On the influence of centerline strain on the stability of a bimorph piezo-actuated microbeam

The nonlinear equation of motion for pre-stretched Euler–Bernoulli beams is derived. The effect of pre-tension and pre-compression in Euler–Bernoulli beams is studied. It is shown that compressive strain affects the bending stiffness much more than tensile strain. Based on the derived equation, the dynamic model of bimorph piezo-actuated beams, which is accurate, yet simple, is then developed. Afterwards, the critical voltage, which makes the piezo-actuated microbeam unstable, is numerically investigated. It is shown that the strain of the centerline is proportional to the beam’s aspect ratio squared. Results show that the more the aspect ratio, the less the critical voltage. In addition, it is illustrated that compared to the cantilever microbeam, the doubly-clamped microbeam is more sensitive to the changes in the aspect ratio.