Abstract
The present article analyzes the thermoelastic vibration for a transversely isotropic piezothermoelastic (PTE) microbeam resonator in the context of Euler-Bernoulli beam theory assimilating the nonlocal stress theory. The heat transport equation for the present problem is framed in the context of memory-dependent Moore-Gibson-Thompson theory adjoining the memory dependent derivative within a slipping interval. The thermoelastic distribution as well as vibrations for thermal moment and thermal deflection for a simply supported microbeam resonator is derived invoking the Laplace and finite Fourier sine integral transforms. In order to arrive at the solutions for thermoelastic vibrations of thermal moment and deflection in the real space-time domain, inversion of the finite Fourier transform has been performed analytically whereas the inversion of the Laplace transform is carried out numerically using the method of Zakian. In order to illustrate the numerical estimates, a PTE material of Lead Zirconate Titanate (PZT-5A) is considered. The main outcome of this research is to highlight how without the piezoelectric effect, oscillation amplitude rises sharply at all time-scales but stabilizes over longer periods. Also, how a higher time-delay parameter can increase oscillation magnitude in thermal moment and deflection, has been focused. Also, how the non-locality of the beam can reduce thermal moment significantly, with minimal effect on deflection, is mentioned. A comparative study between piezoelectric material with the material in absence of piezoelectric effect has been reported.
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