scholarly journals Vibration of Skew Sandwich Plates With Laminated Facings

1997 ◽  
Author(s):  
C. M. Wang ◽  
K. K. Ang ◽  
C. Wang
Keyword(s):  
Ritz Method ◽  
Composite Plates ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Edge Conditions ◽  
System Vibration ◽  
Special Case ◽  
Length Limitation ◽  
Good Agreement

A Rayleigh-Ritz analysis is presented for the free vibration of skew sandwich plates composed of an orthotropic core and laminated facings. By proposing a set of Ritz functions consisting of the product of mathematically complete polynomial functions and the the boundary equations raised to appropriate powers, the Rayleigh-Ritz method can be automated to handle such composite plates with any combination of edge conditions. For convenience and better accurarcy, the Ritz formulation was derived in the skew coordinate system. Vibration frequencies of rectangular plates (a special case of skew plates) obtained via this method have been found to be in good agreement with previous researchers results. Owing to length limitation, only sample vibration frequencies for skew sandwich plates are presented.

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.

Analysis of Buckling of Sandwich Plates with Viscoelastic Core Using Layerwise Theory

2015 ◽  
Vol 798 ◽  
pp. 462-469 ◽  
Author(s):  
Arash Ranjbaran ◽  
Mohammad Reza Khoshravan ◽  
Mahsa Kharazi
Keyword(s):  
Composite Laminates ◽  
Ritz Method ◽  
Computational Cost ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Sandwich Plates ◽  
Layerwise Theory ◽  
Buckling Behavior ◽  
Viscoelastic Core ◽  
Good Agreement

Sandwich plates are one of the important components in construction of engineering and especially aerospace structures. In this paper, buckling analysis of sandwich plates was investigated experimentally and analytically using layerwise theory. The sandwich plate was rectangular and made of two composite laminates as skins and a viscoelastic core. The formulation was based on the first order shear deformation theory and the Rayleigh-Ritz method was used for approximating and determining the displacement field. The behavior of viscoelastic material modeled using Zener three-element model. The results obtained from layerwise theory compared with experimental results and showed good agreement. This study demonstrated that, layerwise theory could describe buckling behavior of sandwich plates with high accuracy and represents more realistic and acceptable description of behavior of the plates with much less computational cost.

Thermal Bending of Thick Rectangular Plates of Bimodulus Composite Materials

1980 ◽  
Vol 22 (6) ◽  
pp. 297-304 ◽  
Author(s):  
J. N. Reddy ◽  
C. W. Ber ◽  
Y. S. Hsu ◽  
V. S. Reddy
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Plate Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Normal Strain ◽  
Rectangular Plates ◽  
Fibre Direction ◽  
Thermal Bending ◽  
Good Agreement

Closed-form and finite-element solutions are presented for thermal bending and stretching of laminated composite plates. The material of each layer is assumed to be elastically and thermoelastically orthotropic and bimodular, i.e., having different properties depending upon whether the fibre-direction normal strain is tensile or compressive. The formulations are based on the thermoelastic version of the Whitney-Pagano laminated plate theory, which includes thickness shear deformations. Numerical results are obtained for deflections and neutral-surface positions associated with normal strains in both of the in-plane coordinates. The closed-form and finite-element results are found to be in good agreement.

Analytical Buckling Loads of Composite Rectangular Plates with Vertical and Rotational Springs Along the Edges

2020 ◽  
pp. 2043002
Author(s):  
Joseph Tenenbaum ◽  
Moshe Eisenberger
Keyword(s):  
Boundary Conditions ◽  
Bending Moment ◽  
Composite Plates ◽  
Static Solution ◽  
Published Data ◽  
Rectangular Plates ◽  
Buckling Loads ◽  
Edge Conditions ◽  
In Series ◽  
Edge Force

In this research, a new analytical solution is used for finding the buckling loads of rectangular plates with vertically and rotationally restrained edges. The solution method in this study is based on the development of a static solution for a plate. The solution is obtained in series form, and the coefficients are solved to match the edge conditions. The solution fits all the combinations of possible boundary conditions, of the deflection, slope, shear force and bending moment along the edges of the plate. In the case of springs, the edge force and moment boundary conditions are modified to include these effects. Any number of edges, from one to four, with both types of stiffening springs can be solved. Using this new method, the exact buckling loads and modes are found. The results are verified with published data, and many new cases are presented for uni-axially and bi-axially loaded isotropic, orthotropic, and composite plates.

Exact Solutions for the Free Vibrations and Buckling of Rectangular Plates With Linearly Varying In-Plane Loading

2001 ◽  
Author(s):  
Arthur W. Leissa ◽  
Jae-Hoon Kang
Keyword(s):  
Solution Procedure ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Transverse Displacement ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Buckling Loads ◽  
Simply Supported ◽  
Edge Conditions ◽  
Elastically Supported

Abstract An exact solution procedure is formulated for the free vibration and buckling analysis of rectangular plates having two opposite edges simply supported when these edges are subjected to linearly varying normal stresses. The other two edges may be clamped, simply supported or free, or they may be elastically supported. The transverse displacement (w) is assumed as sinusoidal in the direction of loading (x), and a power series is assumed in the lateral (y) direction (i.e., the method of Frobenius). Applying the boundary conditions yields the eigenvalue problem of finding the roots of a fourth order characteristic determinant. Care must be exercised to obtain adequate convergence for accurate vibration frequencies and buckling loads, as is demonstrated by two convergence tables. Some interesting and useful results for vibration frequencies and buckling loads, and their mode shapes, are presented for a variety of edge conditions and in-plane loadings, especially pure in-plane moments.

3D Vibration Analysis of Hermetic Capsules by Using Ritz Method

2017 ◽  
Vol 17 (03) ◽  
pp. 1750040
Author(s):  
Jae-Hoon Kang
Keyword(s):  
Eigenvalue Problem ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Legendre Polynomials ◽  
Present Method ◽  
Ritz Method ◽  
Three Dimensional ◽  
Dynamic Equations ◽  
Vibration Frequencies ◽  
Good Agreement

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies of a hermetic capsule comprising a cylinder closed with hemi-ellipsoidal caps at both ends. Unlike conventional shell theories, which are mathematically 2D, the present method is based upon the 3D dynamic equations of elasticity. Displacement components [Formula: see text], [Formula: see text], and [Formula: see text] in the radial, circumferential, and axial directions, respectively, are taken to be periodic in [Formula: see text] and in time, and the Legendre polynomials in the r and z directions instead of ordinary ones. Potential (strain) and kinetic energies of the hermetic capsule are formulated, and the Ritz method is used to solve the eigenvalue problem, thereby yielding upper bound values of the frequencies. As the degree of the Legendre polynomials is increased, frequencies converge to the exact values. Typical convergence studies are carried out for the first five frequencies. The frequencies from the present 3D method are in good agreement with those obtained from other 3D approach and 2D shell theories proposed by previous researchers.

Vibration of Rectangular Mindlin Plates with Intermediate Stiffeners

1994 ◽  
Vol 116 (4) ◽  
pp. 529-535 ◽  
Author(s):  
K. M. Liew ◽  
Y. Xiang ◽  
S. Kitipornchai ◽  
M. K. Lim
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Torsional Rigidity ◽  
Ritz Method ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Algebraic Polynomials ◽  
Plate Structures ◽  
Various Boundary Conditions ◽  
Vibrational Response

A first known investigation into the vibratory characteristics of rectangular Mindlin plates with intermediate stiffeners is presented. The Rayleigh-Ritz method is used, with displacement and rotational functions assumed in the form of mathematically complete algebraic polynomials. Sets of numerical frequency parameters for rectangular plates of various boundary conditions, thicknesses and plate dimensions are presented. In the study, the effects of shear deformation and rotary inertia on the vibrational response of the plate structures are investigated. The influence of torsional rigidity and geometric properties of stiffeners on the natural frequency parameters are included. To validate the proposed formulation, numerical results for some simplified problems have been determined where existing literature for these problems can be found. Finally sets of new vibration frequencies for plates with one or more stiffeners in various directions are presented.

scholarly journals Thermal Buckling Analysis of Laminated Composite plates with General Elastic Boundary Supports

2020 ◽  
Vol 26 (3) ◽  
pp. 1-17
Author(s):  
Mohammed Basheer Alabas ◽  
Wedad Ibrahim Majid
Keyword(s):  
Boundary Condition ◽  
Fourier Series ◽  
Plate Theory ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Thermal Buckling ◽  
Transverse Displacement ◽  
Rectangular Plates ◽  
Elastic Boundary

In this study, the modified Rayleigh-Ritz method and Fourier series are used to determine the thermal buckling behavior of laminated composite thin plates with a general elastic boundary condition applied to in-plane uniform temperature distribution depending upon classical laminated plate theory(CLPT). A generalized procedure solution is developed for the Rayleigh-Ritz method combined with the synthetic spring technique. The transverse displacement of the orthotropic rectangular plates is not a different term as a new shape expansion of trigonometric series. In this solution approach, the plate transverse deflection and rotation due to bending are developed into principle Fourier series with a sufficient smoothness auxiliary polynomial function, the variable of boundary condition can be easily done by only change the boundary spring stiffness of at the all boundaries of laminated composite plate without achieving any replacement to the solution. The accuracy of the current outcome is verified by comparing with the result obtained from other analytical methods in addition to the finite element method (FEM), so the excellent of this technique is proving during numerical examples.

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]

scholarly journals Free In-Plane Vibration of Super-Elliptical Plates

2011 ◽  
Vol 18 (3) ◽  
pp. 471-484 ◽  
Author(s):  
Murat Altekin
Keyword(s):  
Boundary Conditions ◽  
Lagrange Multipliers ◽  
Ritz Method ◽  
Rectangular Plates ◽  
Uniform Thickness ◽  
Plane Vibration ◽  
Good Agreement ◽  
Geometrical Boundary

Free in-plane vibration of super-elliptical plates of uniform thickness was investigated by the Ritz method. A large variety of plate shapes ranging from an ellipse to a rectangle were examined. Two cases were considered: (1) a completely free, and (2) a point-supported plate. The geometrical boundary conditions were satisfied by the Lagrange multipliers. The results were compared with those of rectangular plates. Basically good agreement was obtained. Matching results were reported, and the discrepancies were highlighted.

Sign in / Sign up

Export Citation Format

Share Document