Linear and Nonlinear Mechanics in MEMS

Complex multi-physics phenomena are peculiar of MEMS. Mechanics plays a major role in many cases, in prims in inertia MEMS, but also in many other devices like micromirrors, pressure sensors, ultrasonic transducers. Design for reliability in MEMS implies a good knowledge of all mechanical features, of multi-physics interactions and of various nonlinear responses that can arise in MEMS. A careful, in deep knowledge of intriguing nonlinear mechanical phenomena, can also help in designing future innovative microsystems. This chapter is devoted to recall basic mechanical responses in MEMS with particular focus on the dynamics of oscillating parts. An overview of analytical, semi-analytical, and numerical approaches for the solution of linear and nonlinear responses is first proposed. Then various examples are discussed to put in evidence the main linear and nonlinear responses that are often met in the study, design, and use of Microsystems: oscillators in resonant accelerometers with hardening and softening effects, also induced by coupling with electrical and thermal phenomena, micromirrors showing no nonlinear responses, resonators. Many peculiar, nonstandard, nonlinear phenomena are also briefly discussed, as nonlinear piezoelectricity, internal, and parametric resonances, dissipation due to thermoelasticity and fluid-structure interaction.