The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure graph in an integral causality assignment (MBGI) to get space system introduced. By assigning derivative storage elements, (MBGD) proposed. Based on this MBGD, theorem obtain Two case studies variables are applied. Both c...

This paper presents a finite element formulation for the dynamics analysis of the steady and transient states of a nonlinear piezoelectric beam. A piezoelectric beam with damping is studied under harmonic excitation. A numerical method is used for this analysis. In the paper, the central difference formula of four order is used and compared with the central difference formula of two order in th...