Calculation of free vibration of multistep shear plates

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 shea r plate can be divided into two independent sh:ar bars to determine the nat ural frequencies and mode shapes of the plate. The jkth natural frequency o f a !;hear plate is equal to the square root of the square sum of the jth n atural frequency of a shear bar and the I;th natural frequency of another s hear bar. The jkth mode shape of the shear plate is the product of the jth rr;ode 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 met hod - 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.