AN INVARIANT MANIFOLD APPROACH TO NONLINEAR NORMAL-MODES OF OSCILLATION

A method for determining the amplitude-dependent mode shapes and the c orresponding modal dynamics of weakly nonlinear vibratory systems is d escribed. The method is a combination of a Galerkin projection and inv ariant manifold techniques and is applied to a class of distributed pa rameter vibratory systems. In this paper the general theory for a clas s of conservative systems is outlined and applied to determine the non linear mode shapes and modal dynamics of a linear Euler-Bernoulli team attached to a nonlinear elastic foundation.