Abstract
A system of second-order equations with weak quadratic and cubic non-linearities is considered. It contains a parametric excitation which has multiple harmonic components. A general analysis is carried out using the method of multiple scales. A study is then made of the resonance in which the sum of two excitation frequencies ( λ s, λ t ) is near twice a natural frequency ( ω q ) of the linearized system, i.e. λ s + λ t ≈ 2ω q . The influence of an internal resonance of the form ω q ≈ 3ω r or 3ω q ≈ ω r is also investigated. Results are presented as plots of response amplitudes as functions of a detuning parameter, an excitation amplitude, and a measure of the relative values of λ s and λ t .
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
