Vibration of viscoelastic plates under transverse load by the method of constant deflection contours

A method is developed for determining the behaviour of arbitrarily shaped plates of viscoelastic material under transverse load, which vibrate in normal modes. The method is based upon the concept of contour lines of equal deflection on the surface of the plate. It is shown that a viscoelastic plate will vibrate in the same normal modes as an elastic plate of the same shape and with the same boundary conditions, and that the time behaviour can be found by using the frequency of free vibration of the associated elastic plate. As an illustration of the technique, the solution for the previously unsolved problem of a clamped vibrating elliptic plate of Kelvin material is found, and some numerical results are given. It is shown that the technique is applicable to any panel of viscoelastic material of arbitrary shape with clamped or simply supported boundary condition.