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In this study, the dynamic response behavior of a generalized nonlinear dynamic system is investigated using a newly proposed extended Galerkin method. The algebraic equations of vibration amplitudes are obtained through an integration of the weighted functions. The new method is equivalent to the harmonic balance method but with a much simpler calculation procedure and a higher efficiency. This is the first time to use the method for the analysis of nonlinear systems with high number of modes, manifesting that the method is applicable to forced vibrations of nonlinear behavior. The method is further validated by the numerical Runge-Kutta method.

Forced vibration analysis of multi-degree-of-freedom nonlinear systems with the extended Galerkin method