Free vibration analysis of a thin rectangular plate with multiple circular and rectangular cut-outs

2017 ◽  
Vol 31 (11) ◽  
pp. 5185-5202 ◽  
Author(s):  
Anjibabu Merneedi ◽  
Mohan RaoNalluri ◽  
V. V. Subba Rao
Keyword(s):  
Free Vibration ◽  
Rectangular Plate ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Rectangular Plate

Free Vibration Analysis for Disconnected Thin Rectangular Plate with Four Free Edges on Nonlinear Elastic Foundation

2011 ◽  
Vol 52-54 ◽  
pp. 1309-1314 ◽  
Author(s):  
Yong Gang Xiao ◽  
Cui Ping Yang
Keyword(s):  
Free Vibration ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Vibration Analysis ◽  
Harmonic Balance Method ◽  
Free Vibration Analysis ◽  
Variation Principle ◽  
Thin Rectangular Plate ◽  
Nonlinear Elastic Foundation ◽  
Nonlinear Elastic

In this paper, the free vibration analysis of thin rectangular plate with dowels on nonlinear elastic foundation is investigated. The load transfer on dowels is modeled as vertical springs, whose stiffness depends on the dowel properties and the dowel-plate interaction. Based on Hamilton variation principle, the nonlinear governing equations of thin rectangular plate with discontinuities on nonlinear elastic foundation are established, and the suitable expressions of trial functions satisfying all boundary conditions are proposed. Then, the equations are solved by using Galerkin method and harmonic balance method. The numerical simulation reveals the effects of the dowel parameters and the other ones of the system on free vibration behaves of the disconnected thin rectangular plate.

Free vibration analysis of a rectangular plate carrying multiple various concentrated elements

2003 ◽  
Vol 217 (2) ◽  
pp. 171-183 ◽  
Author(s):  
J-S Wu ◽  
H-M Chou ◽  
D-W Chen
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Normal Mode ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Equation Of Motion ◽  
Mode Shapes

The dynamic characteristic of a uniform rectangular plate with four boundary conditions and carrying three kinds of multiple concentrated element (rigidly attached point masses, linear springs and elastically mounted point masses) was investigated. Firstly, the closed-form solutions for the natural frequencies and the corresponding normal mode shapes of a rectangular ‘bare’ (or ‘unconstrained’) plate (without any attachments) with the specified boundary conditions were determined analytically. Next, by using these natural frequencies and normal mode shapes incorporated with the expansion theory, the equation of motion of the ‘constrained’ plate (carrying the three kinds of multiple concentrated element) were derived. Finally, numerical methods were used to solve this equation of motion to give the natural frequencies and mode shapes of the ‘constrained’ plate. To confirm the reliability of previous free vibration analysis results, a finite element analysis was also conducted. It was found that the results obtained from the above-mentioned two approaches were in good agreement. Compared with the conventional finite element method (FEM), the approach employed in this paper has the advantages of saving computing time and achieving better accuracy, as can be seen from the existing literature.

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