scholarly journals Restoration of boundary conditions at the edges of a rectangular plate for given frequencies of spectrum with an inertial element at the edges

2018 ◽  
Vol 71 (2) ◽  
pp. 18-27
Author(s):  
M.H. Arabyan ◽  
Z.B. Hovhannisyan
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Inertial Element

A Levy-Type Solution for a Rectangular Plate of Variable Thickness

1958 ◽  
Vol 25 (2) ◽  
pp. 297-298
Author(s):  
H. D. Conway
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Variable Thickness ◽  
Thickness Variation ◽  
Type Solution ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Arbitrary Boundary Conditions ◽  
Plate Of Variable Thickness

Abstract A solution is given for the bending of a uniformly loaded rectangular plate, simply supported on two opposite edges and having arbitrary boundary conditions on the others. The thickness variation is taken as exponential in order to make the solution tractable, and thus closely approximates to uniform taper if the latter is small.

scholarly journals Frequency Domain Spectral Element Model for the Vibration Analysis of a Thin Plate with Arbitrary Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Ilwook Park ◽  
Taehyun Kim ◽  
Usik Lee
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Element Model ◽  
Spectral Element ◽  
Plate Element ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Plate Elements ◽  
Rectangular Plate Element

We propose a new spectral element model for finite rectangular plate elements with arbitrary boundary conditions. The new spectral element model is developed by modifying the boundary splitting method used in our previous study so that the four corner nodes of a finite rectangular plate element become active. Thus, the new spectral element model can be applied to any finite rectangular plate element with arbitrary boundary conditions, while the spectral element model introduced in the our previous study is valid only for finite rectangular plate elements with four fixed corner nodes. The new spectral element model can be used as a generic finite element model because it can be assembled in any plate direction. The accuracy and computational efficiency of the new spectral element model are validated by a comparison with exact solutions, solutions obtained by the standard finite element method, and solutions from the commercial finite element analysis package ANSYS.

Static Stability Behaviour of Plate Elements with Non-Uniform, in-Plane Stress Distribution

1979 ◽  
Vol 21 (5) ◽  
pp. 363-365
Author(s):  
P. K. Datta
Keyword(s):  
Stress Distribution ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Plane Stress ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Static Stability ◽  
Buckling Loads ◽  
Plate Elements ◽  
Edge Loading

The results of analytically and experimentally determined buckling loads of a rectangular plate, subjected to partial edge loading and mixed boundary conditions, are presented.

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.

Dynamics of Initially Stressed Plates

1976 ◽  
Vol 43 (2) ◽  
pp. 304-308 ◽  
Author(s):  
H. Reismann ◽  
Z. A. Tendorf
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Stable State ◽  
Time Dependent ◽  
Membrane Stress ◽  
Simply Supported

A formalism is presented for the solution of supported plates of bounded extent, subjected to time-dependent transverse forces and boundary conditions. Initially, and during the course of the motion, the plate is assumed to be in an arbitrary (stable) state of membrane stress. An example of a suddenly loaded, simply supported rectangular plate is presented. The membrane prestress, in the example problem, is assumed to be constant and parallel to two opposite edges of the plate.

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