Stability Analysis of a Capacitive Micro-Bridge Induced by Heat

This paper presents the stability analysis of an electro-statically deflected clamped-clamped micro-beam, which is driven to vibrate around its deflected position by a harmonic thermal load, from the bifurcation perspective in the case of primary resonance. The micro-structure is modelled assuming Euler–Bernoulli beam assumption which accounts for the nonlinear von-Karman strain and the electrostatic forcing. To simulate the static and dynamic responses, a model reduction procedure is carried out by employing the Galerkin method. The static pull-in voltage is obtained and validated with the experimental results offered in the literature. Then, the Averaging method, which is a regular semi-analytic perturbation technique, is applied and the analytical expressions for equilibrium positions as fixed points are presented. At this point, the stability of frequency response branches is examined by assessing the Jacobian matrix. Finally, by performing the coordinate transformation of the systems’ analytical solution from polar to Cartesian, phase portraits at two specific points are illustrated to provide an in-depth description in terms of stability.

Keywords:

Nonlinear Dynamics , MEMS , Stability , Heat-Induced Vibration