Abstract
Accurate modelling of a coupled dynamic electro-mechanical response of circular piezoelectric plates under various loading conditions is of particular importance. Piezoelectric plates are not only basic structural elements, but with certain considerations can be conveniently fit for numerical simulation of piezoelectric sensors and transducers. In this work, a Laplace domain direct boundary element formulation is applied for dynamic analysis of three-dimensional linear piezoelectric moderately thick circular plates. Zero initial conditions, vanishing body forces and the absence of the free electrical charges are assumed. Weakly singular expressions of Laplace domain boundary integral equations for the generalized displacements are employed. Spatial discretization is based on the nodal collocation method. Mixed boundary elements are implemented. The geometry of the elements, generalized displacement and generalized tractions are represented with different shape functions: quadratic, linear and constant, accordingly. Integral expressions of the three-dimensional Laplace domain piezoelectric displacement fundamental solutions are used. After solving the problem on a set of Laplace transform parameter values, time-domain solutions are retrieved from the corresponding Laplace domain solutions by employing a numerical inversion routine. Numerical example is provided to show reliability and accuracy of the proposed boundary element formulation.
Highlights
Due to the direct piezoelectric and converse piezoelectric effects, piezoelectric materials have a very practically significant ability to convert the mechanical energy into the electric energy and vice versa
The mixed boundary elements are used for the spatial discretization of the boundary integral Eq (9) which means that the geometry of the elements and the variation of the generalized displacements and generalized tractions over each element are interpolated by different shape functions: quadratic, linear and constant, respectively
The Laplace domain direct boundary element formulation for dynamic analysis of three-dimensional linear piezoelectric moderately thick circular plates is presented in this paper
Summary
Due to the direct piezoelectric and converse piezoelectric effects, piezoelectric materials have a very practically significant ability to convert the mechanical energy into the electric energy and vice versa. The numerical solution of the three-dimensional piezoelectric static, time-harmonic and transient problems is usually carried out using the Finite Element Method (FEM). Though various BEM formulations has been successfully applied for linear isotropic elastodynamic problems [7,8,9,10,11,12], number of works dedicated to application of BEM to the three-dimensional anisotropic linear elastic and piezoelectric dynamic problems is still low This is due to the fact that the usability of the conventional boundary element formulation depends on the availability of the fundamental solutions. A transient dynamic behaviour of three-dimensional linear piezoelectric moderately thick circular plates is modelled by the Laplace domain direct boundary element formulation. Numerical example is presented to confirm the accuracy and reliability of the proposed formulation
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