• Structural Engineering and Mechanics
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• 제64권3호
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• pp.381-390
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• 2017

Present paper deals with the large amplitude flexural vibration of carbon nanotube reinforced composite (CNTRC) plates. Distribution of CNTs as reinforcements may be uniform or functionally graded (FG). The equivalent material properties of the composite media are obtained according to a refined rule of mixtures which contains efficiency parameters. To account for the large deformations, von $K{\acute{a}}rm{\acute{a}}n$ type of geometrical nonlinearity is included into the formulation. The matrix representation of the governing equations is obtained according to the Ritz method where the basic shape functions are written in terms of the Chebyshev polynomials. Time dependency of the problem is eliminated by means of the Galerkin method and the resulting nonlinear eigenvalue problem is solved employing a direct displacement control approach. Results are obtained for completely clamped and completely simply supported plates. Results are first validated for the especial cases of FG-CNTRC and cross-ply laminated plates. Afterwards, parametric studies are given for FG-CNTRC plates with different boundary conditions. It is shown that, nonlinear frequencies are highly dependent to the volume fraction and dispersion profiles of CNTs. Furthermore, mode redistribution is observed in both simply supported and clamped FG-CNTRC plates.

• Nuclear Engineering and Technology
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• 제41권3호
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• pp.335-346
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• 2009

This paper deals with a hydroelastic vibration analysis of two rectangular plates partially coupled with a liquid, which is bounded by two plates and two rigid side walls. The wet displacement of each plate is assumed to be a combination of the modal functions of a dry uniform beam with a clamped boundary condition. As the liquid is assumed to be an ideal liquid, the displacement potential satisfying the Laplace equation is determined so that the liquid boundary conditions can meet the requirements at the rigid surfaces and the free liquid surface. The wet dynamic modal functions of each plate are expanded by using the finite Fourier transform to obtain an appropriate form of the compatibility requirement along the contacting surfaces between the plates and the liquid. The liquid-coupled natural frequencies of the plates are derived by using the Rayleigh-Ritz method. Finite element analyses using commercial software are carried out to verify the proposed theory. It is observed that the theoretical method agrees excellently with the three-dimensional finite element analyses results. The effects of the liquid depth and the liquid thickness on the normalized natural frequencies are investigated to identify the dynamic characteristics of the liquid coupled system.

• Structural Engineering and Mechanics
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• 제3권1호
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• pp.49-60
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• 1995

In the present study, a finite strip method for the vibration and stability analyses of anisotropic laminated composite plates is developed according to the higher-order shear deformation theory. This theory accounts for the parabolic distribution of the transverse shear strains through the thickness of the plate and for zero transverse shear stresses on the plate surfaces. In comparison with the finite strip method based on the first-order shear deformation theory, the present method gives improved results for very thick plates while using approximately the same number of degrees of freedom. It also eliminates the need for shear correction factors in calculating the transverse shear stiffness. A number of numerical examples are presented to show the effect of aspect ratio, length-to-thickness ratio, number of plies, fibre orientation and stacking sequence on the natural frequencies and critical buckling loads of simply supported rectangular cross-ply and arbitrary angle-ply composite laminates.

• Structural Engineering and Mechanics
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• 제25권6호
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• pp.753-765
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• 2007

The response histories and distribution of dynamic interlaminar stresses in composite laminated plates under free vibration and thermal load is studied based on a thermoelastodynamic differential equations. The stacking sequence of the laminated plates may be arbitrary. The temperature change is considered as a linear function of coordinates in planes of each layer. The dynamic mode of displacements is considered as triangle series. The in-plane stresses are calculated by using geometric equations and generalized Hooke's law. The interlaminar stresses are evaluated by integrating the 3-D equations of equilibrium, and utilizing given boundary conditions and continuity conditions of stresses between layers. The response histories and distribution of interlaminar stress under thermal load are presented for various vibration modes and stacking sequence. The theoretical analyses and results are of certain significance in practical engineering application.

• Steel and Composite Structures
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• 제29권4호
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• pp.493-508
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• 2018

Free vibration analysis of super-elliptical composite thin plates was investigated. Plate is formed by symmetrical quasi-isotropic laminates. Rayleigh-Ritz method was used for parametric analysis based on the governing differential equations of Classical Laminated Plate Theory (CLPT). Simply supported and clamped boundary conditions at the periphery of plates were considered. Parametric study was performed for the effect of different lamination type, aspect ratio, thickness and super-elliptical power on natural frequencies. Convergence study and validation of isotropic case were achieved. A number of design parameters like different dimensions, structure systems, panel sizes, panel thicknesses, lamination sequences, boundary conditions and loading conditions must be considered in the production of composite ships. The number of possible combinations practically may be so high that a parametric study should be carried out in order to determine the optimum design parameters rapidly during the preliminary design stage. The use of Rayleigh-Ritz method could make this parametric study possible. Thereby it might be decreasing the consumption of time, material and labor. Certain results for some different super-elliptical powers presented in tabulated form in Appendix for designers as well.

• Structural Engineering and Mechanics
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• 제53권2호
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• pp.337-354
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• 2015

In this article, free vibration of functionally graded (FG) elliptic plates subjected to various classical boundary conditions has been investigated. Literature review reveals no study has been performed based on functionally graded elliptic plates till date. The mechanical kinematic relations are considered based on classical plate theory. Rayleigh-Ritz technique is used to obtain the generalized eigenvalue problem. The material properties of the FG plate are assumed to vary along thickness direction of the constituents according to power-law form. Trial functions denoting the displacement components are expressed in simple algebraic polynomial forms which can handle any edge support. The objective is to study the effect of geometric configurations and gradation of constituent volume fractions on the natural frequencies. New results for frequency parameters are incorporated after performing a test of convergence. A comparison study is carried out with existing literature for validation in special cases. Three-dimensional mode shapes for circular and elliptic FG plates are also presented with various boundary conditions at the edges.

• Steel and Composite Structures
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• 제18권1호
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• pp.91-120
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• 2015

A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates is presented in this paper. It contains only four unknowns, accounts for a hyperbolic distribution of transverse shear stress and satisfies the traction free boundary conditions. Equations of motion are derived from Hamilton's principle. The Navier-type and finite element solutions are derived for plate with simply-supported and various boundary conditions, respectively. Numerical examples are presented for functionally graded sandwich plates with homogeneous hardcore and softcore to verify the validity of the developed theory. It is observed that the present theory with four unknowns predicts the response accurately and efficiently.

• Architectural research
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• 제15권1호
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• pp.35-42
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• 2013

A study on the free vibration and linear buckling analyses of thick plates is described in this article. In order to determine the natural frequencies and buckling loads of plates, a plate element is developed by using isogeometric approach. The Non-uniform B-spline surface (NURBS) is used to represent both plate geometry and the unknown displacement field of plate. All terms required in isogeometric formulation are consistently derived by NURBS definition. The capability of the present plate element is demonstrated by using several numerical examples. From numerical results, it is found to be that the present isogeometric element can predict accurate natural frequencies and buckling loads of plates.

• Smart Structures and Systems
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• 제19권4호
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• pp.441-448
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• 2017

This paper uses the four-variable refined plate theory for the free vibration analysis of functionally graded material (FGM) rectangular plates. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Equations of motion are derived from the Hamilton's principle. The closed-form solutions of functionally graded plates are obtained using Navier solution. Numerical results of the refined plate theory are presented to show the effect of the material distribution, the aspect and side-to-thickness ratio on the fundamental frequencies. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of functionally graded plates.

• 한국소음진동공학회논문집
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• 제20권9호
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• pp.856-862
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• 2010

In this paper, the power flow analysis(PFA) method was developed to predict the vibrational responses of coupled co-planar orthotropic plates in frequencies ranging from medium to high. To cover the power transmission and reflection at the joint of the orthotropic plates, the wave transmission approach is applied with the assumption that all the incident waves are normal to the joint. Through numerical analyses, the power flow energy density and intensity fields of coupled co-planar orthotropic plates were compared with those of classical modal solutions by changing the frequency and internal loss factor, and they show good agreement in terms of the global decay and the attenuation patterns of the energy density.