Mindlin shear coefficient determination using model comparison

This paper derives an analytical expression of the shear coefficient in the Mindlin plate equation for a plate of infinite spatial extent subjected to forced excitation at definite frequency and wavenumber. The displacement transfer function derived from the Mindlin plate equation is set equal to the displacement transfer function derived from the Rayleigh–Lamb thick plate equation, and the result is a closed-form expression of the shear coefficient. A numerical example is included to illustrate the variation of the shear coefficient with respect to the system parameters. It is shown that the shear coefficient is extremely dependent on wavenumber and only slightly dependent on frequency. Shear coefficients derived in other work for free vibration are compared favorably to the values calculated by this new method at the wavenumber and frequency of the flexural wave response of the plate.