Phase-lagging of the thermoelastic dissipation for a tubular shell model

Abstract

In this work, the thermoelastic damping (TED) effect with the time-lagging is evaluated on the micro- or nano-cylindrical shell. Especially, the mechanism should be considered for the high-frequency ranges in the ultra-low temperature. And thus, the phenomenon can compensate the time-delay of the heat conduction based on the finite speed of heat flux. To develop the mathematical model for the analysis, Love's thin shell theory is basically adopted to derive the equations of motion including the mechanism. Then, the heat conduction equation is considered using the Cattaneo–Vernotte's (CV) theory. To simplify the shell model, an assumption is introduced for transverse-deflection-dominated motion based on Donnel–Mushtari–Valsov (DMV) approximation. Also, the temperature profile is obtained by the dilatation strain and heat conduction equation. Thus, the complex eigenfrequency of the shell including the TED effect is finally obtained using the boundary conditions of the adiabatic surfaces and transverse vibration mode shape. Numerical results are verified with the previous work, and the trends of quality factors (Q-factors) according to the mode numbers and geometrical shapes are shown as in the graphical data.