Modelling a micro-cantilever vibrating in vacuum, gas or liquid under thermal base excitation

• A micro-cantilever excited by vertically moving thermal actuator is formulated.
• Effect of actuator on free vibration and harmonic response is discussed.
• Natural frequencies and harmonic response in presence of fluid mediums is studied.
• Quality factor of the vibration is studied with regards to ambient gas pressure.

The dynamic behaviour of a micro-cantilever that is transversely excited at its base is investigated in this paper. The base actuation is provided by thermal cycles via taking the advantage of thermal expansion. The Euler–Bernoulli equation along with corresponding boundary conditions is used to model the continuous cantilever beam. The resultant boundary value problem takes into account the thermal expansion and stiffness of the actuator at the base as well as the effect of the surrounding gas or liquid. A closed-form analytical model is developed to compute natural frequencies, mode shapes, and harmonic response of the vibrating cantilever, in addition to an integral function for quality factor. The model is validated via a finite element (FE) analysis using ANSYS commercial package. This validation shows that the proposed model can properly predict the cantilever's vibrating behaviour.