Vibrational power flow models for transversely vibrating finite Mindlin plate

In this paper, power flow models were developed to analyze transversely vibrating finite Mindlin plate considering the effects of shear distortion and rotatory inertia, which are very important at high frequencies. The energy governing equations for far-field propagating out-of-plane waves in the Mindlin plate were newly derived by using the classical displacement solutions for out-of-plane motions in the Mindlin plate. The derived energy governing equations are composed of the energetics of three kinds of far-field propagating waves. Below the critical frequency, the energy governing equation for only one kind of far-field propagating wave, which is analogous to that for flexural wave in the Kirchhoff plate, is obtained. On the other hand, above the critical frequency, the energy governing equations for all three kinds of far-field propagating waves are derived. The developed power flow models are in the general forms incorporating not only the Mindlin plate theory but also the Kirchhoff plate theory. To verify the validity and accuracy of the derived models, numerical analyses are performed for the case where the finite Mindlin plates are excited by a harmonic point force, and the spatial distributions and levels of energy density and intensity obtained by the developed power flow solutions for the Mindlin plate are compared with those obtained by the classical displacement solutions for the Mindlin plate, the traditional power flow solutions, and the classical displacement solutions for the Kirchhoff plate for various excitation frequencies and hysteretic damping factors.