2-D GENERAL ANISOTROPIC AND PIEZOELECTRIC TIME-HARMONIC BEM FOR EIGENVALUE ANALYSIS

Abstract eng:
We derive the fundamental generalized displacement solution for two-dimensional piezoelectric solids using the Radon transform and present the direct formulation of the time-harmonic Boundary Element Method (BEM). The formulation includes the general anisotropic solids (and the dielectric solids), as the special case, when the piezoelectric constants disappear. The fundamental solution is separated into the static singular and the dynamics regular parts. The former, being the fundamental solution of the static problems, leads to the static BEM for piezoelectric (and general anisotropic) solids, while the latter leads to the dynamic part of the BEM. Thus, the time-harmonic BEM consists of the static singular boundary element (SSBE) and the dynamic regular boundary element (DRBE). This allows us to reuse the existing SSBE and develop only the DRBE. The unique feature of the boundary integrals in the DRBE is that, after evaluated analytically along the boundary element, they are reduced to simple line integrals along the unit circle. We apply the BEM to the determination of the eigen frequencies of piezoelectric and general anisotropic solids. The eigenvalue problem deals with full non-symmetric complex-valued matrices whose components depend non-linearly on the frequency. We make a comparative study of non-linear eigenvalue solvers: QZ algorithm and the implicitly restarted Arnoldi method (IRAM).

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