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Analysis of dissipative properties of electro-viscoelastic bodies with shunting circuits on the basis of numerical modelling of natural vibrations

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Abstract

The paper is concerned with the problem of optimization of dissipative properties of smart-systems which consist of elastic or viscoelastic bodies and piezoelectric bodies with electrodes connected to electric elements such as resistors, capacitors, and inductors. The systems under consideration can also contain elements made of polymeric materials filled with graphene nanoparticles (graphene composites). These elements are deformable bodies with elastic or viscoelastic properties which can also play the part of resistive elements. The parameters of smart-systems providing maximal dissipative properties are sought by means of analysis of natural vibration frequencies. The mathematical formulation of the natural vibration problem and basic relations for the finite element algorithm of the numerical simulation are presented. The possibility of using finite-element matrices assembled in the ANSYS software package for deformable elements of smart-systems is demonstrated. The procedures of finite element method allow one to reduce the natural vibration problem under consideration to a non-classic variant of the algebraic complex eigenvalue problem. An algorithm developed on the basis of Mueller’s method and the argument principle is recommended to solve this problem. We provide the examples that illustrate the determination of parameters of the electric circuits providing maximum damping and use of the graphene composite element ensuring the multimodal damping.

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Acknowledgements

The work was carried out as part of the implementation of the Program for the creation and development of a world-class scientific center «Supersonic» for 2020-2025 with the financial support of the Ministry of Education and Science of Russia (order of the Government of the Russian Federation dated October 24, 2020, No. 2744-r).

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  1. Institute of Continuous Media Mechanics UB RAS, 1 Akademika Koroleva Str., 614013, Perm, Russia

    Valerii Matveenko, Nataliia Iurlova, Dmitrii Oshmarin & Natalya Sevodina

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  1. Valerii Matveenko
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Matveenko, V., Iurlova, N., Oshmarin, D. et al. Analysis of dissipative properties of electro-viscoelastic bodies with shunting circuits on the basis of numerical modelling of natural vibrations. Acta Mech 234, 261–276 (2023). https://doi.org/10.1007/s00707-022-03193-8

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