A dynamic thermo-mechanical actuator system with contact and Barber's heat exchange boundary conditions

Abstract

This work, motivated by the rapid developments in Micro-Electro-Mechanical Systems (MEMS) structures, especially actuators and grippers, analyses the dynamics of a thermo-mechanical system consisting of a horizontal beam joined at one end to a vertical rod. As a result of thermal expansion or vibration of the rod, the other end may come into contact with another part of the MEMS device and that closes an electrical circuit, which is the actuating or switching function of such a beam–rod system. The interaction between the rod's contacting end and the supporting device is described by a normal compliance contact law for the displacements and by an inclusion-type Barber's heat exchange condition for the temperature. The heat-exchange coefficient is a multi-function taking into account the air resistance in the gap when there is no contact and the contact pressure when contact occurs. The model consists of a nonlinear variational inclusion for the temperature coupled with a nonlinear variational equation for the displacements. The existence of a weak solution to the problem is proved by using the Galerkin method, a regularization of Barber's condition with the Yosida approximation of a maximal monotone operator, and a priori estimates.

Reliability of MEMS inertial devices in mechanical and thermal environments: A review

“…The heat conductivity and CTE vary with temperature, which in turn affects Joule heating and heat conduction, causing different degrees of deformation in the beam structure. Under long-term operating conditions, the structure undergoes fatigue or creep, resulting in cumulative thermal-mechanical coupling damage [ 89 ].…”