Investigation of vibrations of plates with elastic and damping support

In this study, free vibrations of a thin plate supported by linear, torsion springs and damping elements along two edges and simple supports on the other edges are examined. Fourier sine series is applied in order to solve the differential equation. Fourier solution function is formed by superposition of Fourier sine series and minimum degree polynomial. In solution function, polynomial is used in order to prevent discontinuity problems. Solution functions are dependent on boundary conditions. Differential equation of plate with elastic and damping is solved by Galerkin principle and frequency and frequency parameters are obtained using the solution function. For damping plate the root values are found with regard to various damping values. The required coefficients are gained by setting initial values and the solution of damping free vibration of the plate is obtained.The existing method is evaluated concerning undamped conditions indicated in literature and the accuracy of the study is determined and presented. It is also introduced that solution functions of Fourier sine series are applied credibly to solutions of thin plates supported by elastic and damping. It is seen from the results that damping elements positioned on the edges of the plate can be also used to reduce plate vibrations.There are numerous studies on plates. It is observed that there are not adequate studies on the free vibration of plates with boundary damping. In this research, free vibration of plates with elastic and damping support is investigated. The classical Kirchhoff?s Plate Theory is applied.