Piezothermoelastic vibrations of microbeam resonator with memory effects

This study analyzes the thermoelastic vibration of a transversely isotropic piezothermoelastic (PTE) microbeam resonator using the Euler-Bernoulli beam theory. For the present problem, the issue of heat conduction has been framed in the context of memory-dependent dual phase lag model adjoining the memory-dependent derivative within a slipping interval. The thermoelastic vibrations for thermal moment and thermal deflection for a simply supported microbeam resonator have been derived using the Laplace and finite Fourier sine integral transforms. To arrive at the solutions for thermoelastic vibrations of thermal moment and deflection in the real space-time domain, the inversion of the finite Fourier sine transform has been carried out analytically, whereas the inversion of the Laplace transform has been performed numerically using the method of Zakian. Additionally, numerical simulations were conducted to validate the analytical results. To illustrate the numerical estimates, a PTE material of lead zirconate titanate (PZT-5A) is considered. The influence of time delay parameter and the effects of various kernel functions have been discussed. A comparison between materials with and without the piezoelectric effect is presented.