Spectral element formulation for dynamic analysis of a coupled piezoelectric wafer and beam system

A spectral element model is developed to represent the dynamic response of a coupled piezoelectric wafer and beam system (CPBS) in which either a single or collocated piezoelectric wafers are bonded to a base beam. The Mindlin–Herrmann rod theory and the Timoshenko beam theory are employed to represent the displacement field of the base beam. The Euler–Bernoulli beam theory and linear piezoelectricity are used to model the electro-mechanical behavior of the piezoelectric wafer. Detailed spectral element formulation for the CPBS is presented. The validity of the proposed spectral element is demonstrated through numerical examples in time and frequency domains, respectively.