Three-dimensional analytical modeling of vibration behavior of piezoceramic cylindrical shells

Abstract

Dynamic analysis of piezoelectric continuum is quite complex, because it includes the coupling of electrical and mechanical terms. Complexity further increases with the consideration of three-dimensional model analysis. Implementation of the analytical methods in order to obtain a closed-form solution is a cumbersome task even in the case of a moderately complex model. As an alternative, approximation methods are used to circumvent these difficulties. In the present work, Rayleigh–Ritz method is used to obtain the eigenvectors and the eigenfrequencies for the piezoceramic cylindrical shells. Orthogonal polynomials generated using Gram–Schmidt method are used in the Rayleigh–Ritz method to formulate the eigenvalue problem. The present method has an advantage of being adapted by software with great ease and provides much accurate results, which makes it reasonably useful for analysis of more complex piezoceramic structures. The presented approximation method is validated by comparing the results with the previous works done in similar problem and by the finite element analysis.