Free vibration analysis of composite cylindrical shells with non-uniform thickness walls

Saira Javed,K.K. Viswanathan,Z. A. Aziz 국제구조공학회 2016 Steel and Composite Structures, An International J Vol.20 No.5

The paper proposes to characterize the free vibration behaviour of non-uniform cylindrical shells using spline approximation under first order shear deformation theory. The system of coupled differential equations in terms of displacement and rotational functions are obtained. These functions are approximated by cubic splines. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector which are spline coefficients. Four and two layered cylindrical shells consisting of two different lamination materials and plies comprising of same as well as different materials under two different boundary conditions are analyzed. The effect of length parameter, circumferential node number, material properties, ply orientation, number of lay ups, and coefficients of thickness variations on the frequency parameter is investigated.

Vibration analysis of a shear deformed anti-symmetric angle-ply conical shells with varying sinusoidal thickness

Saira Javed,K.K. Viswanathan,Z.A. Aziz,J.H. Lee 국제구조공학회 2016 Structural Engineering and Mechanics, An Int'l Jou Vol.58 No.6

The study is to investigate the free vibration of antisymmetric angle-ply conical shells having non-uniform sinusoidal thickness variation. The arbitrarily varying thickness is considered in the axial direction of the shell. The vibrational behavior of shear deformable conical shells is analyzed for three different support conditions. The coupled differential equations in terms displacement and rotational functions are obtained. These displacement and rotational functions are invariantly approximated using cubic spline. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration characteristic of the shells is examined for cone angle, aspect ratio, sinusoidal thickness variation, layer number, stacking sequence, and boundary conditions.

Free vibration of cross-ply laminated plates based on higher-order shear deformation theory

Saira Javed,K.K. Viswanathan,M.D. Nurul Izyan,Z. A. Aziz,J.H. Lee 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.26 No.4

Free vibration of cross-ply laminated plates using a higher-order shear deformation theory is studied. The arbitrary number of layers is oriented in symmetric and anti-symmetric manners. The plate kinematics are based on higher-order shear deformation theory (HSDT) and the vibrational behaviour of multi-layered plates are analysed under simply supported boundary conditions. The differential equations are obtained in terms of displacement and rotational functions by substituting the stress-strain relations and strain-displacement relations in the governing equations and separable method is adopted for these functions to get a set of ordinary differential equations in term of single variable, which are coupled. These displacement and rotational functions are approximated using cubic and quantic splines which results in to the system of algebraic equations with unknown spline coefficients. Incurring the boundary conditions with the algebraic equations, a generalized eigen value problem is obtained. This eigen value problem is solved numerically to find the eigen frequency parameter and associated eigenvectors which are the spline coefficients.The material properties of Kevlar-49/epoxy, Graphite/Epoxy and E-glass epoxy are used to show the parametric effects of the plates aspect ratio, side-to-thickness ratio, stacking sequence, number of lamina and ply orientations on the frequency parameter of the plate. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

Vibration of antisymmetric angle-ply laminated plates under higher order shear theory

Saira Javed,Z. A. Aziz,K. Karthik,J. H. LEE,K.K. Viswanathan 국제구조공학회 2016 Steel and Composite Structures, An International J Vol.22 No.6

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.

Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness under shear deformation theory

K.K.Viswanathan,Saira Javed,Zainal Abdul Aziz 국제구조공학회 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.45 No.2

Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness is analyzed under shear deformation theory with different boundary conditions by applying collocation with spline approximation. Linear and exponential variation in thickness of layers are assumed in axial direction. Displacements and rotational functions are approximated by Bickley-type splines of order three and obtained a generalized eigenvalue problem. This problem is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of three and five–layered conical shells, made up of two different type of materials are considered. Parametric studies are made for analysing the frequencies of the shell with respect to the coefficients of thickness variations, length-to-radius ratio, length-to-thickness ratio and ply angles with different combination of the materials. The results are compared with the available data and new results are presented in terms of tables and graphs.

Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness under shear deformation theory

Viswanathan, K.K.,Javed, Saira,Aziz, Zainal Abdul Techno-Press 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.45 No.2

Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness is analyzed under shear deformation theory with different boundary conditions by applying collocation with spline approximation. Linear and exponential variation in thickness of layers are assumed in axial direction. Displacements and rotational functions are approximated by Bickley-type splines of order three and obtained a generalized eigenvalue problem. This problem is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of three and five-layered conical shells, made up of two different type of materials are considered. Parametric studies are made for analysing the frequencies of the shell with respect to the coefficients of thickness variations, length-to-radius ratio, length-to-thickness ratio and ply angles with different combination of the materials. The results are compared with the available data and new results are presented in terms of tables and graphs.

Free vibration of symmetric angle ply truncated conical shells under different boundary conditions using spline method

K.K.Viswanathan,Z. A. Aziz,Saira Javed,Y. Yaacob,Babuji Pullepu 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.5

Free vibration of symmetric angle-ply laminated truncated conical shell is analyzed to determine the effects of frequency parameterand angular frequencies under different boundary condition, ply angles, different material properties and other parameters. The governingequations of motion for truncated conical shell are obtained in terms of displacement functions. The displacement functions are approximatedby cubic and quintic splines resulting into a generalized eigenvalue problem. The parametric studies have been made and discussed.