polymer, big deformations, numerical methods. Authors:
Kulikov Roman Georgievich (Perm, Russian Federation) – Ph. D. in Physical and Mathematical Sciences, Ass. Professor, Department of Compute Mathematics and Mechanics, State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: kulrtg@mail.ru). Kulikova Tatiana Georgievna (Perm, Russian Federation) – Ph. D. in Physical and Mathematical Sciences, Ass. Professor, Department of Compute Mathematics and Mechanics, State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: kulrtg@mail.ru).
References: 1. Begishev V.P., Matveenko V.P., Pistsov N.V., Shardakov I.N. Modeling of thermomechanical processes in crystallizing polymers [Modelirovanie termomekhanicheskikh protsessov v kristallizuyushchemsya polimere]. Izvestiya Rossiyskoy akademii nauk. Mekhanika tverdogo tela – Mechanics of Solids, 1997, No. 4, pp. 120–132. 2. Shardakov I.N., Golotina L.A. Modeling of deformation processes in amorphous-crystalline polymers [Modelirovanie deformatsionnykh protsessov v amorfno-kristallicheskikh polimerakh]. Vychislitelnaya mekhanika sploshnykh sred – Computational continuum mechanics, 2009, Vol. 2, No 3, pp. 106–113. 3. Zavyalova T.G., Trufanov N.A. Constitutive relations for a viscoelastic body in a crystallization [Opredelyayushchie sootnosheniya dlya vyazkouprugogo tela v usloviyakh kristallizatsii] // Prikladnaya mekhanika i tekhnicheskaya fizika – Journal of Applied Mechanics and Technical Physics, 2005, Vol. 46, No 4, pp 78–87. 4. Kulikova T.G., Trufanov N.A. Numerical solution of a thermomechanical boundary-value problem for crystallizing viscoelastic polymer [Chislennoe reshenie kraevoy zadachi termomekhaniki dlya kristallizuyushchegosya vyazkouprugogo polimera]. Vychislitelnaya mekhanika sploshnykh sred – Computational continuum mechanics, 2008, Vol. 1, No 2, pp. 38–52. 5. Malkin A.Ya., Begishev V.P. Chemical Forming Polymers [Khimicheskoe formovanie polimerov]. Moscow: Khimiya, 1991, 540 p. 6. Thermophysical and rheological properties of polymers. Handbook [Teplofizicheskie i reologicheskie kharakteristiki polimerov. Spravochnik]. Kiev: Naukova dumka, 1977, 244 p. 7. Piven A.N., Grechannaya N.A., Chernobylskiy N.I. Thermophysical properties of polymeric materials [Teplofizicheskie svoystva polimernykh materialov]. Kiev: Vishcha shkola, 1976, 180 p. 8. Nilsen L. Mechanical properties of polymers and polymer composites [Mekhanicheskie svoystva polimerov i polimernykh kompozitsiy]: Transl. from eng. Moscow: Khimiya, 1978, 312 p. 9. Lure A.I. Nonlinear theory of elasticity [Nelineynaya teoriya uprugosti]. Moscow: Nauka, 1980, 512 p. 10. Kulikova T.G., Trufanov N.A. [Opredelyayushchie sootnosheniya dlya kristallizuyushchegosya polimernogo materiala i poshagovaya protsedura resheniya s uchetom konechnykh deformatsiy]. Vychislitelnaya mekhanika – Computational Mechanics, Perm: Perm, Gos. tekhn. Univ. Publ, 2008, No. 7, pp. 170–180. 11. Adamov A.A., Matveenko V.P., Trufanov N.A., Shardakov I.N. Methods of Applied Viscoelasticity [Metody prikladnoy vyazkouprugosti]. Ekaterinburg: UrO RAN, 2003, 411 p. 12. Kulikova T.G. To the description of crystallizing polymer material’s deformation with regard to large deformations [K opisaniyu deformirovaniya kristallizuyushchegosya polimernogo materiala s uchetom bolshikh deformatsiy]. PSTU Mechanics Bulletin – Vestnik PGTU. Mekhanika, 2010, No. 3, pp.67–85. 13. Zenkevich O. The finite element method in engineering [Metod konechnykh elementov v tekhnike]: Transl. from eng. Moscow: Mir, 1975, 541 p. Calculation of the frame timber structures with FEM MAKSIMOV P.V., VOLKOV A.I. Received: 19.02.2012 Published: 19.02.2012 ![]() Abstract:
The features of the numerical calculation of frame wooden structures by using the finite element method are shown. The mathematical formulation of the problem of mechanics about static deformation of frame constructions which consist of rods and plates is presented. The recommendations on the integration of complex physical and mechanical properties of wood, the implementation of numerical calculations in the package ANSYS are given. Keywords: frame construction, deformation of beams and rods, bending of plates, properties of wood, snow load. Authors:
Maksimov Petr Victorovich (Perm, Russian Federation) – Ph.D. in Technical Science, Ass.Professor, Department of Computational Mathematics and Mechanics, State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: pvmperm@mail.ru). Volkov Anton Igorevich (Perm, Russian Federation) – Student of Department of Computational Mathematics and Mechanics, State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: pvmperm@mail.ru). References: 1. Wooden structures. Guide the designer of industrial buildings [Derevyannye konstruktsii. Spravochnik proektirovshchika promyshlennykh sooruzheniy]. Moscow– Leningrad: Promstroyproekt, 1937, 915 p. 2. Ivanov V.F. Structures made of wood and plastic [Konstruktsii iz dereva i plastmass]. Leningrad–Moscow, 1988, 352 p. 3. Kalinin V.M., Sokova S.D. Assessment of technical condition of buildings [Otsenka tekhnicheskogo sostoyaniya zdaniy]. Moscow: INFRA-M, 2006, 268 p. 4. Komkov V.A., Roshchina. S.I., Timakhova N.S. Technical operation of buildings and structures [Tekhnicheskaya ekspluatatsiya zdaniy i sooruzheniy]. Moscow: INFRA-M, 2005, 288 p.
5. Technical maintenance and repair of buildings and structures [Tekhnicheskoe obsluzhivanie i remont zdaniy i sooruzheniy]. Moscow: Stroyizdat, 1993, 208 p. 6. Stroitelnye normy i pravila: SNiP 2.25.80. Derevyannye konstruktsii: normativno-tekhnicheskiy material [Wooden structures: regulatory and technical material]. Moscow, 1996, 35 p. 7. Stroitelnye normy i pravila: SNiP 2.01.07–85. Nagruzki i vozdeystviya: normativno-tekhnicheskiy material [Loads and effects: regulatory and technical material]. Moscow, 1987, 36 p. 8. Demidov S.P. Theory of elasticity [Teoriya uprugosti]. Moscow: Vyssh. Shk., 1972, 416 p. 9. Smirnov A.F., Aleksandrov A.V., Lashcheninkov B.Ya., Shaposhnikov N.N. Building Mechanics. The core of the system [Stroitelnaya mekhanika. Sterzhnevye sistemy]. Moscow: Stroyizdat, 1981, 512 p. 10. Timoshenko S.P., Voynovskiy-Kriger S. Plates and capsules [Plastinki i obolochki]: Transl. from eng. Under. ed. Shapiro G.S. Moscow: Nauka, 1966, 636 p. 11. Maksimov P.V. The Models of Forced Motion of Micro Accelerometer [O nekotorykh podkhodakh k postroeniyu modeley vynuzhdennogo dvizheniya mikroakselerometra]. PSTU Mechanics Bulletin – Vestnik PGTU. Mekhanika, 2011, No. 1, pp. 55–71. 12. Filin A.P. Elements of theory of shells [Elementy teorii obolochek]. Leningrad: Stroyizdat, Leningr. otd-nie, 1975, 256 p. 13. Zenkevich O. The finite element method in engineering [Metod konechnykh elementov v tekhnike]: Transl. from eng. Moscow: Mir, 1975, 541 p. Research convection heat exchange in the cable channel, laid in the earth NAVALIKHINA E.U., TRUFANOVA N.M. Received: 19.02.2012 Published: 19.02.2012 ![]() Abstract:
The mathematical model of processes convection heat exchange in the cable channel, laid in the ground without taking into account the thermal radiation. Shows the dependence of temperature on the surface of the cable division into finite elements Fields the trajectory of particle motion in the cable channel, the temperature field. Shows the dependence of temperature on the surface of the cable channel on the thermal conductivity of various structural elements in the cable channel. Keywords: mathematical model, convection, the cable channel, heat mass exchange. Authors:
Navalikhina Ekaterina Yurievna (Perm, Russian Federation) – Post-graduate student of the chair «Designing and technology in electrical engineering, State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: ktei@pstu.ru). Trufanova Nataliia Mikhailovna (Perm, Russian Federation) Doctor of Technical Sciences, Professor, Head of the chair «Designing and technology in electrical engineering», State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: ktei@pstu.ru). References: 1. Loytsyanskiy L.G. Mechanics of a liquid and gas [Mekhanika zhidkosti i gaza]. Moscow: Nauka, 1973, 848 p. 2. Shcherbinin A.G, Trufanova N.M., Navalikhina E.Yu., Savchenko V.G. Definition of operational characteristics of the cables laid in the cable channel [Opredelenie ekspluatatsionnykh kharakteristik kabeley, prolozhennykh v kabelnom kanale]. Russian Electrical Engineering – Elektrotekhnika, 2011, No. 11, pp. 16a–20. 3. Kreith F., Black W.Z. Basic Heat Transfer. Harper and Row, Publishers, New York, 1980, 512 ð. 4. Tadmor Z., Gogos K. Principles of polymer processing [Teoreticheskie osnovy pererabotki polimerov]: Transl. from eng. Moscow, Khimiya, 1984, 632 p. 5. Yang Liu. Coupled conduction-convection PROBLEM for an underground duct containing eight insulated cables. International Journal of Computational Engineering Science. Vol. 1, No. 2 (2000) 187–206 Imperial College Press. Numerical analysis of deformation processes in the optical fiber sensors NAYMUSHIN I.G., TRUFANOV N.A., SHARDAKOV I.N. Received: 10.02.2012 Published: 10.02.2012 ![]() Abstract:
In this paper the deformation processes taking place in system of the substrate-adhesive-fiber optic sensor are presented. The task in the theory of linear viscoelasticity. The decision was made numerically using finite-element package ANSYS, to deal with the procedure step method of integration. Deformation distribution on length of the fibre-optical sensor is defined, thanks to it is minimum admissible length of the sensor is established. Dependences for various cases of loads are received and sensor models, evolution of deformations in the sensor is certain. It is revealed, that use of cover DeSolite 3471-1-152À is inadmissible, owing to falling of deformation more than 10 times for a small time interval. Keywords: fiber optic sensor, the theory of linear viscoelastic, relaxation, finite element model, the evolution of strain. Authors:
Naymusin Ilya Gennadievich (Perm, Russian Federation) Student of Department of Computational Mathematics and Mechanics, State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: vmm@cpl.pstu.ac.ru). Trufanov Nikolay Aleksandrovich (Perm, Russian Federation) Doctor of Technical Sciences, Professor, Head of Department of Computational Mathematics and Mechanics, State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, Shardakov Igor Nikolaevich (Perm, Russian Federation) Doctor of Physics and Mathematics, laboratory chief of Modeling of thermomechanical processes in deformable bodies, Institute of Continuous Media Mechanics (614013, Perm, Acad. Koroleva st., 1, Perm, Russian Federation, References: 1. Udd E. Fiber Optic Sensors. An introductory course for engineers and scientists [Volokonno-opticheskie datchiki. Vvodnyy kurs dlya inzhenerov i nauchnykh rabotnikov]. Moscow: Tekhnosfera, 2008, 520 p. 2. Neugodnikov A.P., Akhlebinin M.Yu., Egorov F.A., Bykovskiy V.A. Construction monitoring based on fiber-optic srnsors Experience and results of the application for high-rise buildings [Stroitelnyy monitoring na baze volokonno-opticheskikh datchikov. Opyt i rezul'taty primeneniya dlya vysotnykh zdaniy]. Problemj sovremennogo betona i zhelezobetona: dokl Mezhd. Simp. (Modern Problems of Concrete and Reinforced Concrete: Abstracts. Internat. Symp.). Minsk, 2009. 3. Egorov F.A., Neugodnikov A.P., Bykovskiy V.A. Eksperiment alnoestudy of fiber-optic sensors for monitoring strain of reinforced concrete structures [Eksperimentalnoe issledovanie volokonno-opticheskikh datchikov dlya kontrolya deformatsiy zhelezobetonnykh konstruktsiy] Problemj sovremennogo betona i zhelezobetona: dokl Mezhd. Simp. (Modern Problems of Concrete and Reinforced Concrete: Abstracts. Internat. Symp.). Minsk, 2009. 4. Maksimov R.D., Kochetkov V.A. Prediction of the thermal deformation of hybrid composites with viscoelastic components [Prognozirovanie termicheskogo deformirovaniya gibridnykh kompozitov s vyazkouprugimi komponentami]. Mechanics of Composite Materials – Mekhanika kompozitnykh materialov, 1989, No. 6, pp. 969–979. 5. Malyy V.I., Trufanov N.A. Method quasiconstant operators in the theory of anisotropic viscoelasticity ageless materials [Metod kvazikonstantnykh operatorov v teorii vyazkouprugosti anizotropnykh nestareyushchikh materialov] Mechanics of Solids – Izvestiya AN SSSR. Mekhanika tverdogo tela, 1987, No. 6, pp. 148–154. 6. Kulikov R.G., Trufanov N.A. Iterative method for solving quasistatic nonlinear viscoelastic problems [Iteratsionnyy metod resheniya kvazistaticheskikh nelineynykh zadach vyazkouprugosti]. Vychislitelnaya mekhanika sploshnykh sred – Computational continuum mechanics, 2009, Vol. 2, No. 3, pp. 44–56. 7. Adamov A.A., Matveenko V.P., Trufanov N.A., Shardakov I.N. Methods of Applied Viscoelasticity [Metody prikladnoy vyazkouprugosti]. Ekaterinburg: UrO RAN, 2003, 411 p. 8. Taylor R.L., Pister K.S., Goudreau G.L. Thermomechanical analysis of viscoelastic solids. International journal for numerical methods in engineerin, 1970, Vol. 2, No. 1, pp. 45–59. About the mechanism of the liquid’s axial rising as a result of cylindrical vessel free fall PINAKOV V.I. Received: 10.02.2012 Published: 10.02.2012 ![]() Abstract:
The analytical model, which allow to estimate the height of the liquid’s rising at the concussion of the free fall cylindrical vessel and the hard level is physically grounded and realized. The elastic models of the liquid and vessel’s material are applied. It shown that the pressure waves (flat and cylindrical, converging to the axis of cylinder) are generated in liquid. Their reflection from free surface, which configuration isn’t fixed, at the presence of acute angle of the wetting, can lead to splash of liquid whose height 10 times more then the vessel’s height of fall. Keywords: imponderability, cylindrical acoustic wave, supersonic movement, limiting wetting angle, free surface, capillary constant. Authors:
Pinakov Valerij Ivanovich (Novosibirsk, Russian Federation) – Ph.D. in Technical Science, Lead scientist, Design and technology Department Lavrentyev Institute of Hydrodynamics of Siberian Branch of Russian Academy of Sciences (630090, Novosibirsk, st. Tereshkovoy 29, Russian Federation, e-mail: vip@kti-git.nsc.ru) References: 1. Lavrentev M.A., Shabat B.V. Problems of hydrodynamics and their mathematical models [Problemy gidrodinamiki i ikh matematicheskie modeli]. Moscow: Nauka, 1973, 416 p. 2. Eynshteyn A., Infeld L. Evolution of Physics [Evolyutsiya fiziki]: Transl. from eng. Moscow: Nauka, 1965, 242 p. 3. Landau L.D., Lifshitz E.M. Fluid Mechanics. Vol. 6. 1987, Butterworth-Heinemann. 4. Landau L.D., Lifshitz E.M. Theory of Elasticity. Vol. 7. 1986, Butterworth-Heinemann. 5. Korn G., Korn T. Mathematical Handbook [Spravochnik po matematike]: Transl. from eng. Moscow: Nauka, 1977, 831 p. 6. Kuzmin P.A. Small vibrations and the stability of motion [Malye kolebaniya i ustoychivost dvizheniya]. Moscow: Nauka, 1973, 206 p. 7. Isakovich M.A. General Acoustics [Obshchaya akustika]. Moscow: Nauka, 1973, 496 p. The extent of plastic deformation of the linear part of the pipeline PONOMAREVA M.A. Received: 10.02.2012 Published: 10.02.2012 ![]() Abstract:
An analysis of developments in recent years accidents showed that the main reasons why there have been sudden destruction of sites of pipelines are shortcomings of the design and as-built documentation, as well as plastic deformation. This article discusses the use of fuzzy logic to evaluate the plastic deformation of the linear part of the pipeline this research was obtained by the ratio of the maximum allowable stress values of the linear part of the pipeline during plastic deformation at the fuzzy input parameters (the present case - the internal pressure). Keywords: main pipeline, a fuzzy set, the risk of an accident, plastic deformation. Authors:
Marina Ponomareva (Balashov, Russian Federation) – post graduate student of the Chair of Applied Informatics, Department of Mathematics, Economics and Informatics, Balashov Institute of Saratov State University, (412 300, Saratov region, Balashov, K. Marx Str., 29, Russian Federation, e-mail: mig0109@mail.ru). References: 1. Abdulla-Zade F. A Fuzzy Logic-Zadeh [Nechetkaya logika L-Zade]. available at: http://www.ropnet.ru/ogonyok/win/199699/99-64-65.html, 2011. 2. Lanchakov G.A., Zorin E.E., Stepanenko A.I. The efficiency of pipelines. In 3 part. Part 3. Diagnosis and prediction of resource [Rabotosposobnost truboprovodov. V 3-kh ch. Ch. 3. Diagnostika i prognozirovanie resursa]. Moscow, OOO «Nedra-Biznestsentr», 2003, Ch. 3, 291 p. 3. Pegat A. Fuzzy modeling and control [Nechetkoe modelirovanie i upravlenie]. Moscow: BINOM. Laboratoriya znaniy, 2009, 798 p. 4. Recommendations for the assessment of efficiency of defect sites pipeline [Rekomendatsii po otsenke rabotosposobnosti defektnykh uchastkov gazoprovodov R 51-31323949-42-99]. Moscow: OAO «Gazprom», 1998, 28 p. 5. Stroitelnye normy i pravila: SNiP 2.05.06–85 (2000) Pipelines [Magistralnye truboprovody], Moscow, 2000, 116 p. About one optimization method of the residual stresses in constructions with glass transition SMETANNIKOV O.Yu. Received: 19.02.2012 Published: 19.02.2012 ![]() Abstract:
thermoelasticity problems solving, realized in ANSYS program, is used at numerical calculations. It is shown, that absence of restriction to the type of external force function allows to lower considerably a level of operating loading. Keywords: vitrification, numerical methods, technological stresses, residual stresses, finite element method, optimization Authors:
Smetannikov Oleg Yurijevich (Perm, Russian Federation) – Doctor of Physical and Mathematical Sciences, Department of Computational Mathematics and Mechanics, Perm National Research Polytechnic University (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: sou2009@mail.ru). References: 1. Matveenko V.P., Smetannikov O.Yu., Trufanov N.A., Shardakov I.N. Thermomechanics of polymer materials in a relaxation transition [Termomekhanika polimernykh materialov v usloviyakh relaksatsionnogo perekhoda]. Moscow: FIZMATLIT, 2009, 176 p. 2. Shardakov I.N., Trufanov N.A., Begishev V.P., Shadrin O.A., Smetannikov O.Yu. Description of hereditary effects in the glass transition and softening of epoxybinders [Opisanie nasledstvennykh effektov pri steklovanii i razmyagchenii epoksidnykh svyazuyushchikh]. International Polymer Science and Technology – Plasticheskie massy, 1991, No. 9, pp. 55–58. 3. Smetannikov O.Yu., Trufanov N.A., Shardakov I.N. Mathematical modeling of the formation of residual stresses in the manufacture offiber composites based on glass bonding [Matematicheskoe modelirovanie protsessa obrazovaniya ostatochnykh napryazheniy pri izgotovlenii voloknistykh kompozitov na osnove stekluyushchikhsya svyazuyushchikh]. International Polymer Science and Technology – Plasticheskie massy, 1991, No. 11, pp. 24–26. 4. Smetannikov O.Yu., Trufanov N.A., Shardakov I.N. Defining relations for thermo-mechanical behavior of polymeric materials in the glass transition and softening [Opredelyayushchie sootnosheniya termomekhanicheskogo povedeniya polimernykh materialov v usloviyakh steklovaniya i razmyagcheniya]. Izvestiya Rossiyskoy akademii nauk. Mekhanika tverdogo tela – Mechanics of Solids, 1997, No. 3, pp. 106–114. 5. Begishev V.P., Smetannikov O.Yu., Trufanov N.A., Shardakov I.N. Numerical and experimental analysis of the residual stresses in polymer products conditions of a complex stress state [Chislennyy i eksperimental'nyy analiz ostatochnykh napryazheniy v polimernykh izdeliyakh v usloviyakh slozhnogo napryazhennogo sostoyaniya]. International Polymer Science and Technology – Plasticheskie massy, 1997, No. 8, pp. 29–33. 6. Matveenko V.P., Smetannikov O.Yu., Trufanov N.A., Shardakov I.N. Thermomechanics of polymer materials in a relaxation transition [Termomekhanika polimernykh materialov v usloviyakh relaksatsionnogo perekhoda]. Fizicheskaya mezomekhanika – Physical Mesomechanics, 1999, Vol. 2, No. 4, pp. 23–29. 7. Trufanov N.A., Smetannikov O.Yu., Zavyalova T.G. Numerical solution of boundary-value problems of polymer mechanics with allowance for phase and relaxation transitions [Chislennoe reshenie kraevykh zadach mekhaniki polimerov s uchetom fazovykh i relaksatsionnykh perekhodov]. Mat. Model. – Ìàò. ìîäåëèðîâàíèå, 2000, Vol. 12, No. 7, pp. 45–50. 8. Smetannikov O.Yu. A model of thermo-mechanical behavior of polymeric materials with a relaxation transition [Ob odnoy modeli termomekhanicheskogo povedeniya polimernykh materialov s relaksatsionnym perekhodom]. VESTNIK SamGU, estestvennonauchnaya ser., 2007, No. 9-1 (59), pp. 216–231. 9. Smetannikov O.Yu., Trufanov N.A. Technological and residual stresses in the non-uniform vitrifying cylindrical rod [Tekhnologicheskie i ostatochnye napryazheniya v neodnorodnom stekluyushchemsya tsilindricheskom sterzhne]. Journal on Composite Mechanics and Design – Mekhanika kompozitsionnykh materialov i konstruktsiy, 2009, Vol. 15, No. 2, pp. 180–191. 10. Smetannikov O.Yu., Trufanov N.A. Experimental identification of thermomechanical model for glass polymers [Eksperimentalnaya identifikatsiya modeli termomekhanicheskogo povedeniya stekluyushchikhsya polimerov]. Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2009, No. 4, pp. 133–145. 11. Smetannikov O.Yu., Trufanov N.A. Numerical analysis of technological and residual stress in vitrified media [Chislennyy analiz tekhnologicheskikh i ostatochnykh napryazheniy v stekluyushchikhsya telakh]. Vychislitelnaya mekhanika sploshnykh sred – Computational continuum mechanics, 2008, Vol. 1, No. 1, pp. 92–108. 12. Smetannikov O.Yu. Experimental and numerical study of the evolution of deformation in an epoxy composite circular plate during non-uniform cooling [Eksperimentalnoe i chislennoe issledovanie povedeniya krugloy plastiny iz epoksidnoy smoly pri neravnomernom okhlazhdenii]. Vychislitelnaya mekhanika sploshnykh sred – Computational continuum mechanics, 2009, Vol. 2, No. 3, pp. 96–105. 13. Trufanov A. N., Smetannikov O.Yu., Trufanov N.A. Numerical analysis of residual stresses in preform of stress applying part for PANDA-type polarization maintaining optical fibers. Optical Fiber Technology, 2010, Vol. 16, No. 3, pp. 156–161. 14. Berezin A.V., Trufanov N.A., Shardakov I.N. Technological stresses in composite plate with a honeycomb [Tekhnologicheskie napryazheniya v plastine iz kompozita s sotovym zapolnitelem]. Journal of Machinery Manufacture and Reliability – Problemy mashinostroeniya i nadezhnosti mashin, 1995, No. 3, pp. 88–97. 15. Smetannikov O.Yu. About model of regulation of residual stresses in glass polymers [Ob odnoy modeli regulirovaniya ostatochnykh napryazheniy v izdeliyakh iz stekluyushchikhsya polimerov]. VESTNIK SamGU, estestvennonauchnaya ser., 2008, No. 6(65), pp. 309–321. 16. Smetannikov O.Yu. Optimization of the residual bending flexure of round polymer plate with glass transition at non-uniform cooling [Optimizatsiya ostatochnogo progiba krugloy plastinki iz stekluyushchegosya polimera pri neravnomernom okhlazhdenii]. Vychislitelnaya mekhanika sploshnykh sred – Computational continuum mechanics, 2010, Vol. 3, No 1, pp 81–92. 17. Composite Materials: Handbook [Kompozitsionnye materialy: Spravochnik]. Kiev: Naukova dumka, 1985, 592 p. 18. Tikhonov A.N., Goncharskiy A.V., Stepanov V.V., Yagola A.G. Numerical methods for solving incorrect problems [Chislennye metody resheniya nekorrektnykh zadach]. Moscow: Nauka, 1990, 232 p. Numerical simulation of solidification and structure formation of the metallic ingot SMETANNIKOV O.Yu., SOKOLOVA O.O. Received: 19.02.2012 Published: 19.02.2012 ![]() Abstract:
A three-dimensional viscous fluid flow with the convection and phase transfer is considered. Mathematical models of the filling and solidification processes in a steel ingot and their discrete analogs are developed. A coupled hydrodynamic and thermal problem is solved numerically by the software ProCAST 2010.0 based on a finite-element method. The distribution of the shrinkage porosity in the ingot’s body is received and the influence of the natural convection during the solidification process on the final ingot’s structure is discussed. The prediction of macrostructure formation is made. Keywords: numerical simulation, finite-element method, steel ingot, bottom filling, natural convection, solidification, shrinkage porosity, structural zone. Authors:
Sokolova Olga Olegovna (Perm, Russian Federation) – postgraduate student, Department of Computational Mathematics and Mechanics, Perm State University (614990, 29, Komsomolsky prospect, Perm, Russian Federation, email: o_lli@bk.ru). Smetannikov Oleg Yurijevich (Perm, Russian Federation) – Doctor of Physical and Mathematical Sciences, Department of Computational Mathematics and Mechanics, Perm State University (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: sou2009@mail.ru). References: 1. Voskoboinikov V.G., Kudrin V.A., Yakushev A.M. General metallurgy [Obshchaja metallurgija]. Moscow: IKTs “Academkniga”, 2005, 768 ð. 2. Tsaplin A.I. [Teplofizika vneshnikh vozdeistvij pri kristallizatsii stal’nykh slitkov na mashinah nepreryvnogo lit’ya]. Ekaterinburg, UrO RAN, 1995. 238 p. 3. Romm E.S. [Strukturnye modeli porovogo prostranstva gornykh porod]. Leningrad: Nedra, 1985. 240 p. 4. Vinogradov V.V., Tyazhelnikova I.L. Theoretical aspects of formation of macro- and microstructures during ingot solidification, Herald of the UDGU, 2008, No. 1, P. 37–56. 5. Flemings M. Solidification process. Ìoscow: Ìir, 1977. 424 p.6. Ono A. Solidification of metals. Ìoscow: Ìåtallurgy, 1980. 152 p. 7. Kan [Fizicheskoje metallovedenie]. Ìoscow: Ìåtallurgy, Vol. 2. 624 p. 8. Gandin Ch.-A., Rappaz M. A coupled finite element – cellular automaton model for the prediction of dendritic grain structures in solidification processes, Acta metal mater, 1994, Vol. 42, No. 7, pp 2233-2246. 9. Dubrovskaya A.S., Dongauser K.A. Numerical investigation of influence technological and constructional parameters on the process of manufacturing single-crystal castings of gas turbin engines, Herald of the PSTU, 2011, No. 9, P. 81–102 About a finite element based on the Castigliano variational principle for plane elasticity problems SUKHODOLOVA Y.S., TRUFANOV N.A. Received: 10.02.2012 Published: 10.02.2012 ![]() Abstract:
We investigate the variant of the finite element method for plane elasticity problems, based on Castigliano variational principle. The quantitative characteristics of the convergence of the method on the example of solving the problem of tensile plate of variable load are resulted. We make recommendations for the implementation of the static boundary conditions in plane elasticity problems . Keyword: finite element method, Castigliano variational principle, static boundary conditions. Authors:
Sukhodolova Yuliya Sergeevna (Perm, Russian Federation) – Student of Department of Computational Mathematics and Mechanics, State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, å-mail: Suhodolchik@mail.ru). Trufanov Nikolay Aleksandrovich (Perm, Russian Federation) – Doctor of Technical Sciences, Professor, Head of Department of Computational Mathematics and Mechanics, State National Research Polytechnic University of Perm (614990, 29, Komsomolsky prospect, Perm, Russian Federation, e-mail: vmm@cpl.pstu.ac.ru). References: 1. Zenkevich O. The finite element method in engineering science [Metod konechnykh elementov v tekhnike]: Transl. from eng. Moscow: Mir, 1976, 541 p. 2. Segerlind L.Dzh. Applied finite element analysis [Primenenie metoda konechnykh elementov]. Moscow: Mir, 1979, 392 p. 3. Gallager R. Finite element analysis fundamentals [Metod konechnykh elementov. Osnovy]. Moscow: Mir, 1984, 428 p. 4. Shardakov I.N., Trufanov N.A., Matveenko V.P. Method of geometrical immersion in the theory of elasticity [Metod geometricheskogo pogruzheniya v teorii uprugosti]. Ekaterinburg: UrO RAN, 1999, 298 p. 5. Kamenskikh A.A., Trufanov N.A., Matveenko V.P. Numerical realization of the geometrical immersion based on Castigliano variational principle [Chislennaya realizatsiya metoda geometricheskogo pogruzheniya na osnove variatsionnogo printsipa Kastilyano]. PSTU Mechanics Bulletin – Vestnik PGTU. Mekhanika, Perm, 2010, No. 3, pp. 5–18. 6. Demidov S.P. Theory of elasticity [Teoriya uprugosti]. Moscow: Vyssh. shkola, 1979, 432 c. 7. Pobedrya B.E. Numerical Methods in the Theory of Elasticity and Plasticity [Chislennye metody v teorii uprugosti i plastichnosti]. Moscow: MGU Publ., 1995, 368 p. 8. Norri D., Zh. de Friz An Introduction to Finite Element Analysis [Vvedenie v metod konechnykh elementov]. Moscow: Mir, 1981, pp. 205–207. 9. Timoshenko S.P., Guder Dzh. Theory of Elasticity [Teoriya uprugosti]: Transl. from eng. Under. ed. Shapiro G.S. Moscow: Nauka, 1979, pp. 269–272. Experimental determination of dissipative properties of electro viscoelastic systems with external electric circuits YURLOV Ì.À. Received: 19.02.2012 Published: 19.02.2012 ![]() Abstract:
Piezoelectric elements connected to shunt circuits and bonded to a mechanical structure form a dissipation device that can be designed to add damping to the mechanical system. Due to the piezoelectric effect, part of the vibration energy is transformed into electrical energy that can be conveniently dissipated. This paper aims to experimentally validate the effectiveness of structural vibration suppression by piezoelectric with passive shunt circuits. Two different electric circuits are examined a purely resistive circuit and an inductive–resistive one. A harmonic force is applied to a simple steel cantilevered beam, by varying the inductance and resistance values, the electric circuits are optimized in order to reduce forced vibrations close to the first and the second resonance frequencies. It is proved that the presented technique allows for a substantial reduction of vibration with the inductances in circuit when compared with purely resistive circuit. Also it is important to know that large inductances are frequently required, leading to the necessity of using synthetic inductors – gyrators (obtained from operational amplifiers). Keywords: external electric circuits, shunted piezoelectric, resonant shunt circuits, natural vibration. Authors:
Yurlov Maksim Aleksandrovich (Perm, Russian Federation) research engineer ICMM UB of RAS (614013, Acad. Korolev str., 1, Perm, Russian Federation, e-mail: yurlovm@icmm.ru). References: 1. Niederberger D. Smart damping Materials using Shunt Control. Dissertation for the degree of Dr. of Sci., Zurich, 2005, 210 p. 2. Lee H.-J., Saravanos D. Layerwise finite elements for smart piezoceramic composite plates in thermal environments. NASA TM-106990 AIAA-96-1277, 1996, 48 p. 3. Forward R.L. Electronic damping of vibrations in optical structures. Journal of Applied Optics, 1979, Vol. 18, No. 5, ðp. 690–697. 4. Hagood N.W., Von Flotow A. Damping of structural vibrations with piezoelectric materials and passive electrical networks. Journal of Sound and Vibration, 1991, Vol. 146, No. 2, ðp. 243–268. 5. Moheimani S.O.R., Fleming A.J. Piezoelectric transducers for vibration control and damping, 2006, 272 p. 6. Davis C.L., Lesieutre G.A. Modal strain energy approach to the prediction of resistively-shunted piezoceramic damping. Journal of Sound and Vibration, 1995, Vol. 184, No. 1, ðp. 129–139. 7. Lesieutre G.A. Vibration damping and control using shunted piezoelectric materials. The Shock and Vibration Digest May 1998, 1998, No. 30, ðp. 187–195. 8. Giovanni Caruso. A critical analysis of electric shunt circuits employed in piezoelectric passive vibration damping. Smart Mater. Struct., 2001, No. 10, ðp. 1059–1068. 9. Moheimani S.O.R., Fleming A.J. and Behrens S. On the feedback structure of wideband piezoelectric shunt damping systems. Smart Mater. Struct., 2002, No. 12, ðp.49–56. 10. Park C.H. and Inman D.J. Enhanced Piezoelectric Shunt Design. Shock and Vibration, 2003, Vol. 10, No. 2, pp. 127–133. 11. Wu S.Y. Piezoelectric Shunts with Parallel R-L Circuit for Structural Damping and Vibration Control. Proc. SPIE Smart Structures and Materials, Passive Damping and Isolation; SPIE, 1996, Vol. 2720, pp. 259–269. 12. V.P. Matveyenko, E.P.Kligman Natural Vibration Problem of Viscoelastic Solids as Applied to Optimization of Dissipative Properties of Constructions. Journal of Vibration and Control, 1997, No. 3, pp. 87–102. 13. E.P. Kligman, V.P. Matveenko, N.A. Yurlova. [Dinamicheskie kharakteristiki tonkostennykh elektrouprugikh system]. Mechanics of Solids – Izvestiya RAN, MTT, 2005, No. 2, pp. 179–187. 14. V.P. Matveenko, E.P.Kligman, N.A. Yurlova, M.A. Yurlov. Optimization of the dynamic characteristics of electroviscoelastic systems by means of electric circuits / in Advanced Dynamics and Model Based Control of Structures and Machines (ed. H. Irschik, M. Krommer, A.K. Belyaev) (ISBN 978-3-7091-0796-6), Springer-Verlag/Wien, 2011, pp. 151–158. 15. Matveenko V.P., Kligman E.P., Yurlova N.A., Yurlov M.A. Damping of mechanical vibrations shunted piezoelectric structural elements [Dempfirovanie mekhanicheskikh kolebaniy zashuntirovannymi pezoelektricheskimi strukturnymi elementami]. Journal of Environmental science centers the Black Sea Economic Cooperation – Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva, 2011, No. 2, ðp. 23–35.
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