Modal analysis of magneto-electro-elastic plates using the state-vector approach

The state-vector approach is proposed to analyze the free vibration of magneto-electro-elastic laminate plates. The extended displacements and stresses can be divided into the so-called in-plane and out-of-plane variables. Once the state equation for the out-of-plane variables is obtained, a complex boundary value problem is converted into an equivalent simple initial value problem. Through the state equation, the propagator matrix between the top and bottom interfaces of every layer can be easily derived. The global propagator matrix can also be assembled using the continuity conditions. It is obvious that the order of global propagator matrix is not related to the number of layers. Consequently, this approach possesses certain virtues including simple formulation, less expensive computation, etc. To test the formulation, the developed solution is then applied to a simply supported multilayered plate constructed of piezoelectric and/or piezomagnetic materials. The natural frequencies and corresponding mode shapes are computed and compared with existing results. Furthermore, the fundamental modes along with a couple of other higher modes, which have never been reported in previous literature, are presented. Therefore, this completed set of frequencies and mode shapes can be used as benchmarks for future research in this field. It is also believed that the approach could be useful in the analysis and design of smart structures constructed from piezoelectric/piezomagnetic composites.