free vibration analysis of composite hemispherical shells with cut-out

Abstract

Nowadays growing interest is shown in structural design in different branches of modern technology. Hence various theories for analysis of shell-type structures are developed. The analysis of shells of revolution such as cylindrical and spherical shells for their applications in engineering fields,i.e., aerospace equipment and high speed rockets are immensely interesting subjects for researchers. Since composite materials are widely used because of their structural advantages, mathematical modeling of such structures is of prime interest and importance. In this paper, with using semi analytical finite element , free vibration of composite hemi-spherical shells with cut-out at apex was investigated. The effect of amount of cut-out at apex, fiber angles and boundary conditions were studied, too. For deriving of strain relationship first order shear deformation theory was used. The obtained results from the present analysis are compared with some available published results to show the accuracy and robustness of the present work.

Keywords

Main Subjects


[1] Niordson FI (1984) Free vibration of thin elastic spherical shells. Int J Sol & Structures 20: 667–687.
[2] Ramakrishnan CV, Shah AH (1970) Vibration of aeolotropic spherical shells. J Acoust Sot Amer 47: 1366–1374.
[3] Hoppmann WH, Baronet CN (1963) A study of the vibrations of shallow spherical shells. Trans ASME, J ApplMech 30: 326–334.
[4] Ross EW (1965) Natural frequencies and mode shapes for axisymmetric vibrations of deep spherical shells. ASME, J ApplMech 32: 553–561.
[5] Navaratna DR (1966) Natural vibration of deep spherical shells. AIAA J 4: 2056–2058.
[6] Lam KY, Loy CT (1995) Influence of boundary conditions and fiber orientation on the natural frequencies of thin orthotropic laminated cylindrical shells. Compos Struct31: 21–30.
[7] Archer RR (1962) On the influence of uniform stress states on the natural frequencies of spherical shells.Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics 29: 502–505.
[8] Goncalves PB (1994) Axisymmetric vibrations of imperfect shallow spherical caps under pressure loading. Journal of Sound and Vibration 174(2): 249–260.
[9] Ganesan N,Kadoli R (2004) Studies on linear thermoelastic buckling and free vibration analysis of geometrically perfect hemispherical shells with cut-out. J Sound & Vibration 27(7): 855–879.
[10] Lam KY, Qian Wu (2000) Free vibration of symmetric angle-ply thick laminated composite cylindrical shells. J Compos: part 31: 345–354.
[11] Sang-Youl Lee, Dae-Seouk Chung (2010) Finite element delamination model for vibrating composite spherical shell panels with central cutouts. Finite Elements in Analysis and Design 46(3): 247–256.
[12] Mohamad S Qatu, EbrahimAsadi (2012) Vibration of doubly curved shallow shells with arbitrary boundaries. Applied Acoustics 73(1): 21–27.
[13] Koteswara D Rao, Blessington PJ, R Tarapada (2012) Finite element modeling and analysis of functionally graded (FG) composite shell structures. Procedia Engineering 38: 3192–3199.
[14] YegaoQu, Xinhua Long, Shihao Wu, GuangMeng (2013) A unified formulation for vibration analysis of composite laminated shells of revolution including shear deformation and rotary inertia. Composite Structures 98: 169–191.
[15] Hosseini-Hashemi SH, Fadaee M (2011) On the free vibration of moderately thick spherical shell panel–A new exact closed-form procedure. J Sound Vib 330(17):4352–4367.
[16] Sai Ram KS, SreedharBabu T (2002) Free vibration of composite spherical shell cap with and without a cutout. Computers and Structures 80: 749–1756.
[17] Kadoli R,Ganesan N (2005) A theoretical analysis of linear thermoelastic buckling of composite hemispherical shells with a cut-out at the apex. J Composite Structures 68: 87–101.
[18] Toorani MH,Lakis AA (2000) General equations of anisotropic plates and shells including transverse shear deformations, rotary inertia and initial curvature effects. J Sound Vib 237(4): 561–615.
[19] Kraus H (1967) Thin elastic shells, Chap 1, John Wiely, New York.
[20] Gautham BP,Ganesan N (1992) Free Vibration Analysis of Thick Spherical Shells. J Computers & Structures 45(2): 307–313.