Bifurcations Of Strongly Nonlinear Oscillation System Under Multi-Frequency External Periodic Forces

We consider a class of strongly nonlinear system under parametric excitation and multi-frequency external periodic forces. A large parameter is transformed into a small parameter by using the modified L-P method so that the solution can be expanded. The bifurcation response equation is obtained by using the method of multiple scales. We discuss the degenerate bifurcation of codimension 1 and codimension 2, furthermore, we obtain the various bifurcation diagrams and some new property.The paper contains five parts. In the first section, the development of general mechanics and strongly nonlinear systems is referred. In the second section, an introduction to bifurcation theory and some typical examples are explained. The third section is the most important part of this paper, we discuss the degenerate bifurcation of codimension 1 of the system. The bifurcation response equation and the various bifurcation diagrams are obtained. In the fourth section, we discuss the degenerate bifurcation of codimension 2 of the system. The universal unfolding of the system is obtained by using normal form theory and universal unfolding theory. In the last section, we conclude the paper.