This paper presents the degenerate modes and modal coupling in vibrating rectangular plates with the same boundary conditions along four edges.The spline element method is applied to analyze frequencies and mode shapes of orthotropic rectangular plates with tapered thickness.Some of degenerate mode pairs are split in frequency in vibration of isotropic square plates with the four edges clamped, free or simply supported,respectively . And nondegenerate modes such as X mode or ring mode can occur in tapered square plates and orthotropic rectangular plates having certain width/thickness ratio and aspect ratio.
Free vibration of orthotropic thick plates using the spline element method based on high-order shear deformation theory Harunobu NAGINO, Tomisaku MIZUSAWA, Takashi MIKAMI This paper presents free vibration of orthotropic thick plates using the spline element method based on the Reddy's shear deformation theory. The orthotropic plates are made of Aragonite crystal and wood (sitka spruce). To demonstrate the convergence and accuracy of the present method, several examples are solved, and results are compared with those obtained by other numerical methods based on the theory of elasticity, high-order shear deformation plate theory and Mindlin plate theory. Good convergence and accuracy are obtained. The effects of thickness/width ratio, shear elastic modulus ratio and elastic modulus ratio on frequency parameters of orthotropic thick plates are investigated. Lastly, the applicable limitation of the Reddy's shear deformation theory for strong orthotropic plates is also shown.
This paper presents dynamic responses of rectangular Mindlin plates under the action of impulse uniform load or concentrated load using the BF-spline Ritz method and modal analysis method. The BF-spline Ritz method is used for space domain and the mode superposition method is used for time domain. To demonstrate the accuracy of the present method, several examples are solved, and results are compared with those obtained by analytical methods. Excellent accuracy is obtained by the present method. The effects of width to thickness ratio, dwell time and impulse function on dynamic responses and dynamic amplitude factors of rectangular Mindlin plates are investigated..
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