A NUMERICAL-METHOD FOR DETERMINING NONLINEAR NORMAL-MODES

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