On the evaluation of the response of nonlinear systems by functional series expansion of forced and free responses

Abstract

Two basic series expansions are considered which provide the forced response (zero initial conditions) and the free response (zero input) of nonlinear analytic systems. The whole response is expressed as the sum of a “free response” and of a term which may be computed directly from a “forced response”. Furthermore, it is shown that both the kernels appearing in the series expansion of this term and the kernels characterizing the free response are directly related to the kernels of the forced response starting from zero initial conditions.