On the use of the Trigonometric Ritz method for general vibration analysis of rectangular Kirchhoff plates

A comprehensive study on the use of a set of trigonometric functions, originally proposed by Beslin and Nicolas [Journal of Sound and Vibration 1997;202:633–55], as admissible solutions in the Ritz method for general vibration analysis of rectangular orthotropic Kirchhoff plates is presented. The approach is denoted here as Trigonometric Ritz method (TRM). Since its introduction, application of TRM was limited to a very few plate problems. The aim of this work is to extend the potential of the method on predicting natural flexural frequencies of plates with various complicating factors, including in-plane loads, elastically restrained edges, rigid/elastic concentrated masses, intermediate line and point supports or their combinations. Computational efficiency, stability, convergence and accuracy of the method are discussed and supported by extensive analysis. TRM-based solutions are compared with many reference cases available in the literature obtained with other methods or Ritz functions. Numerical results indicate that TRM exhibits good to excellent accuracy for all cases considered. New solutions are also presented for future comparison purpose.