Acta Mechanica Solida Sinica

, Volume 22, Issue 2, pp 125–136

Characteristic equations and closed-form solutions for free vibrations of rectangular Mindlin plates

• Yufeng Xing
• Bo Liu
Article

Abstract

The direct separation of variables is used to obtain the closed-form solutions for the free vibrations of rectangular Mindlin plates. Three different characteristic equations are derived by using three different methods. It is found that the deflection can be expressed by means of the four characteristic roots and the two rotations should be expressed by all the six characteristic roots, which is the particularity of Mindlin plate theory. And the closed-form solutions, which satisfy two of the three governing equations and all boundary conditions and are accurate for rectangular plates with moderate thickness, are derived for any combinations of simply supported and clamped edges. The free edges can also be dealt with if the other pair of opposite edges is simply supported. The present results agree well with results published previously by other methods for different aspect ratios and relative thickness.

Key words

Mindlin plate free vibration closed-form solution separation of variables

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© The Chinese Society of Theoretical and Applied Mechanics and Technology 2009

Authors and Affiliations

1. 1.The Solid Mechanics Research CenterBeijing University of Aeronautics and AstronauticBeijingChina