Free and Forced Vibration Analysis of Piezoelectric Patches Based on Semi-Analytic Method of Scaled Boundary Finite Element Method

Nowadays, employing piezoelectric pathches which are categorized as a kind of intelligent materials, has been increased in various industries significantly. Development of a precise mathematical model of these materials, plays an important role in comprehending their operational mechanisms as well as developing new techniques based on their coupled electro-mechanical behavior. This is while, high computational cost of available numerical methods which are able to simulate vibrational behavior of piezoelectric materials, especially at high frequencies, is considered as a serious challenge in this area. The purpose of this study is to use a novel semi-analytical method, called Scaled Boundary Finite Element Method (SBFEM), to analyze free and forced vibration of piezoelectric materials. SBFEM enables to analyze any partial derivative equation in a semi-analytical manner, however, with much lower computational cost comparing with other numerical methods. In order to evaluate the accuracy of this method in modeling of different problems occurred in structural health monitoring and fracture mechanics fields, the free and forced vibration of a piezoelectric patch, a piezoelectric patch attached to an aluminum structure, a piezoelectric patch with a circular hole and a cracked piezoelectric patch was analyzed as 4 case studies. Comparison of convergence rate of SBFEM and FEM indicates that the former provides exact results with much less degrees of freedom. In addition, proper matching of results of the 2 above-mentioned approaches, demonstrates the capability of SBFEM to model a variety of problems accurately at a very low computational cost.