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2017 | OriginalPaper | Chapter

Mathematical Models and Finite Element Approaches for Nanosized Piezoelectric Bodies with Uncoulped and Coupled Surface Effects

Authors : Victor A. Eremeyev, A. V. Nasedkin

Published in: Wave Dynamics and Composite Mechanics for Microstructured Materials and Metamaterials

Publisher: Springer Singapore

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Abstract

In this chapter the dynamic problems for piezoelectric nanosized bodies with account for coupled damping and surface effects are considered. For these problems we propose new mathematical model which generalizes the models of the elastic medium with damping in sense of the Rayleigh approach and with surface effects for the cases of piezoelectric materials. Our model of attenuation and surface effects has coupling properties between mechanical and electric fields, both for the damping terms and constitutive equations for piezoelectric materials on the surface. For solving the problems stated the finite element approximations are discussed. A set of effective finite element schemes is examined for finding numerical solutions of week statements for nonstationary problems, steady-state oscillation problems, modal problems and static problems within the framework of modelling of piezoelectric nanosized materials with damping and surface effects. For transient and harmonic problems, we demonstrate that the proposed models allow the use of the mode superposition method. In addition, we note that for transient and static problems we can use efficient finite element algorithms for solving the systems of linear algebraic equations with symmetric quasi-definite matrices both in the case of uncoupled surface effects and in the case of coupled surface effects.

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next chapter On the Theory of Acoustic Metamaterials with a Triple-Periodic System of Interior Obstacles
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Metadata
Title
Mathematical Models and Finite Element Approaches for Nanosized Piezoelectric Bodies with Uncoulped and Coupled Surface Effects
Authors
Victor A. Eremeyev
A. V. Nasedkin
Copyright Year
2017
Publisher
Springer Singapore
Book
Wave Dynamics and Composite Mechanics for Microstructured Materials and Metamaterials

Print ISBN: 978-981-10-3796-2

Electronic ISBN: 978-981-10-3797-9

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-981-10-3797-9_1

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