Prediction of Vibrational Behavior of Composite Cylindrical Shells under Various Boundary Conditions
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Prediction of Vibrational Behavior of Composite Cylindrical Shells under Various Boundary Conditions Milad Hemmatnezhad & Reza Ansari & Mansour Darvizeh
Received: 6 April 2009 / Accepted: 20 October 2009 / Published online: 26 November 2009 # Springer Science + Business Media B.V. 2009
Abstract In this paper, a unified analytical approach is applied to investigate the vibrational behavior of composite cylindrical shells. Theoretical formulation is established based on Sanders’ thin shell theory. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stoke's transformation. The Influence of some commonly used boundary conditions and the effect of variations in shell geometrical parameters on the shell frequencies are studied. The results obtained for a number of particular cases show good agreement with those available in the open literature. The simplicity and the capability of the present method are also discussed. Keywords Composite cylindrical shells . Exact . Arbitrary boundary conditions . Sanders’ theory
1 Introduction The vibration analysis of thin orthotropic cylindrical shells (e.g. frequencies, mode shapes, and modal forces) has been expanded rapidly in the past decades. There are considerable researches and interests in this field due to the importance of shell structures in civil, mechanical and aerospace engineering (e.g. launch vehicles, re-entry vehicles, aircraft fuselages, spacecrafts, etc.) in particular. An excellent collection of research in this area was carried out by Leissa [1]. There are also some good reviews on vibration of composite shell using experimental [2, 3] and analytical methods [4–9]. Due to the complexity of engineering characteristics of composite shell type structures, analytical solutions cannot be obtained in a straight forward manner. Therefore, numerical techniques such as the differential quadrature method (DQM) and the finite element method (FEM) attracted
M. Hemmatnezhad : R. Ansari (*) : M. Darvizeh Department of Mechanical Engineering, University of Guilan, P.O. Box 3756 Rasht, Iran e-mail: [email protected]
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Appl Compos Mater (2010) 17:225–241
intense interest to many research workers. Bert and Malik [10], Sharma et al. [11] and Haftchenari et al. [12] analyzed the free vibration of laminated cylindrical shells with different boundary conditions using DQM. Kadoli and Ganesan [13, 14] studied the buckling and free vibration behavior of composite and piezothermoelastic composite cylindrical shells using FEM. A detailed review on the effects of the inclusion of shear deformation and rotary inertia terms and changes in shell geometry on the frequencies, mode shapes and modal forces can be found in the previous work of the present authors [15]. In that work, theoretical formulations are based on the First order Shear Deformation Theory (FSDT) and the modal forms are assumed to have an axial dependency in the form of a simple Fourier series whose derivatives are legitimized by Stoke’s tran
