Bifurcations of parametric oscillations of beams with three equilibria

Abstract

Nonlinear curvature and nonlinear inertia are taken into account in the beam model. The constant part of the parametric force is proposed to be greater than the buckling one, therefore the beam has three equilibria. One-mode approximation of the beam oscillations is used. Bifurcations of the beam oscillations are analyzed by Melnikov's method. Moreover, beam oscillations close to the stable equilibriums are studied by the multiple scales method.