Vibration analysis of a transversely isotropic piezothermoelastic beam resonators under nonlocal strain gradient theory with DPL model

Abstract

The present work is an attempt to analyse the vibration responses of piezothermoelastic vibration and estimate the thermal deflection and thermal moment of a simply supported Euler–Bernoulli transversely isotropic microbeam resonators under the effect of nonlocal higher order strain gradient effects. Such a theory enables to capture the size-dependent behaviour of microbeams by using two length scale parameters, namely the nonlocal elastic parameter and the strain gradient parameter. The problem is formulated on the basis of the basic governing equations and constitutive relations for the piezothermoelastic material under this theory along with hyperbolic dual phase lag heat conduction model. By considering that the transversely isotropic beam is stress and strain free initially in the absence of external heat source along with the assumption that normal stress along the thickness is zero. We obtain the coupled governing equations for dimensionless thermal moment and deflection. Furthermore, using the Laplace transform along with the finite Fourier sine and inverse Fourier sine transforms, the closed-form expressions for thermal moment and thermal deflection are obtained. Numerical analysis on the basis of analytical results is carried out by taking the properties of piezoelectric lead zirconate titanate (PZT-5A) material. The influence of different factors and important observations have been highlighted to have a detailed understanding of the vibration responses of a transversely isotropic piezoelectric microbeam resonator under nonlocal higher-order strain gradient theory and hyperbolic dual phase lag heat conduction.