Application of multistage homotopy perturbation method to the nonlinear space truss model
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The purpose of this study is to investigate the applicability of multistage homotopy perturbation method (MHPM) to space truss structures composed of discrete members in order to obtain an analytical solution. For this research purpose, a nonlinear dynamic governing equation of the space truss structures was formulated in consideration of geometrical nonlinearity, and homotopy equations were derived using a formulated differential equation. The result of carrying out a dynamic analysis on a single-free-node model and a double-free-nodes model were compared with the classical homotopy perturbation method and the 4th order Runge-Kutta method (RK4), and it was found that the dynamic response by MHPM concurred with the numerical results. Additionally, the pattern of the response and attractor in the phase space could delineate the dynamic snapping properties of the space truss structures under excitations, and the attraction of the model in consideration of damping reflected well the convergence and asymptotic stable.
Keywordsmultistage homotopy perturbation method (MHPM) analytical solution space truss nonlinear dynamic system geometric nonlinearity
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