Modelling the dynamic response of a micro-cantilever excited at its base by an arbitrary thermal input using Laplace transformation

An analytical model for predicting the time-history response of a cantilever beam to arbitrary time-dependent thermal actuation is elaborated in this paper. Base excitation is investigated as a practical method for thermally exciting the micro-cantilever. The beam is considered to be mounted on a layer of material (actuator) that is thermally excited (e.g., by electric current). Thermal expansionicontraction of the base causes the micro-cantilever to vibrate. One-dimensional heat conduction equation is solved for the actuator, along with the Euler-Bernoulli continuous beam equation for the micro-cantilever. An arbitrary time dependant body heat generation is applied on the actuator as the excitation function for the latter equations. Laplace transformation is applied to tackle the time dependency of the partial differential equations. After solving the coupled ordinary differential equation, two methods based on Gaver-Stehfest algorithm and direct numerical integration are considered for the inverse transformation and discussion regarding results and procedures are presented. Moreover, a case study of a thermally actuated resonator with periodic input signal is investigated and conclusions on the practical design and implementation are demonstrated. (C) 2016 Elsevier Inc. All rights reserved.