Transverse bending of infinite and semi-infinite thin elastic plates. III

1958 ◽  
Vol 54 (2) ◽  
pp. 288-299 ◽  
Author(s):  
W. A. Bassali ◽  
M. Nassif ◽  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Isotropic Plate ◽  
Plate Theory ◽  
Outer Boundary ◽  
Exact Expression ◽  
Transverse Displacement ◽  
Elastic Plates ◽  
Classical Plate Theory ◽  
Transverse Bending ◽  
Elastically Restrained ◽  
Limiting Case

ABSTRACTWithin the restrictions of the classical plate theory, complex variable methods are used in this paper to develop an exact expression for the transverse displacement of an infinitely large isotropic plate having a free outer boundary and elastically restrained at an inner circular boundary, the plate being subjected to a general type of loading distributed over the area of a circle. The limiting case of a half-plane clamped along the straight edge and acted upon normally by the same loading is also considered.

Semi-Active Control of Sound Radiated From an Elastic Circular Plate Integrated With Adaptive Tuned Vibration Absorbers

2016 ◽  
Author(s):  
Masoud Hemmatian ◽  
Ramin Sedaghati
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Integral Approach ◽  
Shear Mode ◽  
Transverse Displacement ◽  
Vibration Absorbers ◽  
Classical Plate Theory ◽  
Low Frequencies ◽  
Control Applications ◽  
Radiated Sound

While adaptive tuning of vibration absorbers (ATVA) have been widely studied for vibration control applications, limited studies have been done to explore their potential for noise control applications. This study aims to utilize magnetorheological elastomer (MRE)-based ATVA to control the radiated sound from an elastic plate excited by a plane wave especially at low frequencies. Radiated sound from a clamped circular plate integrated with MRE-based ATVA is analytically studied using classical plate theory. Rayleigh integral approach is, then, used to express the transmitted sound pressure in terms of the plate’s displacement modal amplitude. A MRE-based ATVA under shear mode is investigated. The semi-active Skyhook controller is proposed to attenuate the transverse displacement of the plate and subsequently reduce the radiated sound. The controller determines the current input to the electromagnet and tunes the MRE-based ATVA with the desired stiffness.

Thermostatics of an elastic Cosserat plate containing a circular hole

1971 ◽  
Vol 70 (1) ◽  
pp. 169-174 ◽  
Author(s):  
İ. T. Gürgöze
Keyword(s):  
Temperature Gradient ◽  
General Theory ◽  
Circular Hole ◽  
Thermal Stresses ◽  
Plate Theory ◽  
The Other ◽  
Uniform Temperature ◽  
Classical Plate Theory ◽  
Cosserat Surface ◽  
Limiting Case

AbstractIn this paper, the general theory of a Cosserat surface given by Green, Naghdi and Wainwright(1), has been applied to the problem of a thermo-elastic Cosserat plate containing a circular hole of radius a. We assume that the major surfaces of the plate and the boundary of the hole are thermally insulated and that a uniform temperature gradient τ exists at infinity. In the limiting case, when h/a → 0, where h is the thickness of the plate, the thermal stresses at the circular hole reduce to those obtained by Florence and Goodier (4), by means of the classical plate theory. Results for the other limiting case h/a → ∞ are also given.

The Effect of Transverse Shear Deformation on the Bending of Elastic Plates

1945 ◽  
Vol 12 (2) ◽  
pp. A69-A77 ◽  
Author(s):  
Eric Reissner
Keyword(s):  
General Solution ◽  
Rectangular Plate ◽  
Transverse Shear ◽  
Plate Theory ◽  
Infinite Plate ◽  
Present Theory ◽  
System Of Equations ◽  
Elastic Plates ◽  
Classical Plate Theory

Abstract A system of equations is developed for the theory of bending of thin elastic plates which takes into account the transverse shear deformability of the plate. This system of equations is of such nature that three boundary conditions can and must be prescribed along the edge of the plate. The general solution of the system of equations is obtained in terms of two plane harmonic functions and one function which is the general solution of the equation Δψ − (10/h2)ψ = 0. The general results of the paper are applied (a) to the problem of torsion of a rectangular plate, (b) to the problems of plain bending and pure twisting of an infinite plate with a circular hole. In these two problems important differences are noted between the results of the present theory and the results obtained by means of the classical plate theory. It is indicated that the present theory may be applied to other problems where the deviations from the results of classical plate theory are of interest. Among these other problems is the determination of the reactions along the edges of a simply supported rectangular plate, where the classical theory leads to concentrated reactions at the corners of the plate. These concentrated reactions will not occur in the solution of the foregoing problem by means of the theory given in the present paper.

Response of Annular Plates to Circumferentially and Radially Moving Loads

1993 ◽  
Vol 60 (3) ◽  
pp. 649-661 ◽  
Author(s):  
G. N. Weisensel ◽  
A. L. Schlack
Keyword(s):  
Plate Theory ◽  
Outer Boundary ◽  
Integral Form ◽  
Moving Loads ◽  
Classical Plate Theory ◽  
Concentrated Load ◽  
Annular Plates ◽  
Transverse Loads ◽  
Significant Extension ◽  
Loading Parameter

The forced dynamic response of annular plates to circumferentially and radially moving concentrated transverse loads is investigated utilizing classical plate theory, with damping included, and solved in integral form. The boundary conditions are that the inner boundary of the plate is clamped and the outer boundary is free. An analytical expression in Fourier-Bessel series form is obtained for the forced deflection response to an arbitrarily moving concentrated load. This study includes radially moving loads and is a significant extension of the understanding of circular and annular plate dynamics. This understanding of radially moving loads is used to examine the nature of resonance conditions and corresponding critical values of the load parameters. The shapes of deflection modes of plate vibration are also presented. Damping and loading parameter sensitivities are studied in detail.

Accurate analytical solutions for shear-deformable web-core sandwich plates

2016 ◽  
Vol 19 (5) ◽  
pp. 616-643 ◽  
Author(s):  
Anup Pydah ◽  
K Bhaskar
Keyword(s):  
Analytical Solutions ◽  
Plate Theory ◽  
Three Dimensional ◽  
Sandwich Plates ◽  
Lateral Bending ◽  
Classical Plate Theory ◽  
Transverse Bending ◽  
The Face ◽  
Three Dimensional Elasticity ◽  
Shear Deformable

An accurate discrete model and analytical solutions thereof are presented for shear-deformable web-core sandwich plates. The face-plates are analyzed using the equations of three-dimensional elasticity, while the webs are accurately modelled using the classical plate theory with a plane stress solution for transverse bending and a Levy-type methodology for lateral bending. It is shown that this obviates the need for a complete three-dimensional analysis of the sandwich plate. Results obtained by this approach are used to highlight the effect of shear deformation of the face-plates.

scholarly journals Vibrations of Circular Plates with Elastically Restrained Edge against Translation and Resting on Elastic Foundation

2016 ◽  
Vol 13 (2) ◽  
pp. 187
Author(s):  
L.B. Rao ◽  
C.K. Rao
Keyword(s):  
Elastic Foundation ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Vibration Characteristics ◽  
Graphical Form ◽  
Winkler Foundation ◽  
Stiffness Ratio ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Elastically Restrained

The present paper deals with exact solutions for the free vibration characteristics of thin circular plates elastically restrained against translation and resting on Winkler-type elastic foundation based on the classical plate theory. Parametric investigations are carried out for estimating the influence of edge restraint against translation and stiffness of the elastic foundation on the natural frequencies of circular plates. The elastic edge restraint against translation and the presence of elastic foundation has been found to have a profound influence on vibration characteristics of the circular plate undergoing free transverse vibrations. Computations are carried out for natural frequencies of vibrations for varying values of translational stiffness ratio and stiffness parameter of Winkler-type foundation. Results are presented for twelve modes of vibration both in tabular and graphical form for use in design. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational edge restraint and the foundation stiffness ratio of the Winkler foundation on the natural frequencies of uniform isotropic circular plates. 

Generalized Bending of a Large, Shear Deformable Isotropic Plate Containing a Circular Hole or Rigid Inclusion

2000 ◽  
Vol 68 (2) ◽  
pp. 230-233 ◽  
Author(s):  
C. W. Bert ◽  
H. Zeng
Keyword(s):  
Circular Hole ◽  
Isotropic Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Circular Inclusion ◽  
Experimental Result ◽  
Classical Plate Theory ◽  
Geometric Ratio ◽  
Three Dimensional Elasticity

The problem of a large isotropic plate with a circular hole or rigid circular inclusion is considered here. The plate experiences transverse shear deformation and is subjected to an arbitrary bending field. By using Reissner’s plate theory, a general solution, in terms of Poisson’s ratio ν, a geometric ratio, and bending moment ratio B, is obtained to satisfy both the boundary conditions along the edge and at great distances from the edge. The stress couple concentration factors are calculated and compared with classical plate theory, three-dimensional elasticity theory, higher-order plate theory, and an experimental result.

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.

scholarly journals Vibrations of Circular Plates Resting on Elastic Foundation with Elastically Restrained Edge Against Translation

2018 ◽  
Vol 13 (1) ◽  
pp. 14
Author(s):  
L.B. Rao ◽  
C.K. Rao
Keyword(s):  
Elastic Foundation ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Vibration Characteristics ◽  
Graphical Form ◽  
Winkler Foundation ◽  
Stiffness Ratio ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Elastically Restrained

The present paper deals with exact solutions for the free vibration characteristics of thin circular plates resting on Winkler-type elastic foundation based on the classical plate theory elastically restrained against translation. Parametric investigations are carried out for estimating the influence of edge restraint against translation and stiffness of the elastic foundation on the natural frequencies of circular plates. The elastic edge restraint against translation and the presence of elastic foundation has been found to have a profound influence on vibration characteristics of the circular plate undergoing free transverse vibrations. Computations are carried out for natural frequencies of vibrations for varying values of translational stiffness ratio and stiffness parameter of Winkler-type foundation. Results are presented for twelve modes of vibration both in tabular and graphical form for use in the design. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational edge restraint and the foundation stiffness ratio of the Winkler foundation on the natural frequencies of uniform isotropic circular plates.  

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

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