The dynamic behavior of structures with piezoelectric patches is governed by partial differential equations with strong singularities.\nTo directly deal with these equations, well adapted numerical procedures are required. In this work, the differential quadrature\nmethod (DQM) combined with a regularization procedure for space and implicit scheme for time discretization is used. The\nDQM is a simple method that can be implemented with few grid points and can give results with a good accuracy. However, the\nDQM presents some difficulties when applied to partial differential equations involving strong singularities. This is due to the\nfact that the subsidiaries of the singular functions cannot be straightforwardly discretized by the DQM. A methodological\napproach based on the regularization procedure is used here to overcome this difficulty and the derivatives of the Dirac-delta\nfunction are replaced by regularized smooth functions. Thanks to this regularization, the resulting differential equations can be\ndirectly discretized using the DQM. The efficiency and applicability of the proposed approach are demonstrated in the\ncomputation of the dynamic behavior of beams for various boundary conditions and excited by impulse and Multiharmonics\npiezoelectric actuators. The obtained numerical results are well compared to the developed analytical solution.
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