Spectral-Tchebychev technique for the free and stochastic vibration analysis of functionally graded plates with piezoelectric patches

This paper presents a Spectral-Tchebychev (S-T) dynamic model to examine the free and random vibration properties of functionally gradient plates with piezoelectric patches (FGPPP) under random excitation. Firstly, the plate is divided into several sub-plates according to the position of the piezoelectric patches through the multi-partitioning strategy. Then, the dynamical equations for each sub-plate are derived based on the first-order shear deformation theory (FSDT) and Hamilton's variational principle. The boundary conditions and the coupling relationships of the adjacent plates are handled using the artificial spring technique. Finally, the free and stochastic vibration characteristics of FGPPP are obtained using the Spectral-Tchebychev technique, where the stationary random load is introduced by the pseudo-excitation method (PEM). The rationality and validity of the S-T model in predicting the vibration characteristics of FGPPP are verified by the comparison with the results from literature and FEM. The influence mechanism of some key parameters including the thickness ratio, area ratio, patching position, patching type, power law index, etc., on the vibration characteristics are systematically investigated.

Automated summary

This paper presents a Spectral-Tchebychev (S-T) dynamic model to examine the free and random vibration properties of functionally gradient plates with piezoelectric patches under random excitation. The model considers the division of the plate into sub-plates based on the position of the patches, derivation of dynamical equations using FSDT and Hamilton's variational principle, handling of boundary conditions and coupling relationships, and obtaining vibration characteristics using the Spectral-Tchebychev technique. The results validate the rationality and validity of the S-T model in predicting the vibration characteristics and investigate the influence mechanism of key parameters.