Effect of Boundary Form Disturbances on the Frequency Response of Planar Vibrations of Piezoceramic Plates. Analytical Solution

The general solution of the boundary problem of planar vibrations of parallelogram-shaped piezoceramic plates is constructed. The solution is presented as infinite series, with each term satisfying the motion equations of a piezoceramic plate element. The series coefficients are determined with functional equations, generated by the boundary conditions of the problem. These equations can be solved using the two approaches, based on minimization of the standard deviation and the collocation method. In the case of practical application of finite sums, both approaches lead to the search of solving the systems of linear algebraic equations. Quantitative estimates of the dynamic characteristics of piezoceramic plates are obtained, their analysis permits of evaluating the plate geometry effect. This method provides high accuracy of calculation results.