Modeling and mathematical approach for mechanical natural frequencies of structural plates with free edges

Abstract

The current study aims to demonstrate an easy mathematical procedure and simple to be used by engineers to maintain the mechanical natural frequencies (Eigen values of free vibration) of thin rectangular structural plates with free edges included in boundary conditions. The reason for this easiness and simplicity is that new method of analysis depends mainly on using mechanical minimum energy concept represented in the Rayleigh–Ritz method with appropriate real polynomials as admissible functions. The new procedure guides these functions to satisfy the boundary conditions at the middle points on the free edges of the plate beside the nodal points of the vibration modes along each edge direction. Therefore, there are no complicated or imaginary terms in the developed functions while they lead to surprisingly acceptable and even accurate results when compared with other works and Ansys program models.