Two-to-one internal resonances in continuous systems with arbitrary quadratic nonlinearities

Abstract

Vibrations of a general continuous system with arbitrary quadratic nonlinearities are considered. The nonlinearities are expressed in terms of arbitrary quadratic operators. The two-to-one internal resonance case is considered. A general approximate solution is presented for the system. Amplitude and phase modulation equations are derived. Steady state solutions and their stability are discussed in the general sense. The sufficiency condition for such resonances to occur is derived. Finally the algorithm is applied to a specific problem.