Non-chaotic response of non-linear oscillators under combined deterministic and weak stochastic excitations

Non-linear oscillators under harmonic and/or weak stochastic excitations ar e considered in this paper. Under harmonic excitations alone, an analytical technique based on a set of exponential transformations followed by harmon ic balancing is proposed to solve for a variety of one-periodic orbits. The stability boundaries for such orbits in the associated parameter space are constructed using the Floquet theory. Under a combination of harmonic and weak stochastic excitations, a stochastic perturbation approach around the deterministic orbit is adopted to obtain response statistics in terms of th e evolving moment functions. In the present study, the stochastic perturbat ion is assumed to be an additive white noise process and equations for the evolving moments are derived using Ito differential rule. A fifth order cum ulant neglect closure is used to close the infinite hierarchy of moment equ ations. Limited numerical results are presented to illustrate the implement ation of the proposed scheme. The method is found to be quite versatile and admits ready extensions to Md.o.f. systems under combined harmonic and whi te or non-white, multiplicative or additive random excitations. (C) 1999 Ac ademic Press.