In normal circumstances, many practical engineering problems are nonlinear and can be described by multi-degree-of-freedom (MDOF) dynamical systems. Theoretically speaking, the exact solutions are very scarce, so it is extremely significant to develop the analytic tools for nonlinear systems in engineering. Inasmuch as the homotopy analysis method (HAM) can overcome the foregoing restrictions of conventional perturbation techniques, this method has been widely applied to solve a variety of nonlinear problems. In this paper, the extended homotopy analysis method (EHAM) is presented to establish the analytical approximate periodic solutions for MDOF nonlinear dynamic system. The periodic solutions for the parametric excitation buckled thin plate system of MDOF are applied to illustrate the validity and great potential of this method. In addition, comparisons are conducted between the results obtained by the EHAM and the numerical integration (i.e. Runge-Kutta) method. It is shown that the second-order analytical solutions of the EHAM agree well with the numerical integration solutions, even if time t progresses to a certain large domain in the time history responses.
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