Closed form solutions for free vibrations of rectangular Mindlin plates

<正> A new two-eigenfunctions theory, using theamplitude deflection and the generalized curvature as twofundamental eigenfunctions, is proposed for the freevibration solutions of a rectangular Mindlin plate. The threeclassical eigenvalue differential equations of a Mindlin plateare reformulated to arrive at two new eigenvalue differentialequations for the proposed theory. The closed form eigen-solutions,which are solved from the two differential equationsby means of the method of separation of variables areidentical with those via Kirchhoff plate theory for thin plate,and can be employed to predict frequencies for any combinationsof simply supported and clamped edge conditions.The free edges can also be dealt with if the other pair ofopposite edges are simply supported. Some of the solutionswere not available before. The frequency parameters agreeclosely with the available ones through pb-2 Rayleigh-Ritzmethod for different aspect ratios and relative thickness ofplate.