............................................................(6.6.44)

In the plane the boundary of the region where nontrivial solutions can exist can be given by

.........................................................................................(6.6.45)

 

Exercise Problems

1. Study the response of the single degree of freedom system with both quadratic and cubic nonlinearities. Consider primary, subharmonic and superharmonic resonance conditions. Use either method of multiple scales or the method of normal forms.

References:

1. A. H. Nayfeh and D. T. Mook: Nonlinear Oscillations, Wiley, 1979

2. A. H. Nayfeh, Method of Normal Forms, Wiley,1993

Exercise problems

Q No. 1. Using numerical techniques plot the time response of the system given by Eq. (6.6.1) with primary, subharmonic and superharmonic resonance. Compare the results with those obtained from the perturbation method.

Q No. 2. Study different resonance conditions for the Duffing equation with two frequency excitation terms as given by the following equation.

Ans: One may observe following resonance conditions

Q No. 3 Plot the frequency response curves for the system with sub harmonic and super harmonic resonance condition using equation 6.6.25 and 6.6.45.