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Transverse vibrations in piezothermoelastic beam resonators

In this article, the closed form expressions for the transverse vibrations of a piezothermoelastic beam, based on Euler–Bernoulli theory, have been derived. The effects of electric potential, relaxation times, thermomechanical coupling, and beam dimensions on energy dissipation induced by thermoelastic damping microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) resonators have been investigated under free edge conditions. Analytical expressions for damping and frequency shift of vibration due to electric potential and thermal variations are obtained. The vibrations of such resonators are significantly affected due to surface conditions. Some numerical results with the help of MATLAB programming software in the case of lead zirconate titanate (PZT)-5A material have been presented graphically for illustration of analytical developments.