Relationship Between Vibration Frequencies of Reddy and Kirchhoff Polygonal Plates With Simply Supported Edges

1997 ◽  
Vol 122 (1) ◽  
pp. 77-81 ◽  
Author(s):  
C. M. Wang ◽  
S. Kitipornchai ◽  
J. N. Reddy
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Kirchhoff Plate ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Third Order ◽  
Simply Supported ◽  
Kirchhoff Plate Theory ◽  
The Relationship ◽  
Exact Relationship

This paper presents an exact relationship between the natural frequencies of Reddy third-order plate theory and those of classical Kirchhoff plate theory for simply supported, polygonal isotropic plates, including rectangular plates. The relationship for the natural frequencies enables one to obtain the solutions of the third-order plate theory from the known Kirchhoff plate theory for the same problem. As examples, some vibration frequencies for rectangular and regular polygonal plates are determined using this relationship. [S0739-3717(00)01601-9]

BUCKLING AND VIBRATION OF STEPPED, SYMMETRIC CROSS-PLY LAMINATED RECTANGULAR PLATES

2001 ◽  
Vol 01 (03) ◽  
pp. 385-408 ◽  
Author(s):  
Y. XIANG ◽  
J. N. REDDY
Keyword(s):  
Solution Method ◽  
Natural Frequencies ◽  
Laminated Plates ◽  
The Other ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Buckling Loads ◽  
Simply Supported ◽  
Step Thickness ◽  
Thickness Variations

This paper presents the exact buckling loads and vibration frequencies of multi-stepped symmetric cross-ply laminated rectangular plates having two opposite edges simply supported while the other two edges may have any combination of free, simply supported, and clamped conditions. An analytical method that uses the Lévy solution method and the domain decomposition technique is proposed to determine the buckling loads and natural frequencies of stepped laminated plates. Buckling and vibration solutions are obtained for symmetric cross-ply laminated rectangular plates having two-, three- and four-step thickness variations.

Natural Frequencies Formula for Simply Supported Mindlin Plates

1994 ◽  
Vol 116 (4) ◽  
pp. 536-540 ◽  
Author(s):  
C. M. Wang
Keyword(s):  
Exact Solutions ◽  
Explicit Formula ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Kirchhoff Plate ◽  
Vibration Frequencies ◽  
Simply Supported ◽  
Plate Shape

This paper presents an explicit formula for the vibration frequencies of simply supported Mindlin plates in terms of the corresponding thin (Kirchhoff) plate frequencies. The formula has been obtained from an exact vibration analysis of simply supported rectangular Mindlin plates. When the formula was applied to other simply supported plate shapes such as skew plates, circular and annular sectorial plates, it was found to give almost exact solutions. It appears that the formula can be used to predict the frequencies accurately for any simply supported plate shape and thus should be valuable to designers as Mindlin vibration solutions are scarce.

BUCKLING AND VIBRATION OF ORTHOTROPIC PLATES WITH AN INTERNAL LINE HINGE

2002 ◽  
Vol 02 (04) ◽  
pp. 457-486 ◽  
Author(s):  
P. R. GUPTA ◽  
J. N. REDDY
Keyword(s):  
Solution Method ◽  
Natural Frequencies ◽  
The Other ◽  
Internal Line ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Decomposition Technique ◽  
Orthotropic Plates ◽  
Buckling Loads ◽  
Simply Supported

This paper presents the exact buckling loads and vibration frequencies of orthotropic rectangular plates with internal line hinge and having two opposite edges simply supported while the other two edges may have any combination of free, simply supported, and clamped conditions. An analytical method that uses the Lévy solution method and the domain decomposition technique is employed to determine the buckling loads and natural frequencies of rectangular plates with internal line hinge.

scholarly journals Vibrational analysis of nanoplate with surface irregularity via Kirchhoff plate theory

2021 ◽  
Vol 11 ◽  
pp. 184798042110011
Author(s):  
Mahmoud M Selim ◽  
Taher A Nofal
Keyword(s):  
Natural Frequency ◽  
Plate Theory ◽  
Vibrational Analysis ◽  
Equation Of Motion ◽  
Frequency Equation ◽  
Kirchhoff Plate ◽  
Surface Irregularity ◽  
Structural Element ◽  
Kirchhoff Plate Theory ◽  
Parabolic Form

In this work, an attempt is done to apply the Kirchhoff plate theory to find out the vibrational analyses of a nanoplate incorporating surface irregularity effects. The effects of surface irregularity on natural frequency of vibration of nanomaterials, especially for nanoplates, have not been investigated before, and most of the previous research have been carried for regular nanoplates. Therefore, it must be emphasized that the vibrations of irregular nanoplate are novel and applicable for the nanodevices, in which nanoplates act as the main structure of the nanocomposite. The surface irregularity is assumed in the parabolic form at the surface of the nanoplate. A novel equation of motion and frequency equation is derived. The obtained results provide a better representation of the vibration behavior of irregular nanoplates. It has been observed that the presence of surface irregularity affects considerably on the natural frequency of vibrational nanoplates. In addition, it has been seen that the natural frequency of nanoplate decreases with the increase of surface irregularity parameter. Finally, it can be concluded that the present results may serve as useful references for the application and design of nano-oscillators and nanodevices, in which nanoplates act as the most prevalent nanocomposites structural element.

Effects of In-plane Load on Flutter of Homogeneous Laminated Beam Plates with Delamination

2000 ◽  
Vol 123 (1) ◽  
pp. 61-66 ◽  
Author(s):  
Le-Chung Shiau ◽  
Yuan-Shih Chen
Keyword(s):  
Mach Number ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Compressive Load ◽  
Two Dimensional ◽  
Plate Model ◽  
Laminated Beam ◽  
Simply Supported ◽  
Flutter Boundary ◽  
Homogeneous Beam

The effects of in-plane load on flutter characteristics of delaminated two-dimensional homogeneous beam plates at high supersonic Mach number are investigated theoretically. Linear plate theory and quasi-steady supersonic aerodynamic theory are employed. A simple beam-plate model is developed to predict the effects of in-plane load on flutter boundaries for the delaminated beam plates with simply supported ends. Results reveal that the presence of an in-plane compressive load degrades the stiffness and natural frequencies of the plate and thereby decreases the flutter boundary for the plate. However, for certain geometry, the flutter boundaries were raised due to flutter coalescence modes of the plate altered by the presence of the in-plane load on the plate.

Effect of Shear Deformations on the Bending of Rectangular Plates

1960 ◽  
Vol 27 (1) ◽  
pp. 54-58 ◽  
Author(s):  
V. L. Salerno ◽  
M. A. Goldberg
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Plate Theory ◽  
Order Partial Differential Equation ◽  
Rectangular Plates ◽  
Partial Differential ◽  
Classical Plate Theory ◽  
Simply Supported ◽  
Wide Range

The three partial differential equations derived by Dr. E. Reissner2, 3 have been reduced to a fourth-order partial differential equation resembling that of the classical plate theory and to a second-order differential equation for determining a stress function. The general solution for the two partial differential equations has been applied to a simply supported plate with a constant load p and to a plate with two opposite edges simply supported and the other two edges free. Numerical calculations have been made for the simply supported plate and the results compared with those of classical theory. The calculations for a wide range of parameters indicate that the deviation is small.

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