A Hybrid Method for the Primary Resonance Response of Harmonically Forced Strongly Nonlinear Oscillators

Abstract

A hybrid method is presented to obtain the analytical approximate solution to the primary resonance of harmonically forced strongly nonlinear oscillators. This hybrid method combines the classical perturbation method and the classical harmonic balance method. With the proposed splitting procedure some free parameters are introduced, more accurate and reliable analytical approximation compared to the results obtained by the classical harmonic balance method are presented. The proposed method is not based on the small parameter assumption when perturbation method is applied. It is found that the corrections to erroneous solution when harmonic balance method and Floquet theory are adopted in stability analysis is necessary. The proposed method gives excellent stability results compared to those obtained by using harmonic balance method and Floquet theory. Two examples are presented to illustrate the applicability, validity and convergence of the proposed method. The convergence of the solution in stability analysis by the proposed hybrid method are compared with that obtained by using the Floquet theory and the harmonic balance method. The results obtained by the proposed method are verified by the numerical simulations.