Author

# K. Karthik

Bio: K. Karthik is an academic researcher from Universiti Teknologi Malaysia. The author has contributed to research in topic(s): Antisymmetric relation & Boundary value problem. The author has an hindex of 2, co-authored 3 publication(s) receiving 6 citation(s).

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TL;DR: In this paper, the analysis of vibration of angle-ply plates using spline method for higher order shear theory is addressed to show the capability of the present method in the vicinity of higher-order shear deformation theory and simply supported edges of plates.
Abstract: This paper deals with the analysis of vibration of antisymmetric angle-ply plates using spline method for higher order shear theory. Free vibration of laminated plates is addressed to show the capability of the present method in the vicinity of higher order shear deformation theory and simply supported edges of plates. The coupled differential equations are obtained in terms displacement and rotational functions. These displacement and rotational functions are approximated using cubic and quantic spline. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The antisymmetric angle-ply fiber orientation are taken as design variables. Numerical results enable us to examine the frequencies for various geometric and material parameters and accuracy and effectiveness of the proposed method is also verified by comparative study.

4 citations

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TL;DR: In this paper, the free vibration of angle-ply laminated plates under clamped boundary conditions was analyzed using radial basis functions and Spline functions, and parametric studies were made to investigate the effect of aspect ratio, length-to-thickness ratio, number of layers, fiber orientation and material properties with respect to the frequency parameter.
Abstract: Abstract Two type of numerical approach namely, Radial Basis Function and Spline approximation, used to analyse the free vibration of anti-symmetric angle-ply laminated plates under clamped boundary conditions. The equations of motion are derived using YNS theory under first order shear deformation. By assuming the solution in separable form, coupled differential equations obtained in term of mid-plane displacement and rotational functions. The coupled differential is then approximated using Spline function and radial basis function to obtain the generalize eigenvalue problem and parametric studies are made to investigate the effect of aspect ratio, length-to-thickness ratio, number of layers, fibre orientation and material properties with respect to the frequency parameter. Some results are compared with the existing literature and other new results are given in tables and graphs.

2 citations

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21 Jun 2016
TL;DR: In this paper, the spline and radial basis functions of base mesh free scheme are applied simultaneously to approximate the displacement and rotational functions of angle-ply composite plates, including shear deformation under clamped-clamped boundary conditions.
Abstract: In this study free vibrations of anti-symmetric angle-ply composite plates including shear deformation under clamped-clamped boundary conditions are presented. Two types of numerical methods are adopted to analyze the problem. The spline and radial basis functions base mesh free scheme are applied simultaneously to approximate the displacement and rotational functions. Comparative studies have been made for analyzing the frequency parameters with respect to the material properties, number of layers, fiber orientations, side-to-thickness ratio and aspect ratio. The results are depicted in terms of tables and graphs.

##### Cited by
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TL;DR: In this article, a simple nth-higher-order shear deformation theory was proposed to analyze the vibration behavior of rectangular orthotropic and laminated composite plates, where the transverse displacement is divided into two bending and shear components and the unknown involved functions are reduced to four.
Abstract: In this article, vibration behavior of composite rectangular plates are investigated by using a refined simple nth-higher-order shear deformation theory. Governing equations are derived by using Hamilton’s principle. A closed-form solution via Navier’s technique limits the applicability of solution technique to simply-supported rectangular laminated plates. The transverse displacement is dividing into two bending and shear components and so the unknown involved functions is reduced to four, as against five or more in other plate theories. There is no need for any shear correction factors to the present theory. Moreover, it is variationally consistent, used nth-order polynomial term to represent displacement field and gave rise to transverse shear stresses satisfying free surface conditions. Numerical results due to present theory are compared with data available in the literature to show the accuracy and simplicity of the proposed theory in analyzing the vibration frequencies of rectangular orthotropic and laminated composite plates.

15 citations

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TL;DR: In this article, the free vibration of composite laminated conical shells based on higher order shear deformation theory is analyzed for simply supported end condition and coupled differential equations in terms displacement and rotational functions are invariantly approximated using cubic and quantic spline.
Abstract: The purpose of this research is to analyse the free vibration of composite laminated conical shells based on higher order shear deformation theory. The vibrational behavior of multi-layered conical shells are analyzed for simply supported end condition. The coupled differential equations in terms displacement and rotational functions are obtained. These displacement and rotational functions are invariantly approximated using cubic and quantic spline. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The different materials are used to show the parametric effects of shell’s length ratio, cone angle, stacking sequence and number of lamina on the frequency of the conical shells. The numerical results obtained using spline approximation are validated through existing literature.

8 citations

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TL;DR: A review of the development and applications of shear deformation (SD) laminated composite plate theories can be found in this article, where the authors mainly focus on theoretical models based on SD theories.
Abstract: This review, overviews the development and applications of shear deformation (SD) laminated composite plate theories. The present overview mainly focuses on theoretical models based on SD theories ...

4 citations

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TL;DR: In this article, the free vibration of angle-ply laminated plates with variable thickness is studied and a generalized eigenvalue problem is obtained and solved numerically by employing the eigensolution techniques with eigenvectors as spline coefficients to obtain the required frequencies.
Abstract: Free vibration of antisymmetric angle-ply laminated plates with variable thickness is studied. Higher-order shear deformation plate theory (HSDT) is introduced in the present method to remove the shear correction factors and improve the accuracy of transverse shear stresses. The thickness variations are assumed to be linear, exponential, and sinusoidal. The coupled differential equations are obtained in terms of displacement and rotational functions and approximated using cubic and quantic spline. A generalized eigenvalue problem is obtained and solved numerically by employing the eigensolution techniques with eigenvectors as spline coefficients to obtain the required frequencies. The results of numerical calculations are presented for laminated plates with simply supported boundary conditions. Comparisons of the current solutions and those reported in literature are provided to verify the accuracy of the proposed method. The effects of aspect ratio, number of layers, ply-angles, side-to-thickness ratio, and materials on the free vibration of cylindrical plates are discussed in detail.

2 citations

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TL;DR: In this article, an analytical solution for determining the fundamental frequency of a fully clamped composite anisotropic laminated plate is presented, which is composed of unidirectional composite plies oriented at some angle to one of the plate sides.
Abstract: An analytical solution determining the fundamental frequency of a fully clamped composite anisotropic laminated plate is presented in the paper. The plate is composed of unidirectional composite plies oriented at some angle to one of the plate sides. The plies alternating over the plate thickness differ from each other by only the sign of the angle of orientation. Such a plate is characterised by the structural anisotropy with the extension-twisting and bending-shear coupling effects which are taken into account in the appropriate constitutive equations. The governing equations model the coupled in-plane and out-of-plane plate motions. The vibration problem is solved using the Galerkin method. The beam functions corresponding to the first vibration mode of a beam with clamped ends are employed as the approximating functions. The problem is reduced to a solution of cubic algebraic equation. Based on this solution, effects of the angle of reinforcement orientation and number of plies on the fundamental frequency of the plate with structural anisotropy are investigated. The results are verified using finite element method. An assessment of the anisotropy effect on the frequency value has been performed by comparison with the results obtained based on the orthotropic model of the plate. The formula providing the number of plies for a plate with structural anisotropy is derived for the prescribed fundamental frequency.

1 citations