Abstract
A series solution for the transverse vibration of Mindlin rectangular plates with elastic point supports around the edges is studied. The series solution for the problem is obtained using improved Fourier series method, in which the vibration displacements and the cross-sectional rotations of the midplane are represented by a double Fourier cosine series and four supplementary functions. The supplementary functions are expressed as the combination of trigonometric functions and a single cosine series expansion and are introduced to remove the potential discontinuities associated with the original admissible functions along the edges when they are viewed as periodic functions defined over the entirex-yplane. This series solution is approximately accurate in the sense that it explicitly satisfies, to any specified accuracy, both the governing equations and the boundary conditions. The convergence, accuracy, stability, and efficiency of the proposed method have been examined through a series of numerical examples. Some numerical examples about the nondimensional frequency and mode shapes of Mindlin rectangular plates with different point-supported edge conditions are given.
Highlights
Rectangular plate is of great importance in various engineering branches, such as aerospace, electronics, and mechanical, nuclear, and marine engineering
Few literatures focused on the vibration behavior of Mindlin plates with elastic point supports around the edges
It is much of great significance to study the vibration behavior of Mindlin plates with elastic point supports around the edges
Summary
Rectangular plate is of great importance in various engineering branches, such as aerospace, electronics, and mechanical, nuclear, and marine engineering. Ohya et al [3] investigated the free vibration characteristics of rectangular Mindlin plates which have simultaneous elastic edge and internal supports via the superposition method. Wu and Lu [23] studied the free vibration of rectangular plates with internal columns and elastic edge supports using the powerful pb-2 Ritz method. To the best of the authors’ knowledge, there are no published literatures focused on vibration characteristics of Mindlin plates with point supports around the edges by the method of modified Fourier. A unified, efficient, and accurate formulation to deal with the free vibration of Mindlin plates subjected to arbitrary point-supported boundary condition is necessary and much of great significance. A modified Fourier solution for the free vibration of Mindlin rectangular plates with elastic point supports around the edges is proposed. Some numerical examples of free vibration for Mindlin rectangular plates with different aspect ratio and thickness are conducted under different point-supported conditions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
