Free and Forced Vibration Analysis of Composite Laminated Conical Shells under Different Boundary Conditions Via Galerkin Method

Document Type: Persian

Authors

1 M.Sc., Islamic Azad University, Takestan Branch

2 Associate Professor, Department of Mechanical Engineering, University of Guilan

3 Ph.D. Student, Department of Mechanical Engineering , University of Guilan

Abstract

In this paper, natural frequency and response of forced vibration of composite laminated conical shells under different boundary conditions are investigated. To this end, equations of Donnell's thin shell theory are used as governing equations. The analytical Galerkin method together with beam mode shapes as weighting functions is employed to solve the problem. Due to importance of boundary conditions upon the mechanical behavior of conical shells, the analysis is carried out for all possible boundary conditions. The response of forced vibration is calculated via the modal participation factor method. Numerical comparisons of free vibration with the results in the open literature are made to validate the present methodology.

Keywords


[1] Wilkins D. J., Bert C. W., Egle D. M., Free vibrations of orthotropic sandwich conical shells with various boundary conditions, Journal of Sound and Vibration, Vol. 13, 1970, pp. 211-228.

[2] Irie T., Yamada G., Muramoto Y., Free vibration of joined conical-cylindrical shells, Journal of Sound and Vibration, Vol. 95, 1984,  pp. 31-39.

[3] Thambiratnam, D. P., Zhuge Y., Axisymmetric free vibration analysis of conical shells, Engineering Structures, Vol. 15, 1993, pp. 83-89.

[4] Shu C., An efficient approach for free vibration analysis of conical shells, International Journal of Mechanical Sciences, Vol. 38, 1996, pp. 935-949.

 

[5] Lam K. Y., Hua L., On free vibration of a rotating truncated circular orthotropic conical shell, Composites Part B: Engineering, Vol. 30, 1999, pp. 135-144.

[6] Hu H. T., Ou S. C., Maximization of the fundamental frequencies of laminated truncated conical shells with respect to fiber orientations, Composite Structures, Vol. 52, 2001, pp. 265-275.

[7] Wu C. P., Lee C. Y., Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness, International Journal of Mechanical Sciences, Vol. 43, 2001, pp. 1853-1869.

[8] Hu X. X., Sakiyama T., Matsuda H., Morita C., Vibration of twisted laminated composite conical shells, International Journal of Mechanical Sciences, Vol. 44, 2002, pp. 1521-1541.

[9] Civalek O., An efficient method for free vibration analysis of rotating truncated conical shells, International Journal of Pressure Vessels and Piping, Vol. 83, 2006, pp. 1-12.

[10] Liang S., Chen H. L., Chen T., Wang M. Y., The natural vibration of a symmetric cross-ply laminated composite conical-plate shell, Composite Structures, Vol. 80, 2007, pp. 265-278.

[11] Tripathi V., Singh B. N., Shukla K. K., Free vibration of laminated composite conical shells with random material properties, Composite Structures, Vol.  81, 2007, pp. 96-104.

[12] Civalek O., Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: Discrete singular convolution (DSC) approach, Journal of Computational and Applied Mathematics, Vol. 205, 2007, pp. 251-271.

[13] 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, International Journal of Pressure Vessels and Piping, 86, Vol. 2009, pp. 661-668.

[14] Sofiyev A. H., The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure, Composite Structures, Vol. 89, 2009, pp. 356-366.

[15] 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, Applied Mathematical Modeling, Vol. 34, 2010, pp. 1807-1822.

 [16]conical shells - A finite element approach, Composite Structures, Vol. 94, 2012, pp. 2188-2196.

[17] Sofiyev A. H., Kuruoglu N., Vibration analysis of FGM truncated and complete conical shells resting on elastic foundations under various boundary conditions, Journal of Engineering Mathematics, Vol. 77, 2012, pp. 131- 145.

[18]Malekzadeh P., Heydarpour Y., Free vibration analysis of rotating functionally graded truncated conical shells, Composite structures, Vol. 97, 2013, pp. 176-188.

[19]Civalek O., Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory, Composites Part B: Engineering, Vol. 45, 2013, pp. 1001-1009.

[20] Qatu M. S., Sullivan R. W., Wang W., Recent research advances on the dynamic analysis of composite shells: 2000-2009, Composite structures, Vol. 93. 2010, pp. 14-31.

[21] Soedel W., Vibrations of Shells and Plates, 2004, Marcel Dekker, Inc., New York.

[22] Loy, C. T., Lam, K. Y., Vibration of Cylindrical Shells with Ring Support, International Journal of Mechanical Sciences, Vol. 39, 1997, pp. 445–471.

[23] Irie T., Yamada G., Tanaka K., Natural frequencies of truncated conical shells, Journal of Sound and Vibration, Vol. 92, 1984, pp. 447-453.

[24] Lam K. Y., Li H., On free vibration of rotating truncated orthotropic conical shell, Composite, Vol. 30, 1999, pp. 135-44.

[25] 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, Mechanics Research Communications, Vol. 36, 2009, pp. 595-602

[26] Shu C., Free vibration analysis of composite laminated conical shells by generalized differential quadrature, Journal of Sound and Vibration, Vol. 194, 1996, pp. 587-604.