Damping in microscale modified couple stress thermoelastic circular Kirchhoff plate resonators

The vibrations of circular plate in modified couple stress thermoelastic medium using Kirchhoff- Love plate theory has been presented. The basic equations of motion and heat conduction equation for Lord Shulman (L-S, 1967) theory are written with the help of Kirchhoff-Love plate theory. The thermoelastic damping of micro beam resonators is studied by applying normal mode analysis method. The solutions for the free vibrations of plates under clamped, simply supported and free boundary conditions are obtained. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for generalized couple stress thermoelastic and coupled thermoelastic plates. Numerical results with the help of MATLAB programming software in case of silicon material has been presented. A computer algorithm has been constructed to obtain the numerical results. The thermoelastic damping and frequency shift with varying values of length and thickness for clamped, simply supported and free boundary conditions in the absence and presence of couple stress are presented graphically. Comparisons are made with different modes of vibrations and also with and without couple stress parameter. Some special cases are obtained in the present problem. The thermoelastic damping have many applications in (sensors) resonators in detecting Infrared (IR) and imaging in addition to chemical and biological agent sensing and their temperature dependence in design/construction of precision thermometers and communications