Applicability conditions of a Nonlinear Superposition Technique

The analytical conditions for the applicability of a Non!linear Superposition Technique"NST# are established by using the Normal Form Method "NFM#[ The superpositiontechnique represents the extension of modal analysis to weakly non!linear vibrationsystems[ In this paper it is shown that the NST leads to a non!uniform perturbationexpansion for the solution of dynamical systems when some special non!linear terms arepresent in the dynamical system[ An analytical proof for general dynamical systems anda numerical application to a simple mechanical system is included in the paper