A numerical method for determining nonlinear normal modes

This paper examines a new approach for determining the nonlinear normal modes of undamped non-gyroscopic multiple degree-of-freedom systems. Unlike algebraic solutions that generally assume a solution in the form of a polynomial expansion, this method makes only the assumption of repetitive motion in numerically determining the mode shapes. The advantage of this approach is that the accuracy obtained in the mode shape identification is a function only of the accuracy of the numerical integration used and not of the number of terms in the power series expansion. The drawbacks are that invariance of the modal manifolds cannot be proven and mode bifurcations can be easily overlooked.