Asymptotic Analysis of Buckling of Layered Rectangular Plates Accounting for Boundary Conditions and Edge Effects Induced by Shears

2021 ◽  
pp. 179-202
Author(s):  
Gennadi Mikhasev ◽  
Rovshen Ataev
Keyword(s):  
Asymptotic Analysis ◽  
Boundary Conditions ◽  
Edge Effects ◽  
Rectangular Plates

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

Vibration Analysis of Laminated Composite Rectangular Plates With General Boundary Conditions

2018 ◽  
Author(s):  
Yu Fu ◽  
Jianjun Yao ◽  
Zhenshuai Wan ◽  
Gang Zhao
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Geometric Parameters ◽  
General Boundary ◽  
Rectangular Plates ◽  
General Boundary Conditions ◽  
Benchmark Solutions

In this investigation, the free vibration analysis of laminated composite rectangular plates with general boundary conditions is performed with a modified Fourier series method. Vibration characteristics of the plates have been obtained via an energy function represented in the general coordinates, in which the displacement and rotation in each direction is described as an improved form of double Fourier cosine series and several closed-form auxiliary functions to eliminate any possible jumps and boundary discontinuities. All the expansion coefficients are then treated as the generalized coordinates and determined by Rayleigh-Ritz method. The convergence and reliability of the current method are verified by comparing with the results in the literature and those of Finite Element Analysis. The effects of boundary conditions and geometric parameters on the frequencies are discussed as well. Finally, numerous new results for laminated composite rectangular plates with different geometric parameters are presented for various boundary conditions, which may serve as benchmark solutions for future research.

Hydroelastic Vibration of Rectangular Plates

1996 ◽  
Vol 63 (1) ◽  
pp. 110-115 ◽  
Author(s):  
Moon K. Kwak
Keyword(s):  
Boundary Conditions ◽  
Approximate Formula ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Ritz Method ◽  
Plate Boundary ◽  
Rigid Wall ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Virtual Mass

This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

Large-Amplitude Oscillations of Unsymmetrically Laminated Anisotropic Rectangular Plates Including Shear, Rotatory Inertia, and Transverse Normal Stress

1985 ◽  
Vol 52 (3) ◽  
pp. 536-542 ◽  
Author(s):  
K. S. Sivakumaran ◽  
C. Y. Chia
Keyword(s):  
Boundary Conditions ◽  
Normal Stress ◽  
Transverse Shear ◽  
Plate Theory ◽  
Orientation Angle ◽  
Nonlinear Frequency ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Transverse Normal Stress

This paper is concerned with nonlinear free vibrations of generally laminated anisotropic elastic plates. Based on Reissner’s variational principle a nonlinear plate theory is developed. The effects of transverse shear, rotatory inertia, transverse normal stress, and transverse normal contraction or extension are included in this theory. Using the Galerkin procedure and principle of harmonic balance, approximate solutions to governing equations of unsymmetrically laminated rectangular plates including transverse shear, rotatory inertia, and transverse normal stress are formulated for various boundary conditions. Numerical results for the ratio of nonlinear frequency to linear frequency of unsymmetric angle-ply and cross-ply laminates are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, and aspect ratio and for different boundary conditions. Present results are also compared with available data.

A new Fourier series method and displacement function for in-plane vibration and power flow characteristics analysis of isotropic rectangular plates

2019 ◽  
Vol 50 (6) ◽  
pp. 176-194
Author(s):  
Kavikant Mahapatra ◽  
SK Panigrahi
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Power Flow ◽  
Flow Characteristics ◽  
Displacement Function ◽  
Rectangular Plates ◽  
Series Method ◽  
Plane Vibration ◽  
Fourier Series Method ◽  
Beam Displacement

The generation of in-plane vibration in plates is an important issue and frequently occurs due to the presence of excitations in the ship’s hull due to turbulent fluid flows, turbulent airflow excitation on aerospace structures, gear system subjected to axial excitation, assemblies housing piezoelectric crystals and sandwiched plates, and so on. The present analysis aims to establish a universal and numerically efficient method for determination of in-plane vibration characteristics of isotropic rectangular plates both for conventional and general boundary conditions. The new in-plane Fourier series and displacement function of the plate have been developed using beam displacement functions in x and y directions, respectively, under in-plane condition. A modified Fourier series assumption for the in-plane beam displacement has been utilised and further developed as plate displacement function. The computational efficiency of the present method is compared in terms of convergence of natural frequency parameter, speed of execution and manual convenience to reduce human errors with the frequently used Fourier series method by various researchers. Rayleigh–Ritz procedure has been applied to determine the in-plane natural frequencies. The mode shapes for few conventional and generally varying boundary conditions have been presented and analysed. The dynamic response has been obtained and analysed in terms of the in-plane mobility and power flow characteristics of the plate under varying boundary conditions. The validity of results obtained by the current method has shown excellent accuracy and faster convergence with the existing results. The present results can provide a benchmark to analyse the dynamic in-plane response of plate systems being used for built-up structures in real engineering applications.

scholarly journals Dynamic analysis of submerged microscale plates: the effects of acoustic radiation and viscous dissipation

2016 ◽  
Vol 472 (2187) ◽  
pp. 20150728 ◽  
Author(s):  
Zhangming Wu ◽  
Xianghong Ma
Keyword(s):  
Viscous Fluid ◽  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Stokes Equations ◽  
Acoustic Radiation ◽  
Navier Stokes ◽  
Rectangular Plates ◽  
Fluid Loading ◽  
Navier Stokes Equations ◽  
Loading Impedance

The aim of this paper is to study the dynamic characteristics of micromechanical rectangular plates used as sensing elements in a viscous compressible fluid. A novel modelling procedure for the plate–fluid interaction problem is developed on the basis of linearized Navier–Stokes equations and no-slip conditions. Analytical expression for the fluid-loading impedance is obtained using a double Fourier transform approach. This modelling work provides us an analytical means to study the effects of inertial loading, acoustic radiation and viscous dissipation of the fluid acting on the vibration of microplates. The numerical simulation is conducted on microplates with different boundary conditions and fluids with different viscosities. The simulation results reveal that the acoustic radiation dominates the damping mechanism of the submerged microplates. It is also proved that microplates offer better sensitivities (Q-factors) than the conventional beam type microcantilevers being mass sensing platforms in a viscous fluid environment. The frequency response features of microplates under highly viscous fluid loading are studied using the present model. The dynamics of the microplates with all edges clamped are less influenced by the highly viscous dissipation of the fluid than the microplates with other types of boundary conditions.

A GENERALIZED ANALYTICAL APPROACH FOR THE BUCKLING ANALYSIS OF THIN RECTANGULAR PLATES WITH ARBITRARY BOUNDARY CONDITIONS

2011 ◽  
Vol 11 (01) ◽  
pp. 1-21 ◽  
Author(s):  
EUGENIO RUOCCO ◽  
VINCENZO MINUTOLO ◽  
STEFANO CIARAMELLA
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Analytical Approach ◽  
Elastic Stability ◽  
Rectangular Plates ◽  
The Finite Element Method ◽  
Dimensional Model ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Numerical Discretization

An analytical approach for studying the elastic stability of thin rectangular plates under arbitrary boundary conditions is presented. Because the solution is given in closed-form, the approach can be regarded as "exact" under the Kirchhoff–Love assumption. The proposed procedure allows us to obtain the buckling load and modal displacements that do not depend on the number of elements adopted in the numerical discretization using, say, the finite element method. Due to the fact that the longitudinal variation of the displacements is taken into account, the two-dimensional model established for the plate is considered "complete." Such an approach overcomes the shortcomings of conventional modeling presented in the literature. In order to demonstrate the generality of the proposed approach, several examples are prepared and the results obtained are compared with finite element and analytical solutions existing elsewhere.

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