Hydroelastic Instability of Infinite Strips Under Shearing Load on an Elastic Foundation

1984 ◽  
Vol 51 (2) ◽  
pp. 263-268 ◽  
Author(s):  
J. Tani
Keyword(s):  
Elastic Foundation ◽  
Fourier Transforms ◽  
Plate Theory ◽  
Inviscid Flow ◽  
The Other ◽  
Simply Supported ◽  
Deflection Plate ◽  
Small Deflection ◽  
Divergence Velocity ◽  
The Galerkin Method

The paper examines the hydroelastic instability of an infinitely long plate subjected to shearing load with two different boundary conditions, one side of which is exposed to an incompressible inviscid flow, and the other side supported on an elastic foundation. The analysis is based on the small deflection plate theory and the classical linearized potential flow theory. The Galerkin method and Fourier transforms are used. It is found that the effects of the shearing load and the elastic foundation on the divergence velocity can be illustrated by a single curve for both clamped and simply supported cases.

Effect of Nonhomogeneity on Vibration of Orthotropic Rectangular Plates of Varying Thickness Resting on Pasternak Foundation

2009 ◽  
Vol 131 (1) ◽  
Author(s):  
Roshan Lal ◽  
Dhanpati
Keyword(s):  
Differential Equation ◽  
Plate Theory ◽  
The Other ◽  
Thickness Variation ◽  
Order Partial Differential Equation ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Varying Thickness ◽  
Aspect Ratios ◽  
Displacement Mode

Free transverse vibrations of nonhomogeneous orthotropic rectangular plates of varying thickness with two opposite simply supported edges (y=0 and y=b) and resting on two-parameter foundation (Pasternak-type) have been studied on the basis of classical plate theory. The other two edges (x=0 and x=a) may be any combination of clamped and simply supported edge conditions. The nonhomogeneity of the plate material is assumed to arise due to the exponential variations in Young’s moduli and density along one direction. By expressing the displacement mode as a sine function of the variable between simply supported edges, the fourth order partial differential equation governing the motion of such plates of exponentially varying thickness in another direction gets reduced to an ordinary differential equation with variable coefficients. The resulting equation is then solved numerically by using the Chebyshev collocation technique for two different combinations of clamped and simply supported conditions at the other two edges. The lowest three frequencies have been computed to study the behavior of foundation parameters together with other plate parameters such as nonhomogeneity, density, and thickness variation on the frequencies of the plate with different aspect ratios. Normalized displacements are presented for a specified plate. A comparison of results with those obtained by other methods shows the computational efficiency of the present approach.

scholarly journals Stability plate with longitudinal constructive discontinuity

2011 ◽  
Vol 9 (1) ◽  
pp. 23-33
Author(s):  
Snezana Mitic ◽  
Ratko Pavlovic
Keyword(s):  
Exact Solutions ◽  
Analytical Approach ◽  
Plate Theory ◽  
Elastic Stability ◽  
The Other ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Thin Plate Theory ◽  
The Stability ◽  
Different Thickness

The influence of longitudinal constructive discontinuity on the stability of the plate in the domain of elastic stability is solved based on the classical thin plate theory. The constructive discontinuities divide the plate into fields of different thickness. The plate has two opposite edges simply supported while the other two edges can take any combination of free, simply supported and clamped conditions. The Levy method is used for the solution of the problem of stability, with the aim of developing an analytical approach when researching the stability of plates with longitudinal constructive discontinuities and also with the aim of obtaining exact solutions for plates with non-uniform thickness. The exact solutions for stability presented herein are very valuable as they may serve as benchmark results for researches in this area.

Comparison of the Two Formulations of w-u-v and w-F in Nonlinear Plate Analysis

2002 ◽  
Vol 69 (4) ◽  
pp. 547-552 ◽  
Author(s):  
J. Lee
Keyword(s):  
Large Deflection ◽  
Plate Theory ◽  
Airy Function ◽  
Transverse Displacement ◽  
Simply Supported ◽  
Deflection Plate ◽  
Plate Equations ◽  
Plate Analysis ◽  
Plane Displacement ◽  
Hamiltonian Property

In a moderately large deflection plate theory of von Karman and Chu-Herrmann, one may consider thin-plate equations of either the transverse and in-plane displacements, w-u-v formulation, or the transverse displacement and Airy function, w-F formulation. Under the Galerkin procedure, we examine if the modal equations of two plate formulations preserve the Hamiltonian property which demands energy conservation in the conservative limit of no damping and forcing. In the w-F formulation, we have shown that modal equations are Hamiltonian for the first four symmetric modes of a simply-supported plate. In contrast, the corresponding modal equations of w-u-v formulation do not exhibit the Hamiltonian property when a finite number of sine terms are included in the in-plane displacement expansions.

Stresses and Deflections in an Elastically Restrained Circular Plate Under Uniform Normal Loading Over a Segment

1959 ◽  
Vol 26 (1) ◽  
pp. 44-54
Author(s):  
W. A. Bassali ◽  
M. Nassif
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Exact Expression ◽  
Normal Loading ◽  
Complex Variable Methods ◽  
Deflection Plate ◽  
Small Deflection ◽  
In Series ◽  
Elastically Restrained ◽  
Elastic Constraint

Abstract Within the limits of the small-deflection plate theory and using complex variable methods, an exact expression is developed in series form for the solution of the problem of a thin circular plate elastically restrained along the boundary and subjected to uniform normal loading over a segment of the plate. The elastic constraint considered includes as particular cases the rigidly clamped and simply supported boundaries. For a rigidly clamped boundary the results are expressed in finite terms. Some details of calculations of deflections, moments, and shears based on the theory are provided in tables and curves. Timoshenko’s notation [1] is used in the paper. Other symbols will be defined as they appear in the text.

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory

2021 ◽  
pp. 109963622199386
Author(s):  
Hessameddin Yaghoobi ◽  
Farid Taheri
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Sheet Thickness ◽  
Analytical Investigation ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Vibration Stability ◽  
Shear Deformation Plate Theory

An analytical investigation was carried out to assess the free vibration, buckling and deformation responses of simply-supported sandwich plates. The plates constructed with graphene-reinforced polymer composite (GRPC) face sheets and are subjected to mechanical and thermal loadings while being simply-supported or resting on different types of elastic foundation. The temperature-dependent material properties of the face sheets are estimated by employing the modified Halpin-Tsai micromechanical model. The governing differential equations of the system are established based on the refined shear deformation plate theory and solved analytically using the Navier method. The validation of the formulation is carried out through comparisons of the calculated natural frequencies, thermal buckling capacities and maximum deflections of the sandwich plates with those evaluated by the available solutions in the literature. Numerical case studies are considered to examine the influences of the core to face sheet thickness ratio, temperature variation, Winkler- and Pasternak-types foundation, as well as the volume fraction of graphene on the response of the plates. It will be explicitly demonstrated that the vibration, stability and deflection responses of the sandwich plates become significantly affected by the aforementioned parameters.

scholarly journals An Application of Hankel Transforms in Axially Symmetric Potential Flow

1956 ◽  
Vol 9 (3) ◽  
pp. 128-131
Author(s):  
A. G. Mackie
Keyword(s):  
New York ◽  
Incompressible Fluid ◽  
Circular Hole ◽  
Potential Flow ◽  
Fourier Transforms ◽  
The Other ◽  
Axially Symmetric ◽  
Symmetric Potential ◽  
Physical Interest ◽  
Hankel Transforms

In his book on Hydrodynamics, Lamb obtained a solution for the potential flow of an incompressible fluid through a circular hole in a plane wall. More recently Sneddon (Fourier Transforms, New York, 1951) obtained Lamb's solution by an elegant application of Hankel transforms.Since the streamlines in this solution are symmetric about the wall, it is not of particular physical interest. In this note, Sneddon's method is used to give a solution in which the fluid is infinite in extent on one side of the aperture but issues as a jet of finite diameter on the other side.

Dynamic Response of the Spectral Element Model by Using the FFT

2007 ◽  
Vol 345-346 ◽  
pp. 845-848
Author(s):  
Joo Yong Cho ◽  
Han Suk Go ◽  
Usik Lee
Keyword(s):  
Fourier Transforms ◽  
Initial Conditions ◽  
Element Model ◽  
Spectral Element ◽  
Dynamic Responses ◽  
Analysis Method ◽  
Euler Beam ◽  
Exact Analytical Solutions ◽  
Simply Supported ◽  
Spectral Analysis Method

In this paper, a fast Fourier transforms (FFT)-based spectral analysis method (SAM) is proposed for the dynamic analysis of spectral element models subjected to the non-zero initial conditions. To evaluate the proposed SAM, the spectral element model for the simply supported Bernoulli-Euler beam is considered as an example problem. The accuracy of the proposed SAM is evaluated by comparing the dynamic responses obtained by SAM with the exact analytical solutions.

scholarly journals Analytical solution to bending of stiffened and continuous antisymmetric laminates

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Liecheng Sun ◽  
Issam E. Harik
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Displacement Function ◽  
The Other ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
Coupling Problem ◽  
Simply Supported ◽  
General Response

AbstractAnalytical Strip Method is presented for the analysis of the bending-extension coupling problem of stiffened and continuous antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being free, clamped, simply supported, isotropic beam supports, or point supports.

Large Deflections of a Simply Supported Beam Subjected to Moment at One End

1984 ◽  
Vol 51 (3) ◽  
pp. 519-525 ◽  
Author(s):  
P. Seide
Keyword(s):  
Linear Theory ◽  
Bending Moment ◽  
Critical Value ◽  
The Other ◽  
Large Deflections ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Elastica Theory ◽  
Angle Of Rotation

The large deflections of a simply supported beam, one end of which is free to move horizontally while the other is subjected to a moment, are investigated by means of inextensional elastica theory. The linear theory is found to be valid for relatively large angles of rotation of the loaded end. The beam becomes transitionally unstable, however, at a critical value of the bending moment parameter MIL/EI equal to 5.284. If the angle of rotation is controlled, the beam is found to become unstable when the rotation is 222.65 deg.

Sign in / Sign up

Export Citation Format

Share Document