Thermoelastic damping in piezothermoelastic nanobeam resonators under the strain gradient theory with micro-inertia and non-fourier heat conduction

Thermoelastic damping (TED) is a primary source of energy dissipation in oscillating structures. The classical TED model is inadequate for micro- and nanoscale structures due to small-scale effects. In this paper, TED in transversely isotropic piezoelectric micro- and nanobeams is investigated using the Lord-Shulman heat conduction model and the Mindlin Form II strain gradient theory of elasticity with the micro-inertia effect. To account for small-scale effects, the Helmholtz free energy density is defined as a function of the strain tensor, strain gradient tensor, electric field vector, and temperature field, considering these parameters as independent state variables. The kinetic energy depends on both the velocity vector and the velocity gradient tensor. As an illustrative example, the free vibration of simply supported piezothermoelastic Euler-Bernoulli beams with isothermal boundary conditions is analyzed. The governing equations and boundary conditions are derived using a variational formulation. The results are compared with those obtained from the classical TED model. The influence of beam thickness, thermal relaxation time, vibration mode number, initial temperature, and micro-stiffness and micro-inertia length-scale coefficients on the TED in piezoelectric microbeam resonators is discussed. This study is of practical significance for the design of high-efficiency thermoelastic devices and systems.