О ПРИМЕНЕНИИ ШУНТИРОВАННОГО ПЬЕЗОЭЛЕМЕНТА ДЛЯ ОБЕСПЕЧЕНИЯ НАИЛУЧШИХ ДИССИПАТИВНЫХ ХАРАКТЕРИСТИК ВЯЗКОУПРУГИХ ОБОЛОЧЕК

Юрлова, Н.А.; Ошмарин, Д.А.; Севодина, Н.В.

doi:10.15593/pem.mech/2024.4.08

О ПРИМЕНЕНИИ ШУНТИРОВАННОГО ПЬЕЗОЭЛЕМЕНТА ДЛЯ ОБЕСПЕЧЕНИЯ НАИЛУЧШИХ ДИССИПАТИВНЫХ ХАРАКТЕРИСТИК ВЯЗКОУПРУГИХ ОБОЛОЧЕК

Н.А. Юрлова, Д.А. Ошмарин, Н.В. Севодина

Сведения об авторах

Н.А. Юрлова
Институт механики сплошных сред УрО РАН, Пермь, Российская Федерация
Д.А. Ошмарин
Институт механики сплошных сред УрО РАН, Пермь, Российская Федерация
Н.В. Севодина
Институт механики сплошных сред УрО РАН, Пермь, Российская Федерация

https://doi.org/10.15593/pem.mech/2024.4.08

Работа посвящена исследованию характера зависимости динамических характеристик электро-вязкоупругой системы, представляющей собой кусочно-однородное тело, состоящее из упругих, вязкоупругих, электроупругих (пьезоэлектрических) элементов, а также внешних пассивных электрических цепей, присоединенных к электродированным поверхностям пьезоэлементов, от параметров, определяющих ее геометрическую конфигурацию (размеры и расположение вязкоупругого и пьезоэлектрического элементов, формирующих систему, по отношению к конструкции и друг к другу). В таких системах для демпфирования колебаний реализуются два механизма диссипации энергии: за счет внут- реннего трения в вязкоупругих частях и за счет преобразования части энергии механиче- ских колебаний в электрическую с последующим ее рассеиванием в электрических цепях. В качестве внешних электрических цепей рассмотрены резистивная (R) и последовательная резонансная (RL) цепи. Исследование проводилось на основе численного решения задачи о собственных колебаниях для тонкостенной пространственной конструкции – полуцилиндрической оболочки. Рассмотрены все возможные геометрические конфигурации расположения вязкоупругих и пьезоэлектрических элементов. Найдены варианты компоновки конструкции, которые могут обеспечить наилучшие демпфирующие свойства в некотором диапазоне частот за счет реализации либо механизма внутреннего трения, либо преобразования энергии колебаний пьезоэлементом. В результате проведения серии вычислительных экспериментов получены количественные оценки, демонстрирующие, как изменяются демпфирующие свойства системы при использовании отдельно каждого из рассматриваемых механизмов диссипации энергии колебаний, а также совместно. Сделаны количественные оценки изменения диссипативных свойств оболочки, демонстрирующие, в каких случаях оба механизма диссипации энергии приводят к повышению демпфирующих характеристик электровязкоупругих систем, а в каких – к их снижению.

Ключевые слова

электровязкоупругостьпьезоэлементшунтирующие электрические цепикоэффициент демпфирования колебанийкоэффициент электромеханической связисобственные частоты и моды колебанийоболочкачисленное моделирование.

The Use of a Shunted Piezoelectric Element to Ensure the Best Dissipative Characteristics of Viscoelastic Shells

The paper studies the dependence of the dynamic characteristics of an electro-viscoelastic system, which is a piecewise homogeneous body consisting of elastic, viscoelastic, electroelastic (piezoelectric) elements, as well as external passive electrical circuits attached to the electroded surfaces of piezoelectric elements, on the parameters determining its geometric configuration (dimensions and location of viscoelastic and piezoelectric elements, forming the system, in relation to structure and each other). In these systems, two methods of energy dissipation are used to reduce vibration: internal friction in viscoelastic materials and the conversion of mechanical vibration energy into electrical energy which is then dissipated in electrical circuits. Resistive (R) and resonant (RL) circuits are considered as examples of external electrical circuits. The study was conducted based on a numerical solution to the natural vibration problem for a thin-walled, spatial structure having the form of a semi-cylindrical shell. All possible geometrical configura- tions for the arrangement of viscoelastic and piezoelectric components were considered. There were found designs that could provide optimal damping properties within a specific frequency range, either via internal friction or by converting vibration energy using a piezoelectric compo- nent. As a result of a series of computational experiments, we obtained quantitative estimates demonstrating how the damping properties of the system change when each of the considered vibration energy dissipation mechanisms is used separately or jointly. The obtained quantitative estimates of changes in the dissipative properties of the shell show, in which cases both energy dissipation mechanisms lead to an increase in the damping characteristics of electro-viscoelastic systems, and in which cases they lead to a decrease.

Keywords

electroviscoclasticitypiezoelectric elementshunting electrical circuitsvibration damping coefficientelectromechanical coupling coefficientnatural frequencies and modes of vibrationsshellnumerical modeling.

Литература

1.Kumar, A. Passive Constrained Layer Damping: A State of the Art Review / A. Kumar, R.K. Behera // IOP Conf. Ser.: Mater. Sci. Eng. – 2019. – Vol. 653. – art. No. 012036. DOI: 10.1088/1757-899X/653/1/012036 Scholar
2.Nashif, A.D. Vibration Damping / A.D. Nashif, D.I.G. Jones, J.P. Henderson. – Wiley, 1985. – 453 p. Scholar
3.Sun, C.T. Vibration Damping of Structural Elements / C.T. Sun, Y.P. Lu. – Prentice-Hall, 1995. – 372p. Scholar
4.Stanway, R. Active constrained-layer damping: A state-of- the-art review Proceedings of the Institution of Mechanical Engi- neers, Part I / R. Stanway, J.A. Rongong, N.D. Sims // Journal of Systems and Control Engineering. – 2003. – Vol. 217, no 6. – P. 437–456. DOI: 10.1177/095965180321700601 Scholar
5.Trindade, M.A. Hybrid Active-Passive Damping Treatments us- ing Viscoelastic and Piezoelectric Materials: Review and Assessment / M.A. Trindade, A. Benjeddou // Journal of Vibration and Control. – 2002. – Vol. 8, no. 6. – P. 699–745. DOI: 10.1177/1077546029186 Scholar
6.Sahoo, S.R. Active damping of geometrically nonlinear vi- brations of smart composite plates using elliptical SCLD treatment with fractional derivative viscoelastic layer / S.R. Sahoo, M.C. Ray // European Journal of Mechanics – A/Solids. – 2019. – Vol. 78. – art. No. 103823. DOI: 10.1016/j.euromechsol.2019.103823 Scholar
7.Sahoo, S.R. Active control of laminated composite plates using elliptical smart constrained layer damping treatment / S.R. Sahoo, M.C. Ray // Composite Structures. – 2019. – Vol. 211. – P. 376–389. DOI: 10.1016/j.compstruct.2018.12.004 Scholar
8.Ватульян, А.О. К исследованию колебаний цилиндра с вязкоупругим покрытием / А.О. Ватульян, В.В. Дударев // Вы- числительная механика сплошных сред. – 2021. – Т. 14, № 3. – P. 312–321. DOI: 10.7242/1999-6691/2021.14.3.26 Scholar
9.Park, C.H. Modeling of a Hybrid Passive Damping System / C.H. Park, S.J. Ahn, H.C. Park // Journal of Mechanical Science and Technology, 2005. – Vol. 19, no. 1. – P. 127–135. DOI: 10.1007/BF02916111 Scholar
10.Trindade, M.A. Optimization of passive constrained lay- er damping treatments applied to composite beams / M.A. Trin- dade // Latin American Journal of Solids and Structures, 2007. – Vol. 4, no. 1. – P. 19–38. Scholar
11.Vibration Control of Beams with Active Constrained Layer Damping / F.-M. Li, K. Kishimoto, Y.-S. Wang, Z.-B. Chen, W.-H. Huang // Smart Materials and Structures, 2008. – Vol. 17, no. 6, art. No. 065036. DOI: 10.1088/0964-1726/17/6/065036 Scholar
12.Trindade, M.A. Optimization of Active-Passive Damping Treatments using Piezoelectric and viscoelastic Materials / M.A. Trindade // Smart Materials and Structures. – 2007. – Vol. 16. – P. 2159–2168. DOI: 10.1088/0964-1726/16/6/018 Scholar
13.Vibration Control of Plate by Active and Passive Con- strained Layer Damping / S. Meena, N. Kumar, S.P. Singh, B.C. Nakra // Advances in vibration engineering. – 2009. – Vol. 8(4). – P. 345–356. Scholar
14.Gupta, A. An actively constrained viscoelastic layer with the inclusion of dispersed graphite particles for control of plate vibration / A. Gupta, S. Panda, R.S. Reddy // Journal of Vibration and Control. – 2020. – Vol. 27, no. 17–18. – P. 2152–2163. DOI: 10.1177/1077546320956533 Scholar
15.Mead, D.J. The Forced Vibration of a Three-Layer, Damped Sandwich Beam with Arbitrary Boundary Conditions / D.J. Mead, S. Markus // Journal of Sound and Vibration. – 1969. – Vol. 10, no. 2. – P. 163–175. DOI: 10.1016/0022-460X(69)90193-X Scholar
16.Design of an Active Damping System for Vibration Con- trol of Wind Turbine Towers / H. Bai, Y. Aoues, J.-M. Cherfils, D. Lemosse // Infrastructures. – 2021. – Vol. 6, no. 11. – art. No. 162. DOI: 10.3390/infrastructures6101162 Scholar
17.Vinyas, M. Influence of active constrained layer damp- ing on the coupled vibration response of functionally graded mag- neto-electro-elastic plates with skewed edges / M. Vinyas, D. Ha- rursampath, T. Nguyen-Thoi // Defence Technology. – 2020. – Vol. 16, no. 5. – P. 1019–1038. DOI: 10.1016/j.dt.2019.11.016 Scholar
18.Active Vibration Control of Composite Cantilever Beams / Z. Huang, F. Huang, X. Wang, F. Chu // Materials (Basel). – 2022. – Vol. 16, no. 1. – art. No. 95. DOI: 10.3390/ma16010095 Scholar
19.Modeling and topology optimization of cylindrical shells with partial CLD treatment / R.Z. Zhu, X.N. Zhang, S.G. Zhang, Q.Y. Dai, Z.Y. Qin, F.L. Chu // International Journal of Mechani- cal Sciences. – 2022. – Vol. 220. – art. No. 107145. DOI: 10.1016/j.ijmecsci.2022.107145 Scholar
20.Vibration Control of an Aero Pipeline System with Ac- tive Constraint Layer Damping Treatment / J. Zhai, J. Li, D. Wei, P. Gao, Y. Yan, Q. Han // Applied Sciences. – 2019. – Vol. 9, no. 10. – art. No. 2094. DOI: 10.3390/app9102094 Scholar
21.Yang, Q. Development of Multi-Staged Adaptive Filter- ing Algorithm for Periodic Structure-Based Active Vibration Con- trol System / Q. Yang, K. Lee, B. Kim // Appl. Sci. – 2019. – Vol. 9. – art. No. 611. DOI: 10.3390/app9030611 Scholar
22.Panda, S. A design of active constrained layer damping treatment for vibration control of circular cylindrical shell struc- ture / S. Panda, A. Kumar // Journal of Vibration and Control. – 2016. – Vol. 24, no. 24. – P. 5811–5841. DOI: 10.1177/1077546316670071 Scholar
23.Algorithm for solving problems related to the natural vi- brations of electro-viscoelastic structures with shunt circuits using ANSYS data / N.A. Iurlova, D.A. Oshmarin, N.V. Sevodina, M.A. Iurlov // International Journal of Smart and Nano Materials. – 2019. – Vol. 10, no. 2. – P. 156–176. DOI: 10.1080/19475411.2018.1542356 Scholar
24.Численный алгоритм поиска компоновок электро- упругих тел с внешними электрическими цепями для получе- ния наилучших демпфирующих характеристик / Н.А. Юрлова, Д.А. Ошмарин, Н.В. Севодина, М.А. Юрлов // Вестник Перм- ского национального исследовательского политехнического университета. Механика. – 2020. – № 3. – С. 108–124. DOI: perm.mech/2020.3.11 Scholar
25.Hagood, N.W. Damping of structural vibrations with pi- zoelectric materials and passive electrical networks / N.W. Ha- good, A. Von Flotow // Journal of Sound and Vibration. – 1991. – Vol. 146, no. 2. – P. 243–268. DOI: 10.1016/0022- 460X(91)90762-9 Scholar
26.Trindade, M.A. Effective electromechanical coupling coefficients of piezoelectric adaptive structures: critical evaluation and optimization / M.A. Trindade, A. Benjeddou // Mech. Adv. Mater. Struct. – 2009. – Vol. 16, no. 3. – P. 210–223. DOI: 10.1080/15376490902746863 Scholar
27.Comparison of passive damping treatments based on constrained viscoelastic layers and multi-resonant piezoelectric networks / B. Lossouarn, L. Rouleau, R. Darleux, J.-F. Deü // Journal of Structural Dynamics. – 2021. – Vol. 1. – P. 30–48. DOI: 10.25518/2684-6500.63 Scholar
28.Effects of viscoelastic bonding layer on performance of piezoelectric actuator attached to elastic structure / I.A. Ali, M.A. Alazwari, M.A. Eltaher, A.A. Abdelrahman // Mater. Res. Express. – 2022. – Vol. 9. – art. No. 045701. DOI: 10.1088/2053- 1591/ac5cae Scholar
29.Партон, В.З. Электромагнитоупругость пьезоэлек- трических и электропроводных тел / В.З. Партон, Б.А. Кудряв- цев. – М.: Наука, 1988. – 471 р. Scholar
30.Карнаухов, В.Г. Механика связанных полей в элемен- тах конструкций: в 5 т. Т. 4: Электротермовязкоупругость / В.Г. Карнаухов, И.Ф. Киричок. – Киев: Наукова Думка, 1988. – 316 с. Scholar
31.Analysis of dissipative properties of electro-viscoelastic bodies with shunting circuits on the basis of numerical modelling of natural vibrations / V. Matveenko, N. Iurlova, D. Oshmarin, N.V. Sevodina // Acta Mech. – 2023. – Vol. 234. – P. 261–276. DOI: 10.1007/s00707-022-03193-8 Scholar
32.Задача о собственных колебаниях электро-вязко- упругих тел с внешними электрическими цепями и конечно- элементные соотношения для ее численной реализации / В.П. Матвеенко, Д.А. Ошмарин, Н.В. Севодина, Н.А. Юрлова // Вычислительная механика сплошных сред. – 2016. – Т. 9, № 4. – С. 476–485. DOI: 10.7242/1999-6691/2016.9.4.40 Scholar
33.Matveenko, V.P. Damping of vibrations of smart- systems incorporating piezoelectric elements and shunt circuits with parameters derived from the models of continuum and dis- crete mechanics / V.P. Matveenko, N.A. Iurlova, D.A. Oshmarin // Mechanics of Advanced Materials and Structures. – 2023. – P. 1– 11. DOI: 10.1080/15376494.2023.2241134 Scholar
34.An approach to determination of shunt circuits parame ters for damping vibrations / V.P. Matveenko, N.A. Iurlova, D.A. Oshmarin, N.V. Sevodina, M.A. Iurlov // International Journal of Smart and Nano Materials. - 2018. - Vol. 9, no. 2. - P. 135-149. DOI: 10.1080/19475411.2018.1461144 Scholar
35.Zienkiewicz, O.C. The finite element method: Its Basis and Fundamentals. - 6th ed. / O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu. - Oxford: Elsevier Butterworth-Heinemann, 2000. - 802 p. Scholar
36.Kligman, E.P. Natural Vibration Problem of Viscoelastic Solids as Applied to Optimization of Dissipative Properties of Constructions / E.P. Kligman, V.P. Matveenko // Journal of Vibra tion and Control. - 1997. - Vol. 3, no. 1. - P. 87-102. DOI: 10.1177/107754639700300 Scholar
37.Weaver, Jr.W. Vibration problems in engineering, 5th ed. / Jr.W. Weaver, S.P. Timoshenko, D.H. Young. - Wiley, 1990. - 497 p. Scholar
38.Матвеенко, В.П. Приложения метода Мюллера и принципа аргумента к задачам на собственные значения в механике деформируемого твердого тела / В.П. Матвеенко, М.А. Севодин, Н.В. Севодина // Вычислительная механика сплошных сред. - 2014. - Vol. 7, no. 3. - P. 331-336. DOI: 10.7242/1999-6691/2014.7.3.32 Scholar

1.Kumar A., Behera R.K. Passive Constrained Layer Damp- ing: A State of the Art Review. IOP Conf. Ser.: Mater. Sci. Eng., 2019, Vol. 653, art. No. 012036. doi: 10.1088/1757- 899X/653/1/012036 Scholar
2.Nashif A.D., Jones D.I.G., Henderson J.P. Vibration Damp- ing. Wiley, 1985. - 453p. Scholar
3.Sun C.T., Lu Y.P. Vibration Damping of Structural Ele- ments. Prentice-Hall, 1995,372p. Scholar
4.Stanway R., Rongong J.A., Sims N.D. Active constrained- layer damping: A state-of-the-art review Proceedings of the Insti- tution of Mechanical Engineers, Part I. Journal of Systems and Control Engineering, 2003, Vol. 217, No 6, pp. 437-456. doi: 10.1177/095965180321700601 Scholar
5.Trindade M.A., Benjeddou A. Hybrid Active-Passive Damping Treatments using Viscoelastic and Piezoelectric Materi- als: Review and Assessment. Journal of Vibration and Control, 2002, Vol. 8, No. 6, pp. 699-745. doi: 10.1177/1077546029186 Scholar
6.Sahoo S.R., Ray M.C. Active damping of geometrically nonlinear vibrations of smart composite plates using elliptical SCLD treatment with fractional derivative viscoelastic layer. Eu- ropean Journal of Mechanics - A/Solids, 2019, Vol. 78, art. No. 103823. doi: 10.1016/j.euromechsol.2019.103823 Scholar
7.Sahoo S.R., Ray M.C. Active control of laminated compo- site plates using elliptical smart constrained layer damping treat- ment. Composite Structures, 2019, Vol. 211, pp. 376-389. doi: 10.1016/j.compstruct.2018.12.004 Scholar
8.Vatulyan A.O., Dudarev B.B. K issledovaniyu kolebanij cilindra s vyzakouprugim pokrytiem [A study of vibrations of a cylinder with a viscoelastic coating]. Computational Continuum Mechanics, 2021, Vol. 14, No. 3, pp. 312-321. https://doi.org/10.7242/1999-6691/2021.14.3.26 Scholar
9.Park C.H., Ahn S.J., Park H.C. Modeling of a Hybrid Pas- sive Damping System. Journal of Mechanical Science and Tech- nology, 2005, Vol. 19, No. 1, pp. 127-135. doi: 10.1007/BF02916111 Scholar
10.Trindade M.A. Optimization of layer damping treatments applied to composite beams. Latin American Journal of Solids and Structures, 2007, No 4, 19-38. Scholar
11.Li F.-M., Kishimoto K., Wang Y.-S., Chen Z.-B., Huang W.-H. Vibration Control of Beams with Active Constrained Layer Damping. Smart Materials and Structures, 2008, Vol. 17, No. 6, art. No. 065036. doi: 10.1088/0964-1726/17/6/065036 Scholar
12.Trindade M.A. Optimization of Active-Passive Damping Treatments using Piezoelectric and viscoelastic Materials. Smart Materials and Structures, 2007, Vol. 16, 2159-2168. doi: 10.1088/0964-1726/16/6/018 Scholar
13.Meena S., Kumar N., Singh S.P., Nakra B.C. Vibration Con- trol of Plate by Active and Passive Constrained Layer Damping. Advances in vibration engineering, 2009, Vol. 8, No. 4, pp. 345-356. Scholar
14.Gupta A., Panda S., Reddy R.S. An actively constrained viscoelastic layer with the inclusion of dispersed graphite particles for control of plate vibration. Journal of Vibration and Control, 2020, Vol. 27, No. 17-18, pp. 2152-2163. doi: 10.1177/1077546320956533 Scholar
15.Mead D.J., Markus S. The Forced Vibration of a Three- Layer, Damped Sandwich Beam with Arbitrary Boundary Condi- tions. Journal of Sound and Vibration, 1969, Vol. 10, No. 2, pp.163-175. doi: 10.1016/0022-460X(69)90193-X Scholar
16.Bai H., Aoues Y., Cherfils J.-M., Lemosse D. Design of an Active Damping System for Vibration Control of Wind Turbine Towers. Infrastructures, 2021, Vol. 6, No. 11, art. No. 162. doi: 10.3390/infrastructures6110162 Scholar
17.Vinyas M., Harrusampath D., Nguyen-Thoi T. Influence of active constrained layer damping on the coupled vibration re- sponse of functionally graded magneto-electro-elastic plates with skewed edges. Defence Technology, 2020, Vol. 16, No.5, pp. 1019-1038. doi: 10.1016/j.dt.2019.11.016. Scholar
18.Huang Z, Huang F, Wang X, Chu F. Active Vibration Control of Composite Cantilever Beams. Materials (Basel). 2022, Vol. 16, No. 1, art. No. 95. doi: 10.3390/ma16010095 Scholar
19.Zhu R.Z., Zhang X.N., Zhang S.G., Dai Q.Y., Qin Z.Y., Chu F.L. Modeling and topology optimization of cylindrical shells with partial CLD treatment. International Journal of Mechanical Sciences. 2022, Vol. 220, art. No. :107145. doi: 10.1016/j.ijmecsci.2022.107145 Scholar
20.Zhai J, Li J, Wei D, Gao P, Yan Y, Han Q. Vibration Con- trol of an Aero Pipeline System with Active Constraint Layer Damping Treatment. Applied Sciences, 2019, Vol. 9, No. 10, art. No. 2094. doi: 10.3390/app9102094 Scholar
21.Yang Q., Lee K., Kim B. Development of Multi-Staged Adaptive Filtering Algorithm for Periodic Structure-Based Active Vibration Control System. Applied Sciences, 2019, Vol. 9, No. 3, art. No. 611. Doi: 10.3390/app9030611 Scholar
22.Panda S., Kumar A. A design of active constrained layer damping treatment for vibration control of circular cylindrical shell structure. Journal of Vibration and Control. 2016, Vol. 24, No. 24, pp. 5811-5841. doi:10.1177/1077546316670071 Scholar
23.Iurlova N.A., Oshmarin D.A., Sevodina N.V., Iurlov M.A. Algorithm for solving problems related to the natural vibra- tions of electro-viscoelastic structures with shunt circuits using ANSYS data. International Journal of Smart and Nano Materials, 2019, Vol. 10, No. 2, pp. 156-176. doi: 10.1080/19475411.2018.1542356 Scholar
24.Iurlova N.A., Oshmarin D.A., Sevodina N.V., Iurlov M.A.. Chislennyj algoritm poiska komponovok elektrouprugih tel s vneshnimi elektricheskimi cepyami dlya polucheniya nailuchshih dempfiruyushchih harakteristik [Numerical search algorithm for layouts of electroelastic bodies with external electrical circuits to obtain the best damping characteristics]. PNRPU Mechanics Bulle- tin, 2020, No. 3, pp.108-124. doi: 10.15593/perm.mech/2020.3.11 Scholar
25.Hagood N., Von Flotow A. Damping of structural vibra- tions with piezoelectric materials and passive electrical networks, Journal of Sound and Vibration, 1991, Vol. 146, No. 2, pp. 243- 268. doi: 10.1016/0022-460X(91)90762-9 Scholar
26.Trindade M.A., Benjeddou A. Effective electromechani- cal coupling coefficients of piezoelectric adaptive structures: criti- cal evaluation and optimization. Mech. Adv. Mater. Struct., 2009, Vol. 16, No. 3, pp.210–223. doi: 10.1080/15376490902746863 Scholar
27.Lossouarn B., Rouleau L., Darleux R., Deü J.-F. Compari- son of passive damping treatments based on constrained viscoelastic layers and multi-resonant piezoelectric networks. Journal of Structural Dynamics. 2021, Vol. 1, pp.30-48. doi: 10.25518/2684-6500.63 Scholar
28.Ali I.A., Alazwari M.A., Eltaher M.A., Abdelrahman A.A. Effects of viscoelastic bonding layer on performance of piezoelectric actuator attached to elastic structure. Mater. Res. Express, 2022, Vol. 9, art. No. 045701. doi: 10.1088/2053-1591/ac5cae Scholar
29.Parton V.Z., Kudryavtsev B.A. Electro-magneto- elasticity: Piezo-electrics and Electrically Conductive Solids. New York, Gordon and Breach Science Publishers Ltd., 1988, 503p. Scholar
30.Karnauhov V.G., Kirichok I.F. Mekhanika sviazannykh polei v elementakh konstruktsii. (v 5 T.); T.4: Elektrotermovyazkouprugost' [The mechanics of coupled fields in structural elements. (in 5 V.); V.4: Electrothermoviscoelasticity]. Kiev: Nauk. dumka. 1988. 316 s. Scholar
31.Matveenko V., Iurlova N., Oshmarin D., Sevodina N.V. Analysis of dissipative properties of electro-viscoelastic bodies with shunting circuits on the basis of numerical modelling of natu- ral vibrations. Acta Mech., 2023, Vol. 234, pp. 261–276. https://doi.org/10.1007/s00707-022-03193-8 Scholar
32.Matveenko V.P., Oshmarin D.A., Sevodina N.V., Yur- lova N.A. Problem on natural vibrations of electroviscoelastic bodies with external electric circuits and finite element relations for its implementation. Computational Continuum Mechanics, 2016, Vol 9, No. 4, pp. 476-485. doi: 10.7242/1999- 6691/2016.9.4.40 Scholar
33.Matveenko V.P., Iurlova N.A., Oshmarin D.A. Damping of vibrations of smart-systems incorporating piezoelectric elements and shunt circuits with parameters derived from the models of continuum and discrete mechanics. Mechanics of Advanced Materials and Structures. 2023, pp.1-11. https://doi.org/10.1080/15376494.2023.2241134 Scholar
34.Matveenko V.P., Iurlova N.A., Oshmarin D.A., Sevodina N.V., Iurlov M.A. An approach to determination of shunt circuits parameters for damping vibrations. International Journal of Smart and Nano Materials. 2018, Vol. 9, No. 2, pp. 135-149. doi: 10.1080/19475411.2018.1461144 Scholar
35.Zienkiewicz O.C., Taylor R.L., Zhu J.Z. The finite ele- ment method: Its Basis and Fundamentals, 6th ed. Oxford: Elsevier Butterworth-Heinemann, 2000, 802 p. Scholar
36.Matveyenko V.P., Kligman E.P. Natural vibration prob- lem of viscoelastic solids as applied to optimization of dissipative properties of constructions. Journal of Vibration and Control. 1997, Vol. 3 (1), pp. 87-102. doi: 10.1177/107754639700300107 Scholar
37.Weaver Jr., W., Timoshenko, S.P. and Young, D.H. Vi- bration problems in engineering, 5th edition. Wiley, 1990, 497 p. Scholar
38.Matveenko V., Sevodin M., Sevodina N. Applications of Muller’s method and the argument principle to eigenvalue problems in solid mechanics. Computational Continuum Mechanics. 2014, Vol.7, No.3, pp. 331-336. doi: 10.7242/1999-6691/2014.7.3.32 Scholar

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Опубликована: 25.11.2024
В выпуске: 25.11.2024
Выпуск: № 4 (2024)

О ПРИМЕНЕНИИ ШУНТИРОВАННОГО ПЬЕЗОЭЛЕМЕНТА ДЛЯ ОБЕСПЕЧЕНИЯ НАИЛУЧШИХ ДИССИПАТИВНЫХ ХАРАКТЕРИСТИК ВЯЗКОУПРУГИХ ОБОЛОЧЕК

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The Use of a Shunted Piezoelectric Element to Ensure the Best Dissipative Characteristics of Viscoelastic Shells

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