Free vibration of layered magneto-electro-elastic beams by SS-DSC approach

Based on three-dimensional elasticity theory, semi-analytical solutions for free vibration of arbitrary layered magneto-electro-elastic beams are derived applying the state space approach (SSA) and discrete singular convolution (DSC) algorithm. The thickness direction of beams is chosen as the transfer direction in SSA, and the DSC is employed to discretize the length direction. Hence, the original partial differential equations are transformed into a state equation consisting of first-order ordinary differential equations. The application of DSC can implement various boundary conditions, which cannot be solved in the conventional SSA. Numerical examples are presented to study the method in details.