Damping in micro-scale generalized thermoelastic circular plate resonators

The out-of-plane vibrations of a generalized thermoelastic circular plate are studied under different environmental temperature, plate dimensions and boundary conditions. The analytical expressions for thermoelastic damping of vibration and phase velocity of circumferential surface wave modes are obtained. It is noticed that the damping of vibrations and phase velocities of circumferential surface wave modes significantly depend on thermal relaxation time in addition to thermoelastic coupling in circular plates under resonance conditions. The surface conditions also impose significant effects on the vibrations of such resonators. The expressions for displacement and temperature fields in the plate resonator are also derived and obtained. Some numerical results have also been presented for illustration purpose in case of silicon material plate.

Research highlights
► Maximum value of damping increases and critical thickness decreases due to thermal relaxation.
► Critical thickness decreases by 29.3% in non-Fourier plates as compared to Fourier one.
► Phase velocity of surface waves increases in circumferential direction due to thermal relaxation and sequence of modes.
► Critical thickness increases with thermal diffusivity but decreases with temperature.
► The surface wave velocity is higher in clamped non-Fourier plates than Fourier one in contrast to simply supported.