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Free vibration analysis of truncated conical fiber metallaminate (FML) shells

Published online by Cambridge University Press:  18 December 2013

Faramarz Ashenai Ghasemi ,
Reza Ansari  and
Rahim Bakhodai Paskiabi
Faramarz Ashenai Ghasemi*
Affiliation:
Department of Mechanical Engineering, Shahid Rajaee Teacher Training University (SRTTU), 16788-15811 Lavizan, Tehran, Iran
Reza Ansari
Affiliation:
Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
Rahim Bakhodai Paskiabi
Affiliation:
Department of Mechanical Engineering, Shahid Rajaee Teacher Training University (SRTTU), 16788-15811 Lavizan, Tehran, Iran
*
⋆ Corresponding author:Faramarzashenaighasemi@yahoo.com
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Abstract

In this paper, an analytical solution is developed for free vibration analysis of conicalfiber metal shells. In order to find constitutive relations, the assumptions of thinshells are used and the governing equations are based on Love’s theory. The Galerkin methodis employed to solve the governing equations in which beam functions are used toapproximate the mode shapes. Using beam functions enables us to assess the effects ofdifferent boundary conditions on the frequency response of the shells. Numericalcomparisons of the present and previously published results confirm the accuracy of thecurrent approach. Additionally, the influences of geometrical parameters and embeddingaluminum plies in different layers of the structure on natural frequency of the conicalshells with various boundary conditions are investigated. It can be observed that the morethe aluminum plies are used, the greater natural frequency of the structure will bereached. Except the clamped-free boundary conditions, the results also indicate that ifthe aluminum plies are embedded in the top and bottom layers of the laminate, naturalfrequency reaches its maximum value.

Keywords

Conical shellfree vibrationGalerkin methodbeam function
Type
Research Article
Information
Mechanics & Industry , Volume 14 , Issue 5 , 2013 , pp. 367 - 382
Copyright
© AFM, EDP Sciences 2013

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References

Wilkins, D.J., Bert, C.W., Egle, D.M., Free vibrations of orthotropic sandwich conical shells with various boundary conditions, J. Sound. Vib. 13 (1970) 211–228 CrossRefGoogle Scholar
Ramsey, H., Contrast between elastic and plastic buckling of axially compressed conical shells with edge constraint, Int. J. Mech. Sci. 20 (1978) 37–46 CrossRefGoogle Scholar
Irie, T., Yamada, G., Muramoto, Y., Free vibration of joined conical-cylindrical shells, J. Sound. Vib. 95 (1984) 31–39 CrossRefGoogle Scholar
Zhou, H., Liu, D., Mechanical analysis of the elastic buckling of an orthogonal anisotropic circular conical shell under uniform external pressure, Int. J. Pres. Ves. Pip. 48 (1991) 111–122 CrossRefGoogle Scholar
Thambiratnam, D.P., Zhuge, Y., Axisymmetric free vibration analysis of conical shells, Eng. Struct. 15 (1993) 83–89 CrossRefGoogle Scholar
Shu, C., An efficient approach for free vibration analysis of conical shells, Int. J. Mech. Sci. 38 (1996) 935–949 CrossRefGoogle Scholar
Spagnoli, A., Chryssanthopoulos, M.K., Elastic buckling and post buckling behaviour of widely-stiffened conical shells under axial compression, Eng. Struct. 21 (1999) 845–855 CrossRefGoogle Scholar
Lam, K.Y., Hua, L., On free vibration of a rotating truncated circular orthotropic conical shell, Compos. Part B: Eng. 30 (1999) 135–144 CrossRefGoogle Scholar
Spagnoli, A., Different buckling modes in axially stiffened conical shells, Eng. Struct. 23 (2001) 957–965 CrossRefGoogle Scholar
Hu, H.T., Ou, S.C., Maximization of the fundamental frequencies of laminated truncated conical shells with respect to fiber orientations, Compos. Struct. 52 (2001) 265–275 CrossRefGoogle Scholar
Wu, C.P., Lee, C.Y., Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness, Int. J. Mech. Sci. 43 (2001) 1853–1869 CrossRefGoogle Scholar
Hu, X.X., Sakiyama, T., Matsuda, H., Morita, C., Vibration of twisted laminated composite conical shells, Int. J. Mech. Sci. 44 (2002) 1521–1541 CrossRefGoogle Scholar
Goldfeld, Y., Arbocz, J., Rothwell, A., Design and optimization of laminated conical shells for buckling, Thin Wall. Struct. 43 (2005) 107–133 CrossRefGoogle Scholar
Ross, C.T.F., Little, A.P.F., Adeniyi, K.A., Plastic buckling of ring-stiffened conical shells under external hydrostatic pressure, Ocean Eng. 32 (2005) 21–36 CrossRefGoogle Scholar
Civalek, O., An efficient method for free vibration analysis of rotating truncated conical shells, Int. J. Pres. Ves. Pip. 83 (2006) 1–12 CrossRefGoogle Scholar
Gupta, N.K., Mohamed Sheriff, N., Velmurugan, R., A study on buckling of thin conical frusta under axial loads, Thin Walled. Struct. 44 (2006) 986–996 CrossRefGoogle Scholar
Liang, S., Chen, H.L., Chen, T., Wang, M.Y., The natural vibration of a symmetric cross-ply laminated composite conical-plate shell, Compos. Struct. 80 (2007) 265–278 CrossRefGoogle Scholar
Tripathi, V., Singh, B.N., Shukla, K.K., Free vibration of laminated composite conical shells with random material properties, Compos. Struct. 81 (2007) 96–104 CrossRefGoogle Scholar
Civalek, O., Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: Discrete singular convolution (DSC) approach, J. Comput. Appl. Math. 205 (2007) 251–271 CrossRefGoogle Scholar
Sofiyev, A.H., Kuruoglu, N., Turkmen, M., Buckling of FGM hybrid truncated conical shells subjected to hydrostatic pressure, Thin Walled. Struct. 47 (2009) 61–72 CrossRefGoogle Scholar
Sofiyev, A.H., Korkmaz, K.A., Mammadov, Z., Kamanli, M., The vibration and buckling of freely supported non-homogeneous orthotropic conical shells subjected to different uniform pressures, Int. J. Pres. Ves. Pip. 86 (2009) 661–668 CrossRefGoogle Scholar
Sofiyev, A.H., The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure, Compos. Struct. 89 (2009) 356–366 CrossRefGoogle Scholar
Sofiyev, A.H., Kuruoglu, N., Halilov, H.M., The vibration and stability of non-homogeneous orthotropic conical shells with clamped edges subjected to uniform external pressures, Appl. Math. Model. 34 (2010) 1807–1822 CrossRefGoogle Scholar
Sofiyev, A.H., Influence of the initial imperfection on the non-linear buckling response of FGM truncated conical shells, Int. J. Mech. Sci. 53 (2011) 753–761 CrossRefGoogle Scholar
Lachut, J.B., On elasti–plastic buckling of cones, Thin Walled. Struct. 49 (2011) 45–52 CrossRefGoogle Scholar
Sofiyev, A.H., Non-linear buckling behavior of FGM truncated conical shells subjected to axial load, Int. J. Nonlinear Mech. 46 (2011) 711–719 CrossRefGoogle Scholar
Sofiyev, A.H., Kuruoglu, N.K., The non-linear buckling analysis of cross-ply laminated orthotropic truncated conical shells, Compos. Struct. 93 (2011) 3006–3012 CrossRefGoogle Scholar
Nedelcu, M., GBT formulation to analyses of the buckling behaviour of isotropic conical shells, Thin Walled. Struct. 49 (2011) 812–818 CrossRefGoogle Scholar
A. Vlot, Historical overview In: Fibre metal laminates, an introduction, Dordrecht, Kluwer Academic Publishers, 2001
M.S. Qatu, Vibration of laminated shells and plates, San Diego CA, Elsevier, 2004
W. Soedel, Vibrations of shells and plates New York, Marcel Dekker, 1993
Loy, C.T., Lam, K.Y., Vibration of Cylindrical Shells with Ring Support, Int. J. Mech. Sci. 39 (1997) 445–471 CrossRefGoogle Scholar
Irie, T., Yamada, G., Tanaka, K., Natural frequencies of truncated conical shells, J. Sound. Vib. 92 (1984) 447–453 CrossRefGoogle Scholar
Li, F.M., Kishimoto, K., Huang, W.H., The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh-Ritz method, Mech. Res. Commun. 36 (2009) 595–602 CrossRefGoogle Scholar
Shu, C., Free vibration analysis of composite laminated conical shells by generalized differential quadrature, J. Sound. Vib. 194 (1996) 587–604 CrossRefGoogle Scholar