A modal analysis of forced vibrations caused by a time-harmonic force from a piezoelectric plate standing on a rigid foundation is presented. A 3D linearized elasticity theory for solids under initial stress (TLTESIS) is used. It is assumed that a uniformly distributed normal loadings acting on the lateral surfaces of the plate yield the initial stress state. The piezoelectric plate is under the action of a time-harmonic force poled in various directions. A mathematical model is developed, and the problem is solved employing the 3D finite-element method (3D-FEM). Some numerical results illustrating the influence of changes in the poling direction and other important factors, such as the initial stress, on the dynamic behavior of the plate are presented.
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Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 58, No. 1, pp. 97-114, January-February, 2021. Russian DOI: 10.22364/mkm.58.1.06.
Appendix A
Appendix A
Depending on the case considered, the matrix \( \overset{\sim }{\mathbf{M}} \) of constitutive equations changes accordingly. Although our analysis is modal, the numerical results and discussions given here were presented for three different cases. The matrices \( \overset{\sim }{\mathbf{M}} \) for polarization in the directions of Ox1, Ox2, and Ox3 axes are
and
respectively.
Acknowledgements. The author wishes to express deep thanks to the anonymous referees for their constructive comments and suggestions, which significantly improved the quality of the paper.
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Daşdemir, A. A Modal Analysis of Forced Vibration of a Piezoelectric Plate with Initial Stress by the Finite-Element Simulation. Mech Compos Mater 58, 69–80 (2022). https://doi.org/10.1007/s11029-022-10012-7
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DOI: https://doi.org/10.1007/s11029-022-10012-7