Nonlinear Dynamics of Closed Spherical Shells

We investigate the axisymmetric dynamics of forced closed spherical shells. The nonlinear equations of motion are formulated using a variational approach and surface analysis. First, we revisit the linear eigenvalue problem. Then, using the method of multiple scales, we assess the possibility of the activation of two-to-one internal resonances between the different types of modes. Lastly, we examine the shell’s nonlinear responses to an axisymmetric primary-resonance excitation and analyze their bifurcations.

Dynamic Analysis of MEMS Resonators Under Primary-Resonance Excitation

We present a dynamic analysis and simulation of electrically actuated microelectromechanical systems (MEMS) resonators under primary-resonance excitation. We use a shooting technique, perturbation techniques, and long-time integration of the equation of motion to investigate the global dynamics of the resonators. We study the dynamic pull-in instability and show various scenarios and mechanisms for its occurrence. Our results show that dynamic pull-in can occur through a saddle-node bifurcation, a period-doubling bifurcation, or homoclinic tangling, depending on factors such as the initial conditions of the device and the level of the electrostatic force.