AN ENERGY ANALYSIS OF EQUILIBRIUM AND BIFURCATION OF A SNAP-THROUGH OSCILLATOR

An energy analysis is carried out for a snap-through oscillator to study its equilibrium and the bifurcation. The equilibrium equation is established based on the principle of the potential energy, and the stability of the equilibrium configurations can be determined via the extreme values of the potential energy. For different configurations of the spring, the equilibrium configurations and their bifurcation are numerically determined through the ratio of the spring stiffness to the mass changes. The results demonstrate that there are a stable equilibrium configuration and an unstable equilibrium one under the condition of a small control parameter. As the control parameter increases to a critical value, an additional stable equilibrium configuration and an additional unstable equilibrium bifurcation appear.