Dynamic Modeling of the Multilayered Piezoelectric Beams Based on the Pseudo-Stroh Formalism

In this paper, a semi-analytical solution for the dynamic behavior of the multilayered piezoelectric beams is derived. The beam is assumed to be simply supported and the interfaces between the layers are considered perfect. In each layer of the beams, the pseudo-Stroh formalism is developed and the set of partial differential equations is reduced to a system of second order ordinary equation of time. To solve that equation in time domain, the time interval is divided into several sub-intervals having equal length. In each sub-interval of time, the Lagrange polynomials have been used and a discrete eigenvalue problem is then obtained. The solutions are therefore constructed and interpolated in the time domain. Those solutions have been propagated throughout the thickness direction of beams using the propagator matrix method. In the computation process, the elastic material graphite epoxy (named E) and the piezoelectric material BaTiO3 (named B) are used. The layering effect and the surfaces boundary conditions effect on the dynamic response of the three-layered piezoelectric beams are clearly illustrated. The obtained results can be helpful as benchmark.