Determination of the steady state response of viscoelastically corner point-supported rectangular orthotropic plates

Vibration of orthotropic rectangular plates having viscoelastic point supports at the corners is analyzed. The Lagrange’s equations is used to examine the free vibration characteristics and steady state response to a sinusoidally varying force affecting at the center of a viscoelastically point-supported orthotropic elastic plate of rectangular shape. In the study, for applying the Lagrange’s equations, the trial function denoting the deflection of the plate is expressed in the polynomial form: This procedure may be considered as the classical Rayleigh–Ritz method. By using the Lagrange’s equations, the problem is reduced to the solution of a system of algebraic equations. The influence of the mechanical properties, and of the damping of the supports to the mode shapes and to the steady state response of the viscoelastically point-supported rectangular plates is investigated numerically for the concentrated load at center for various values of the mechanical properties characterizing the anisotropy of the plate material and for various damping and stiffness of the supports. The results are given for the frequencies and mode shapes of the first three symmetrical modes. Convergence studies are made. The validity of the obtained results is demonstrated by comparing them with other solutions based on the Kirchhoff–Love plate theory.