Dynamic Analysis of Piezoelectric Structures by the Dual Reciprocity Boundary Element Method
G. Dziatkiewicz and P. Fedelinski

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 17, No. 1, pp. 35-46, 2007
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Keywords piezoelectric material, coupled fields, eigenvalue problem, dynamics, boundary element method, dual reciprocity method.
Abstract The aim of the present work is to show the formulation and application of the dual reciprocity boundary element method (BEM) to free vibrations of two-dimensional piezoelectric structures. The piezoelectric materials are modelled as homogenous, linear -- elastic, transversal isotropic and dielectric. Displacements and electric potentials are treated as generalized displacements and tractions and electric charge flux densities are treated as generalized tractions. The static fundamental solutions, which are required in the proposed approach, are derived using the Stroh formalism. The domain inertial integral is transformed to the equivalent boundary integral using the dual reciprocity method (DRM). The boundary quantities are interpolated using constant elements. The developed method is used to compute frequencies and mode shapes of natural vibrations of two-dimensional piezoelectric structures. The boundary conditions are imposed using the condensation method. In this method, the degrees of freedom, which correspond to the prescribed generalized displacements are eliminated. The eigenvalue problem is solved using the Lanczos method. The numerical results computed by the present method and finite element method are compared with the available analytical solutions given in the literature.
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