scholarly journals Effect of Various Edge Conditions on Free-Vibration Characteristics of Isotropic Square and Rectangular Plates

2018 ◽  
Author(s):  
Muzamal Hussain ◽  
Muhammad Nawaz Naeem
Keyword(s):  
Free Vibration ◽  
Vibration Characteristics ◽  
Rectangular Plates ◽  
Edge Conditions

Combinations for the Free Vibration Behaviors of Anisotropic Rectangular Plates Under General Edge Conditions

1999 ◽  
Author(s):  
Yoshihiro Narita
Keyword(s):  
Free Vibration ◽  
Structural Design ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Technical Information ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Plate Models ◽  
Edge Conditions ◽  
Anisotropic Rectangular Plates

Abstract The free vibration behavior of rectangular plates provides important technical information in structural design, and the natural frequencies are primarily affected by the boundary conditions as well as aspect and thickness ratios. One of the three classical edge conditions, i.e., free, simple supported and clamped edges, may be used to model the constraint along an edge of the rectangle. Along the entire boundary with four edges, there exist a wide variety of combinations in the edge conditions, each yielding different natural frequencies and mode shapes. For counting the total number of possible combinations, the present paper introduces the Polya counting theory in combinatorial mathematics, and formulas are derived for counting the exact numbers. A modified Ritz method is then developed to calculate natural frequencies of anisotropic rectangular plates under any combination of the three edge conditions and is used to numerically verify the numbers. In numerical experiments, the number of combinations in the free vibration behaviors is determined for some plate models by using the derived formulas, and are corroborated by counting the numbers of different sets of the natural frequencies that are obtained from the Ritz method.

An exact solution for free vibration of thin functionally graded rectangular plates

2010 ◽  
Vol 225 (3) ◽  
pp. 526-536 ◽  
Author(s):  
A Hasani Baferani ◽  
A R Saidi ◽  
E Jomehzadeh
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Different Boundary Conditions

The aim of this article is to find an exact analytical solution for free vibration characteristics of thin functionally graded rectangular plates with different boundary conditions. The governing equations of motion are obtained based on the classical plate theory. Using an analytical method, three partial differential equations of motion are reformulated into two new decoupled equations. Based on the Navier solution, a closed-form solution is presented for natural frequencies of functionally graded simply supported rectangular plates. Then, considering Levy-type solution, natural frequencies of functionally graded plates are presented for various boundary conditions. Three mode shapes of a functionally graded rectangular plate are also presented for different boundary conditions. In addition, the effects of aspect ratio, thickness—length ratio, power law index, and boundary conditions on the vibration characteristics of functionally graded rectangular plates are discussed in details. Finally, it has been shown that the effects of in-plane displacements on natural frequencies of functionally graded plates under different boundary conditions have been studied.

Combinations for the Free-Vibration Behaviors of Anisotropic Rectangular Plates Under General Edge Conditions

1999 ◽  
Vol 67 (3) ◽  
pp. 568-573 ◽  
Author(s):  
Y. Narita
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Ritz Method ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Vibration Behavior ◽  
Edge Conditions ◽  
Important Field ◽  
Anisotropic Rectangular Plates

The free-vibration behavior of rectangular plates constitutes an important field in applied mechanics, and the natural frequencies are known to be primarily affected by the boundary conditions as well as aspect and thickness ratios. Any one of the three classical edge conditions, i.e., free, simply supported, and clamped edges, may be used to model the constraint along an edge of the rectangle. Along the entire boundary with four edges, there exist a wide variety of combinations in the edge conditions, each yielding different natural frequencies and mode shapes. For counting the total number of possible combinations the present paper introduces the Polya counting theory in combinatorial mathematics. Formulas are derived for counting the exact numbers. A modified Ritz method is then developed to calculate natural frequencies of anisotropic rectangular plates under any combination of the three classical edge conditions and is used to numerically verify the numbers. In this numerical study the number of combinations in the free-vibration behavior is determined for some plate models by using the derived formulas. Results are corroborated by counting the numbers of different sets of the natural frequencies that are obtained from the modified Ritz method. [S0021-8936(00)02203-0]

Free-Vibration Analysis of Rectangular Plates With Clamped-Simply Supported Edge Conditions by the Method of Superposition

1977 ◽  
Vol 44 (4) ◽  
pp. 743-749 ◽  
Author(s):  
D. J. Gorman
Keyword(s):  
Differential Equation ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Formidable Challenge ◽  
Edge Conditions ◽  
Governing Differential Equation

In this paper attention is focused on the free-vibration analysis of rectangular plates with combinations of clamped and simply supported edge conditions. Plates with at least two opposite edges simply supported are not considered as they have been analyzed in a separate paper. It is well known that the family of problems considered here have presented researchers with a formidable challenge over the years. This is because they are not directly amenable to Le´vy-type solutions. It has been pointed out in the literature that most of the existing solutions are approximate in that they either do not satisfy exactly the governing differential equation or the boundary conditions, or both. In a new approach taken by the author the method of superposition is exploited for handling these dynamic problems. It is found that solutions of any degree of exactitude are easily obtained. The governing differential equation is completely satisfied and the boundary conditions are satisfied to any degree of exactitude by merely increasing the number of terms in the series. Convergence is shown to be remarkably rapid and tabulated results are provided for a large range of parameters. The immediate applicability of the method to problems involving elastic restraint or inertia forces along the plate edges has been discussed in an earlier publication.

The Effect of Thermal Prestress on the Free Vibration Characteristics of Clamped Rectangular Plates: Theory and Experiment

1997 ◽  
Vol 119 (2) ◽  
pp. 243-249 ◽  
Author(s):  
K. D. Murphy ◽  
L. N. Virgin ◽  
S. A. Rizzi
Keyword(s):  
Free Vibration ◽  
Experimental Approach ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Rectangular Plates ◽  
Modal Coupling ◽  
Out Of Plane ◽  
Post Buckling ◽  
Initial Geometric Imperfections ◽  
Theory And Experiment

In a combined theoretical and experimental approach, the free vibration characteristics of a uniformly heated, fully clamped (out-of-plane), rectangular plate are considered. Specifically, this work focuses on the behavior of the small amplitude natural frequencies as the temperature is increased from the ambient. The effects of initial geometric imperfections, modal coupling, imperfect clamping (in-plane) and post-buckling are addressed. Comparisons between theory and experiment show excellent agreement.

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