Abstract
The governing differential equations for free vibration of a one-step shear plate and a multistep shear plate are established. It is shown that a shear plate can be divided into two independent shear bars to determine the natural frequencies and mode shapes of the plate. The jkth natural frequency of a shear plate is equal to the square root of the square sum of the jth natural frequency of a shear bar and the kth natural frequency of another shear bar. The jkth mode shape of the shear plate is the product of the jth mode shape of a shear bar and the kth mode shape of another shear bar. In this paper, two methods—transfer matrix method and recurrence formula method—are proposed to determine the natural frequencies and mode shapes of multistep shear plates. A numerical example shows that the present methods are easy to implement and are efficient.
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