Santwana Mukhopadhyay’s research while affiliated with Indian Institute of Technology BHU and other places

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.

The present work introduces a theoretical framework according to the Moore–Gibson–Thompson (MGT) heat conduction-based generalized thermoelasticity theory by using the Eringen’s nonlocal elasticity theory to analyze the reflection and propagation of plane waves in a homogeneous, isotropic biological tissue medium. The scalar and vector potential functions of displacement vector in the form of Helmholtz decomposition are adopted here. Three basic types of waves consisting of two dispersive attenuated coupled longitudinal waves and one uncoupled transverse shear wave are identified. Attempt is made to solve the dispersion relation equations to derive the expressions for propagation speeds and attenuation coefficients of plane waves analytically. Detailed analysis on wave characteristics is made by studying the problem under MGT theory along with three other generalized thermoelasticity theories, namely LS, GN-III, and TPL theories. Propagation speeds and attenuation coefficients of all three types of waves are shown to be affected by the working angular frequency under MGT, LS, GN-III, and TPL model of thermoelasticity with nonlocal elasticity theory. Furthermore, reflection of waves for incident longitudinal and incident transverse wave is investigated by finding the reflection coefficients. An analysis and visual investigation are conducted on the wave characteristics of the propagating plane waves with respect to the employed angular frequency, thermal boundaries, and characteristics of incident waves. An in-depth comparative analysis is also presented for various results under MGT, LS, GN-III, and TPL theories.

The current work investigates the transverse vibration of a piezothermoelastic (PTE) nanobeam in the frame of dual-phase-lag thermoelasticity theory. Closed-form analytical expression for the thermoelastic damping (TED) in terms of quality factor for a homogeneous transversely isotropic PTE beam is derived by using Euler–Bernoulli beam theory and complex frequency approach. The size effect of the nanostructured beam is tackled by applying modified couple stress theory (MCST). Detailed analysis on damping of vibration owing to thermal fluctuations and electric potential in the present context under three sets of boundary conditions is attempted to investigate the influences of two-phase-lag parameters, piezoelectric parameter, thermal effect and size-dependent behaviour on energy dissipation caused by TED in PTE beam resonators. Analytical results are illustrated with the help of graphical plots on numerical findings for lead zirconate titanate (PZT-5A) PTE material. The investigation brings out some significant key findings and observations in view of the present heat conduction model.

The present work investigates the vibration of a piezothermoelastic nanobeam in the frame of Moore–Gibson– Thompson (MGT) thermoelasticity theory. Closed form analytical expressions for the thermoelastic damping in terms of quality factor and frequency shift for a homogeneous transversely isotropic piezothermoelastic (PTE) beam is derived by using Euler–Bernoulli beam theory and complex frequency approach. Detailed analysis of damping of vibration owing to thermal fluctuations and electric potential in the present context under three sets of boundary conditions is attempted to investigate the influence of modes of vibration, electric potential, and beam length on energy dissipation caused by thermoelastic damping in PTE beam resonators. Analytical results are illustrated with the help of graphical plots on numerical findings in the case of the nanobeam resonator of Lead Zirconate Titanate (PZT-5A) material. The investigation brings out some significant key findings and observations in view of MGT heat conduction model.

The current work attempts to look at the consequence of the external supply of heat source which has an effect of thermal radiation towards the surrounding in accordance with the linearized form of Stefan–Boltzmann law (SBL) on the propagation of waves within a thermoelastic medium. Formulation of the problem is accomplished by considering the recent thermoelasticity theory based on the Moore–Gibson–Thompson (MGT) heat conduction equation. Here, a deformable thermal conductor, particularly a long, thin, and solid rod of thermoelastic material, is considered to study the behavior of the suggested theory in detail. After formulation of the problem and employing the Laplace transform technique, the solutions for the displacement, temperature, and stress fields in the Laplace transform domain are obtained. Further, the analytical solutions for all the field variables in the case of short-time approximation are derived by incorporating Laplace inversion. The investigation concentrates on certain key findings and observations under this model and compares them to those predicted by previously proposed models in this direction.