Nonlinear thermo-mechanical behaviour of MEMS resonators

This paper investigates the static deflection as well as the nonlinear resonant behaviour of an electrically actuated MEMS resonator subject to a temperature rise. The deformable electrode is actuated by a harmonic AC load superimposed to a constant DC load. Taking into account thermal effects, the size-dependent equation of motion is derived by means of the extended Hamilton’s principle together with the modified couple stress theory. The effect of temperature rise on the mechanical properties of the microresonator is also taken into account. Based on the Galerkin method, a high-dimensional discretised model of the microresonator is obtained which is solved by means of the pseudo-arclength continuation technique. In particular, the non-trivial deflected configuration of the deformable electrode, as well as the static pull-in voltage, is obtained. The nonlinear resonant behaviour of the system is analyzed when the system is actuated by the AC voltage near the primary resonance. The effect of temperature rise on the static and dynamic responses of the system is highlighted. Furthermore, it is shown that when the mechanical properties are considered temperature-dependent, rather than constant, the behaviour of the system changes significantly.