Equilibriums and their stabilities of the snap-through mechanism

A snap-through mechanism is investigated with the focus on its equilibriums and their stabilities. The snap-through mechanism consists of two inclined linear springs connected to a damper and a mass. The influence of the gravitation effects of the mass on the equilibriums, which has been neglected in all previous works, is taken into account in the investigation. The equilibrium equation is derived from the dynamical equation. The Lyapunov linearized stability theory is applied to determine the stability of the equilibrium. A dimensionless control parameter is introduced. For the sufficient small control parameter or the sufficient larger inclination angle, there are four equilibriums, two stable and two unstable. If the control parameter is larger than the critical value or the absolute value of the angle is smaller than a critical value, a stable and an unstable equilibriums disappear via a saddle-node bifurcation.