A general electromechanical model for plates with integrated piezo-patches using spectral-Tchebychev method

This paper presents a general electromechanical model for predicting the dynamics of thin or moderately thick plates with surface-integrated piezo-patches. Using spectral Tchebychev (ST) technique, the boundary value problem governing the electroelastic dynamics of the two dimensional (2D) plate and piezo-patch structure is developed with Mindlin plate theory assumptions. Mass and stiffness contributions of piezo-patch(es) as well as two-way electromechanical coupling behavior are incorporated in the model for both modal analysis and frequency response calculations. To validate the accuracy of the developed solution technique, the modal analysis results are compared against the existing Rayleigh-Ritz solution from the literature as well as the finite-element simulation results for various piezo-patch sizes on thin and moderately thick host plates; and it is shown that the maximum difference in the predicted natural frequencies between the ST and FE results are below 1%. The electromechanical frequency response functions (FRFs) including the vibration response and electrical output of the system under a transverse point force excitation are obtained using the ST model and the results are shown to match perfectly with the finite element (FE) simulations. Additionally, comparisons of the electromechanical FRFs calculated based on Rayleigh-Ritz method from the literature versus the developed framework is presented to highlight that the exclusion of shear deformation terms in the former model leads to an inaccurate estimation of electroelastic behavior for the case of thicker plates with integrated piezo-patches. Finally, the investigated case studies demonstrate that the computational efficiency of the developed method is significantly higher than that of FE simulations.