Vibrations of Axially Moving Vertical Rectangular Plates in Contact with Fluid

2016 ◽  
Vol 16 (02) ◽  
pp. 1450092 ◽  
Author(s):  
Yan Qing Wang ◽  
Sen Wen Xue ◽  
Xiao Bo Huang ◽  
Wei Du
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Fluid Pressure ◽  
Added Mass ◽  
Vibration Characteristics ◽  
Rectangular Plates ◽  
Moving Plate ◽  
Bernoulli’S Equation ◽  
Aspect Ratios ◽  
Axially Moving

The vibration characteristics of an axially moving vertical plate immersed in fluid and subjected to a pretension are investigated, with a special consideration to natural frequencies, complex mode functions and critical speeds of the system. The classical thin plate theory is adopted for the formulation of the governing equation of motion of the vibrating plates. The effects of free surface waves, compressibility and viscidity of the fluid are neglected in the analysis. The velocity potential and Bernoulli’s equation are used to describe the fluid pressure acting on the moving plate. The effect of fluid on the vibrations of the plate may be regarded as equivalent to an added mass on the plate. The formulation of added mass is obtained from kinematic boundary conditions of the plate–fluid interfaces. The effects of some system parameters such as the moving speed, stiffness ratios, location and aspect ratios of the plate and the fluid-plate density ratios on the above-mentioned vibration characteristics of the plate–fluid system are investigated in detail. Various different boundary conditions are considered in the study.

Stability and Dynamics of Axially Moving Unidirectional Plates Partially Immersed in a Liquid

2014 ◽  
Vol 14 (04) ◽  
pp. 1450010 ◽  
Author(s):  
Yan Qing Wang ◽  
Xing Hui Guo ◽  
Zhen Sun ◽  
Jian Li
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Plate Theory ◽  
Fluid Pressure ◽  
Added Mass ◽  
Chaotic Motions ◽  
Bernoulli’S Equation ◽  
Singular Functions ◽  
Axially Moving ◽  
The Stability

The stability and dynamics of an axially moving unidirectional plate partially immersed in a liquid and subjected to a nonlinear aerodynamic excitation are investigated. The method of singular functions is adopted to study the dynamic characteristics of the unidirectional plates with discontinuous characteristics. Nonlinearities due to large-amplitude plate motions are considered by using the classical nonlinear thin plate theory, with allowance for the effect of viscous structural damping. The velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the unidirectional plate. The effect of fluid on the vibrations of the plate may be equivalent to added mass of the plate. The formulation of added mass is obtained from kinematic boundary conditions of the plate–fluid interfaces. The system is discretized by Galerkin's method while a model involving two degrees of freedom, is adopted. Attention is focused on the behavior of the system in the region of dynamic instability, and several motions are found by numerical simulations. The effects of the moving speed and some other parameters on the dynamics of the system are also investigated. It is shown that chaotic motions can occur in this system in several certain regions of parameter space.

Buckling Analysis of Thin Functionally Graded Rectangular Plates Resting on Elastic Foundation

2010 ◽  
Author(s):  
Meisam Mohammadi ◽  
A. R. Saidi ◽  
Mehdi Mohammadi
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Plate Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Coupled Equations ◽  
Aspect Ratios ◽  
Special Cases

In the present article, the buckling analysis of thin functionally graded rectangular plates resting on elastic foundation is presented. According to the classical plate theory, (Kirchhoff plate theory) and using the principle of minimum total potential energy, the equilibrium equations are obtained for a functionally graded rectangular plate. It is assumed that the plate is rested on elastic foundation, Winkler and Pasternak elastic foundations, and is subjected to in-plane loads. Since the plate is made of functionally graded materials (FGMs), there is a coupling between the equations. In order to remove the existing coupling, a new analytical method is introduced where the coupled equations are converted to decoupled equations. Therefore, it is possible to solve the stability equations analytically for special cases of boundary conditions. It is assumed that the plate is simply supported along two opposite edges in x direction and has arbitrary boundary conditions along the other edges (Levy boundary conditions). Finally, the critical buckling loads for a functionally graded plate with different boundary conditions, some aspect ratios and thickness to side ratios, various power of FGM and foundation parameter are presented in tables and figures. It is concluded that increasing the power of FGM decreases the critical buckling load and the load carrying capacity of plate increases where the plate is rested on Pasternak in comparison with the Winkler type.

A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges

2010 ◽  
Vol 224 (9) ◽  
pp. 1831-1841 ◽  
Author(s):  
M Mohammadi ◽  
A R Saidi ◽  
E Jomehzadeh
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Fg Plates

In this article, a novel analytical method for decoupling the coupled stability equations of functionally graded (FG) rectangular plates is introduced. Based on the Mindlin plate theory, the governing stability equations that are coupled in terms of displacement components are derived. Introducing four new functions, the coupled stability equations are converted into two independent equations. The obtained equations have been solved for buckling analysis of rectangular plates with simply-supported two edges and arbitrary boundary conditions along the other edges (Levy boundary conditions). The critical buckling loads are presented for different loading conditions, various thickness to side and aspect ratios, some powers of FG materials, and various boundary conditions. The presented results for buckling of moderately thick FG plates with two simply-supported edges are reported for the first time.

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.

scholarly journals An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Xue Kai ◽  
Wang Jiufa ◽  
Li Qiuhong ◽  
Wang Weiyuan ◽  
Wang Ping
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Cross Sectional ◽  
Fourier Cosine ◽  
Cosine Series ◽  
The Matrix ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

An analysis method is proposed for the vibration analysis of the Mindlin rectangular plates with general elastically restrained edges, in which the vibration displacements and the cross-sectional rotations of the mid-plane are expressed as the linear combination of a double Fourier cosine series and four one-dimensional Fourier series. The use of these supplementary functions is to solve the possible discontinuities with first derivatives at each edge. So this method can be applied to get the exact solution for vibration of plates with general elastic boundary conditions. The matrix eigenvalue equation which is equivalent to governing differential equations of the plate can be derived through using the boundary conditions and the governing equations based on Mindlin plate theory. The natural frequencies can be got through solving the matrix equation. Finally the numerical results are presented to validate the accuracy of the method.

scholarly journals The Effect of Using Different Elastic Moduli on Vibration of Laminated CFRP Rectangular Plates

2019 ◽  
Vol 2 (1) ◽  
pp. 19-27
Author(s):  
Yoshihiro Narita ◽  
Michio Innami ◽  
Daisuke Narita
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Linear Regression Analysis ◽  
Laminated Composite ◽  
Thin Layers ◽  
Test Accuracy ◽  
Rectangular Plates ◽  
Classical Boundary ◽  
Definition Of

This paper deals with effects of using different sets of material constants on the natural frequencies of laminated composite rectangular plates. The plate is symmetrically laminated by thin layers composed of recently developed carbon fiber reinforced plastic (CFRP) materials. Numerical experiments are conducted by using a semi-analytical solution based on the thin plate theory and the lamination theory. The displacements are assumed to accommodate any combination of classical boundary conditions. The material property is expressed by a set of four elastic constants, and some typical sets of values are cited from the recent literature. Furthermore, a new standard set of discretized constants is proposed to uncover the underlying characteristics of the existing constants. The convergence study is carried out first, and the lowest five natural frequencies are calculated for five sets of classical boundary conditions including totally free through totally clamped cases. Next, a new definition of frequency parameters is introduced to promote more physically meaningful comparison among the obtained results, and the effect of using slightly different constants is clarified for unified comparison and insights. It is also discussed to derive approximate frequency formulas by linear regression analysis and to test accuracy of the formulas.

An exact solution for free vibration of thin functionally graded rectangular plates

2010 ◽  
Vol 225 (3) ◽  
pp. 526-536 ◽  
Author(s):  
A Hasani Baferani ◽  
A R Saidi ◽  
E Jomehzadeh
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Different Boundary Conditions

The aim of this article is to find an exact analytical solution for free vibration characteristics of thin functionally graded rectangular plates with different boundary conditions. The governing equations of motion are obtained based on the classical plate theory. Using an analytical method, three partial differential equations of motion are reformulated into two new decoupled equations. Based on the Navier solution, a closed-form solution is presented for natural frequencies of functionally graded simply supported rectangular plates. Then, considering Levy-type solution, natural frequencies of functionally graded plates are presented for various boundary conditions. Three mode shapes of a functionally graded rectangular plate are also presented for different boundary conditions. In addition, the effects of aspect ratio, thickness—length ratio, power law index, and boundary conditions on the vibration characteristics of functionally graded rectangular plates are discussed in details. Finally, it has been shown that the effects of in-plane displacements on natural frequencies of functionally graded plates under different boundary conditions have been studied.

Thermo-mechanical induced vibration characteristics of shear deformable functionally graded ceramic—metal plates using finite element method

2010 ◽  
Vol 225 (1) ◽  
pp. 50-65 ◽  
Author(s):  
M Talha ◽  
B N Singh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Temperature Field ◽  
Boundary Conditions ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Aspect Ratios ◽  
Shear Deformable ◽  
Element Method

This paper deals with the thermomechanical-induced vibration characteristics of shear deformable functionally graded material (FGM) plates. Theoretical formulations are based on higher-order shear deformation theory with a significant improvement in the transverse displacement using finite-element method. The mechanical properties of the plate are assumed to be temperature-dependent and graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The temperature field is ascertained to be a uniform distribution over the plate surface and varied in the thickness direction only. The fundamental equations for FGM plates are derived using variational approach by considering traction-free boundary conditions on the top and bottom faces of the plate. A C0 continuous isoparametric Lagrangian finite-element with 13 degrees of freedom (DOF) per node have been used to accomplish the results. Convergence and comparison studies have been performed for square plates to demonstrate the efficiency of the present model. The numerical results are obtained for different thickness ratios, aspect ratios, volume fraction index, and temperature rise with different boundary conditions. The results reveal that the temperature field and the gradient in the material properties have significant effect on the vibration characteristics of the FGM plates.

scholarly journals Frequency Equations and Modes of Free Vibrations of Rectangular Plates with Various Edge Conditions

1994 ◽  
Vol 208 (5) ◽  
pp. 307-319 ◽  
Author(s):  
C W Bert ◽  
M Malik
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Free Vibrations ◽  
Edge Condition ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Edge Conditions ◽  
Classical Boundary ◽  
Free Edges

This paper considers linear free vibrations of thin isotropic rectangular plates with combinations of the classical boundary conditions of simply supported, clamped and free edges and the mathematically possible condition of guided edges. The total number of plate configurations with the classical boundary conditions are known to be twenty-one. The inclusion of the guided edge condition gives rise to an additional thirty-four plate configurations. Of these additional cases, twenty-one cases have exact solutions for which frequency equations in explicit or transcendental form may be obtained. The frequency equations of these cases are given and, for each case, results of the first nine mode frequencies are tabulated for a range of the plate aspect ratios.

Dynamic Instability of Stiffened Plates with Cutout Subjected to In-Plane Uniform Edge Loadings

2003 ◽  
Vol 03 (03) ◽  
pp. 391-403 ◽  
Author(s):  
A. K. L. Srivastava ◽  
P. K. Datta ◽  
A. H. Sheikh
Keyword(s):  
Boundary Conditions ◽  
Dynamic Stability ◽  
Dynamic Instability ◽  
Plate Theory ◽  
Stiffened Plates ◽  
Numerical Examples ◽  
Different Boundary Conditions ◽  
Reissner Plate ◽  
Aspect Ratios ◽  
Instability Regions

This paper is concerned with the dynamic stability of stiffened plates with cutout subjected to harmonic in-plane edge loadings. The plate is modelled using the Mindlin–Reissner plate theory and the method of Hill's infinite determinants is applied to analyze the dynamic instability regions. Stiffened plates with cutout possessing different boundary conditions, aspect ratios, and cutout sizes considering and neglecting in-plane displacements have been analyzed for dynamic instability. The boundaries of the instability regions, including those of the principal one, are computed and presented graphically. These results are given in a non-dimensional form and illustrated by means of numerical examples.

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