Vibratory characteristics of multistep nonuniform orthotropic shear plates with line spring supports and line masses.

TLDR: It is proved that it is possible to separate a shear plate as two independent shear beams for free-vibration analysis and the function for describing the distribution of mass of each step plate can be selected as an arbitrary one.

Abstract: A new exact approach for free-vibration analysis of multistep nonuniform orthotropic shear plates with line spring supports and line masses is presented. The governing differential equation for free vibrations of an orthotropic shear plate with variably distributed mass and stiffness is established. It is proved that it is possible to separate a shear plate as two independent shear beams for free-vibration analysis. 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 beam and the kth natural frequency of another shear beam. The jkth mode shape of the shear plate is the product of the jth mode shape of a shear beam and the kth mode shape of another shear beam. In this paper, the function for describing the distribution of mass of each step plate can be selected as an arbitrary one, and the distribution of shear stiffness is expressed as a functional relation with the mass distribution, and vice versa. The exact solutions of one-step shear plates with varying cross section are obtained first for eight cases. Then, the derived exact solutions are used to establish the frequency equation of a multistep nonuniform orthotropic shear plate with spring supports and line masses using the transfer matrix method and the recurrence method developed in this paper. The numerical example shows that the calculated results are in good agreement with the experimental data, and the proposed procedure is an exact and efficient method.