Abstract
The non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, became the most significant effects in the nano-scale beam. In the present study, a generalized solution for the generalized thermoelastic vibration of a bounded nano-beam resonator induced by ramp type of heating is developed and the solutions take into account the above two effects. The Laplace transforms and direct method are used to determine the lateral vibration, the temperature, the displacement, the stress and the energy of the beam. The effects of the relaxation time and the ramping time parameters have been studied with some comparisons.
Highlights
A generalized solution for the generalized thermoelastic vibration of a bounded nano-beam resonator induced by ramp type of heating is developed and the solutions take into account the above two effects
The generalized thermoelasticity theories have been developed with the aim of removing the paradox of infinite speed of heat propagation inherent in the classical dynamical coupled thermoelasticity theory (Biot-CTE) [1], Lord and Shulman (L-S) [2] obtained a wave-type heat equation by postulating a new law of heat conduction to replace the classical Fourier’s law
The original time t and the ramping time parameter t0 will be considered in the picoseconds (1−100) ×10−12 sec and the relaxation time τ0 in the range (1−100) ×10−14 sec
Summary
The generalized thermoelasticity theories have been developed with the aim of removing the paradox of infinite speed of heat propagation inherent in the classical dynamical coupled thermoelasticity theory (Biot-CTE) [1], Lord and Shulman (L-S) [2] obtained a wave-type heat equation by postulating a new law of heat conduction to replace the classical Fourier’s law. Manolis and Beskos [6] examined the thermally induced vibration of structures consisting of beams, exposed to rapid surface heating They have studied the effects of damping and axial loads on the structural response. Ai Kah Soh et al studied the vibration of micro/nanoscale beam resonators induced by ultra-short-pulsed laser by considering the thermoelastic coupling term in [8,9]. The sudden jump of the load is merely an idealized situation because it is impossible to realize a pulse described mathematically by a step function; even very rapid rise-time (of the order of 10–9 s) may be slow in terms of the continuum This is true in the case of second sound effects when the thermal relaxation times for typical metals are less than 10–9 s [14]. The effects of the relaxation time and the ramping time parameters will be studied and represented graphically
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