Analysis of Natural Frequencies for a Laminated Composite Plate with Piezoelectric Patches using the First and Second Eigenvalue Derivatives

In this paper, the first and second order approximations of Taylor expansion are used for calculating the change of each natural frequency by modifying an arbitrary parameter of a system with a known amount and based on this approximation, the inverse eigenvalue problem is transformed to a solvable algebraic equation. The finite element formulation, based on the classical laminated plate theory (CLPT) is presented for laminated composite plates with piezoelectric patches. Using the proposed FE model, sensitivity analysis is carried out, to find the effects of the changes made in the design parameters such as the piezoelectric patch thickness and the fiber angles in each layer on the natural frequencies of the structure. The inverse eigenvalue problem is solved in order to find the thickness of piezoelectric patches and stacking sequence for relocating the natural frequencies.