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.

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.

Effect of Pasternak Foundation on Axisymmetric Vibration of Polar Orthotropic Annular Plates of Varying Thickness

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Seema Sharma ◽  
U. S. Gupta ◽  
R. Lal
Keyword(s):  
Plate Theory ◽  
Mode Shapes ◽  
Thickness Variation ◽  
Axisymmetric Vibration ◽  
Classical Plate Theory ◽  
Energy Principle ◽  
Annular Plates ◽  
Edge Conditions ◽  
Modes Of Vibration ◽  
Polar Orthotropic

Free axisymmetric vibrations of polar orthotropic annular plates of variable thickness resting on a Pasternak-type elastic foundation have been studied based on the classical plate theory. Hamilton’s energy principle has been used to derive the governing differential equation of motion. Frequency equations for an annular plate for two different combinations of edge conditions have been obtained employing Chebyshev collocation technique. Numerical results thus obtained have been presented in the form of tables and graphs. The effect of foundation parameter and thickness variation together with various plate parameters such as rigidity ratio, radius ratio, and taper parameter on natural frequencies has been investigated for the first three modes of vibration. Mode shapes for specified plates have been presented. A close agreement of results with those available in the literature shows the versatility of the present technique.

Asymptotic Solutions of the Von Karman Equations for a Circular Plate Under a Concentrated Load

1985 ◽  
Vol 52 (2) ◽  
pp. 326-330 ◽  
Author(s):  
J. P. Frakes ◽  
J. G. Simmonds
Keyword(s):  
Dimensionless Parameter ◽  
Plate Theory ◽  
Integral Form ◽  
Load Curve ◽  
Concentrated Load ◽  
Singular Perturbation Methods ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Simple Support ◽  
Von Kármán

Reissner’s form of the axisymmetric von Karman equations for a centrally, point-loaded plate are written in dimensionless differential and integral form. To concentrate on essentials, we take Poisson’s ratio to be one-third (so that the limiting Fo¨ppl membrane equations have one-term solutions) and boundary conditions of simple support. A dimensionless parameter β measures the relative bending stiffness. A nine-term perturbation solution in powers of ε = β–6, the first term of which corresponds to linear plate theory, is constructured using MACSYMA. Although the resulting deflection-load power series appears to converge only if |ε| < 1/40, successive Aitken-Shanks’ transformations yield an expression valid up to ε ≈ 1. Solutions as β → 0 are constructed using singular perturbation methods and two terms of the deflection-load curve are computed numerically, the first term corresponding to the exact nonlinear membrane solution. A graph shows that there is a region of overlap of the large and small β-approximations to the deflection-load curve.

Free Vibration of Composite Annular Plates Embedded with SMA Fibers in the Circumferential Direction

2007 ◽  
Vol 353-358 ◽  
pp. 1306-1309
Author(s):  
Shi Rong Li ◽  
Wen Shan Yu ◽  
Liang Liang Fan
Keyword(s):  
Temperature Rise ◽  
Shooting Method ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Plate Theory ◽  
Constitutive Law ◽  
Axisymmetric Vibration ◽  
Classical Plate Theory ◽  
One Dimensional ◽  
Annular Plates

Based on Brinson’s one-dimensional thermo-constitutive law of SMA and classical plate theory, linear non-axisymmetric vibration of uniform heated composite annular plate embedded with circumferential SMA fibers is investigated. Natural frequencies of the annular plates with immovably clamped boundary condition, depending on the temperature rise are obtained by using shooting method. The characteristic curves of first four natural frequencies of non-axisymmetric vibration versus temperature rise are plotted. Influences of the volume fraction and the initial strain of SMA on the natural frequencies of plate are analyzed. The numerical results show that, the activation of SMA can enhance the natural frequency both in the inverse martensite transformation temperature range and the thermal buckling temperature.

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.

scholarly journals Nonlinear Dynamic Analysis for Rectangular FGM Plates with Variable Thickness Subjected to Mechanical Load

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Khuc Van Phu ◽  
Le Xuan Doan ◽  
Nguyen Van Thanh
Keyword(s):  
Variable Thickness ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Rectangular Plates ◽  
Classical Plate Theory

 In this paper, the governing equations of rectangular plates with variable thickness subjected to mechanical load are established by using the classical plate theory, the geometrical nonlinearity in von Karman-Donnell sense. Solutions of the problem are derived according to Galerkin method. Nonlinear dynamic responses, critical dynamic loads are obtained by using Runge-Kutta method and the Budiansky–Roth criterion. Effect of volume-fraction index k and some geometric factors are considered and presented in numerical results.

A Study on Adhesively Bonded Aluminum Plates Under Shock-Wave Loading

2017 ◽  
Author(s):  
Salih Yildiz ◽  
Yiannis Andreopoulos ◽  
Robert E. Jensen ◽  
Daniel Shaffren ◽  
Doug Jahnke ◽  
...  
Keyword(s):  
Shock Wave ◽  
Plate Theory ◽  
Dissimilar Materials ◽  
Laminated Plates ◽  
Shock Wave Loading ◽  
Wave Loading ◽  
Classical Plate Theory ◽  
Film Adhesive ◽  
Aluminum Plates ◽  
Application Fields

Adhesive joint technology has been developed gradually, and the application fields of this type of joints have been expanded increasingly since they reduce the weight of the applications, provide uniform stress distribution across the joints, allow to bond similar, and dissimilar materials, and contribute to dampen the shock, and vibration. However, the performance of the adhesive joints under high loading rate such as blast or ballistic loading has been studied by few researchers. In this study, fully laminated plates consisting of 6061 aluminum plates (15” in diameter and 1/16” thick) and FM300K epoxy film adhesive were tested under shock wave loading. Full displacement field over the testing plates were obtained by TRC-SDIC technique, and the strain on the plates were computed by classical plate theory for large deflections. FEM model was analyzed and the results were compared with experimental results.

Bending of Circular and Ring-Shaped Plates on an Elastic Foundation

1954 ◽  
Vol 21 (1) ◽  
pp. 45-51
Author(s):  
Herbert Reismann
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Series Solution ◽  
Circular Disk ◽  
Symmetric Problem ◽  
Concentrated Load ◽  
Transverse Loads ◽  
Infinite Extent ◽  
Theory Of Plates ◽  
Pure Moment

Abstract This paper develops a method for the evaluation of deflections, moments, shears, and stresses of a circular or ring-shaped plate on an elastic foundation under transverse loads. A series solution is derived for plates subjected to edge and/or concentrated loads and is given in terms of tabulated functions. It is exact within the assumptions underlying the classical theory of plates and includes, as a particular case, the known solution of the corresponding radially symmetric problem. Two examples displaying radial asymmetry are worked. A solution is given for (a) a circular plate resting on an elastic foundation, clamped at the boundary and subjected to an arbitrarily placed concentrated load, and (b) a plate of infinite extent, resting on an elastic foundation and clamped to the boundary of a rigid circular disk to which a pure moment is applied.

Determination of vibration of single-layered graphene sheets using nonlocal modified couple stress theory

2021 ◽  
pp. 2250011
Author(s):  
F. Attar ◽  
R. Khordad ◽  
A. Zarifi
Keyword(s):  
Couple Stress ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Nonlocal Parameter ◽  
Modified Couple Stress Theory ◽  
Length Scale ◽  
Vibration Modes ◽  
Classical Plate Theory ◽  
Stress Theory ◽  
Modified Couple Stress

The free vibration of single-layered graphene sheet (SLGS) has been studied by nonlocal modified couple stress theory (NMCS), analytically. Governing equation of motion for SLGS is obtained via thin plate theory in conjunction with Hamilton’s principle for two cases: (1) using nonlocal parameter only for stress tensor, (2) using nonlocal parameter for both stress and couple stress tensors. Navier’s approach has been used to solve the governing equations for simply supported boundary conditions. It is found that the frequency ratios decrease with increasing nonlocal parameter and also with enhancing vibration modes, but increase with raising length scale parameter. The nonlocal and length scale parameters are more prominent in higher vibration modes. The obtained results have been compared with the previous studies obtained by using classical plate theory, the modified couple stress theory and nonlocal elasticity theory, separately.

Sign in / Sign up

Export Citation Format

Share Document