Homotopy Perturbation–Based Dynamic Analysis of Structural Systems

Abstract

This paper presents the dynamic analysis of structural systems using the homotopy perturbation method (HPM). HPM was applied to the first-order differential equations of motion defined by the state vector. This approach is in the framework of time-history matrix analyses. According to the formulas obtained from HPM, response of the system was achieved by sequential product of the characteristic matrix of the system. This method was theoretically compared with the exponential matrix method (EMM). Based on the obtained formulas, nonlinear structural analysis was performed in addition to the linear method. The applicability and efficiency of the proposed method were tested with the classical and nonclassical damping structures and with different dynamic behaviors. Solutions of this method were compared with solutions of EMM and the time-integration method (TIM). The results of the proposed method were in good agreement with those of the two other methods in linear and nonlinear analyses.