Exact compact characteristic equations and new results for free vibrations of orthotropic rectangular Mindlin plates

This paper presents correct results for a paper by Liu and Xing (2011) [1] that had errors, greatly simplifies its formulations, overcomes its numerical stability problem, and provides some new results. In their early paper, Liu and Xing obtained exact closed-form solutions for free vibrations of orthotropic rectangular Mindlin plates by using the separation of variables method. The equations presented therein are correct, but the numerical values of the frequencies listed have some errors because the shear rigidities of the three-ply laminates were not correctly computed. In addition, the exact characteristic equations of the early paper can also be greatly simplified and the compact equations are presented herein. The characteristic equations in the early paper may have computational stability problem when plates become very thin. This paper overcome such computational difficulty. Some new exact frequency parameters are also included in this work.