Response of Multidegree-of-Freedom Systems with Quadratic and Cubic Nonlinearities to Harmonic Excitation, with Application to a Shallow Arch. 1. Single-Frequency Excitation

摘要

An infinite set of ordinary differential equations with weak quadratic and cubic nonlinearities is considered. The authors study the oscillations of the system under harmonic excitations. Damping is included. The authors apply the method of multiple scales to investigate various resonance conditions, including primary, superharmonic, subharmonic, and combination resonances. Conditions of internal resonance are also considered, leading to situations in which several resonances occur simultaneously. Both transient and steady-state responses are analyzed, and various phenomena are described.