Calculating the frequency of composite plate and composite spherical shell with different boundary conditions
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2018-11-05 https://doi.org/10.14419/ijet.v7i4.25887 -
Abstract
In this work, the Fourier-Ritz approach is used to calculate the natural non- dimensional frequency of composite plate and composite spherical shell with different arrangements of layers (cross and angle ply and symmetrical and anti-symmetrical layers) and different boundary conditions. The Fourier-Ritz approach is the modified Fourier series in connection with a  Ritz technique  to deduce the formulation based on the classical shallow shell theory. Additionally, the Finite Element method (FEM) (ANSYS Software Version 17.2) is used in this work for predicting the natural non- dimensional frequency of composite plate and composite spherical shell. The effect of (b/a) ratio on non- dimensional frequency of composite plate and composite spherical shell is studied for different layers arrangements when the boundary conditions are (CCCC) and (SSSS). The comparisons between the non- dimensional frequency results are made.
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References
[1] Leissa, A. W., Lee, J. K., and Wang, A. J. ‘Vibrations of cantilevered shallow cylindrical shells of rectangular planform’, J. Sound Vib., vol. 78, pp. 311-328, 1981. https://doi.org/10.1016/S0022-460X(81)80142-3.
[2] Narita, Y., and Leissa, A. W. ‘Vibrations of corner point supported shallow shells of rectangular planform’, Earthq. Eng. Struct D, vol. 12, pp. 651-661, 1984. https://doi.org/10.1002/eqe.4290120506.
[3] Qatu, M. S., and Leissa, A. W. ‘Free vibrations of completely free doubly curved laminated composite shallow shells’, J. Sound Vib., vol. 151, pp. 9-29, 1991. https://doi.org/10.1016/0022-460X(91)90649-5.
[4] Lim, C. W., and Liew, K. M. A. ‘pb-2 Ritz formulation for flexural vibration of shallow cylindrical shells of rectangular plan form’, J. Sound Vib., vol. 73, pp. 343-375, 1994. https://doi.org/10.1006/jsvi.1994.1235.
[5] Young, P. G., and Dickinson, S. M. ‘Vibration of a class of shallow shells bounded by edges described by polynomials, part I: theoretical approach and validation’, J. Sound Vib., vol. 181, pp. 203-214, 1995. https://doi.org/10.1006/jsvi.1995.0135.
[6] Young, P. G., and Dickinson, S. M. ‘Vibration of a class of shallow shells bounded by edges described by polynomials Part II: natural frequency parameters for shallow shells of various different plan forms’, J. Sound Vib., vol. 181, pp. 215-230, 1995. https://doi.org/10.1006/jsvi.1995.0136.
[7] Qatu, M. S. ‘Vibration studies on completely free shallow shells having triangular and trapezoidal plan forms’, Appl Acoust, vol. 44, pp. 215-231, 1995. https://doi.org/10.1016/0003-682X(94)00020-V.
[8] Qatu, M. S. ‘Vibration analysis of cantilevered shallow shells with triangular and trapezoidal plan forms’, J. Sound Vib., vol. 191, pp. 219-231, 1996. https://doi.org/10.1006/jsvi.1996.0117.
[9] Zhang, X. M., Liu, G. R., and Lam, K. Y. ‘Frequency analysis of cylindrical panels using a wave propagation approach’, Appl. Acoust, vol. 62, pp. 527-543, 2001. https://doi.org/10.1016/S0003-682X(00)00059-1.
[10] Qatu, M. S. ‘Effect of in plane edge constraints on natural frequencies of simply supported doubly curved shallow shells’, Thin-Wall Struct., vol. 49, pp. 797-803, 2011. https://doi.org/10.1016/j.tws.2011.01.001.
[11] Monterrubio, L. E. ‘Free vibration of shallow shells using the Rayleigh—Ritz method and penalty parameters’, Proc. Inst. Mech. Eng., Part C, J. Mech. Eng. Sci., vol. 223, pp. 2263-2272, 2009. https://doi.org/10.1243/09544062JMES1442.
[12] Qatu, M. S., and Asadi, E. ‘Vibration of doubly curved shallow shells with arbitrary boundaries’, Appl. Acoust., vol. 73, pp. 21-27, 2012. https://doi.org/10.1016/j.apacoust.2011.06.013.
[13] Liew, K. M., and Lim, C. W. ‘A higher-order theory for vibration analysis of curvilinear thick shallow shells with constrained boundaries’, J. Vib. Control, vol. 1, pp. 15-39, 1995.
[14] Liew, K. M., and Lim, C. W. ‘A higher-order theory for vibration of doubly curved shallow shells’, J. Appl. Mech., vol. 63, pp. 587-593, 1996. https://doi.org/10.1115/1.2823338.
[15] Liew, K. M., Lim, C. W. ‘Vibration of thick doubly-curved stress-free shallow shells of curvilinear plan form’, J. Eng. Mech., vol. 123, pp. 413-421, 1997. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:5(413).
[16] Matsunaga, H. ‘Vibration and stability of thick simply supported shallow shells subjected to in-plane stresses’, J. Sound Vib., vol. 225, pp. 41-60, 1999. https://doi.org/10.1006/jsvi.1999.2234.
[17] Bhimaraddi, A. ‘Free vibration analysis of doubly curved shallow shells on rectangular planform using three-dimensional elasticity theory’, Int. J. Solids Struct., vol. 27, pp. 897-913, 1991. https://doi.org/10.1016/0020-7683(91)90023-9.
[18] Liew, K. M., and Lim, C. W. ‘A Ritz vibration analysis of doubly-curved rectangular shallow shells using a refined first-order theory’, Comput. Methods Appl. Mech. Eng. vol. 127, pp. 145-162, 1995. https://doi.org/10.1016/0045-7825(95)00837-1.
[19] Chakravorty. D., and Bandyopadhyay, J. N. ‘On the free vibration of shallow shells’, J. Sound Vib., vol. 185, pp. 673-684, 1995. https://doi.org/10.1006/jsvi.1995.0408.
[20] Liew, K. M., and Lim, C. W. ‘Vibration studies on moderately thick doubly-curved elliptic shallow shells’, Acta. Mech., vol. 116, pp. 83-96, 1996. https://doi.org/10.1007/BF01171422.
[21] Lim, C. W., Li, Z. R., and Wei, G. W. ‘DSC-Ritz method for high-mode frequency analysis of thick shallow shells’, Inter J. Numer. Methods Eng., vol. 62, pp. 205-232, 2005. https://doi.org/10.1002/nme.1179.
[22] Qatu, M. S. ‘Natural vibration of free, laminated composite triangular and trapezoidal shallow shells’, composites structure, vol. 31, pp. 9–19, 1995.
[23] Khdeir, A. A., Reddy, J. N. ‘Free and forced vibration of cross-ply laminated composite shallow arches’, Int. Solids Structure, vol. 34, pp. 1217–34, 1997. https://doi.org/10.1016/S0020-7683(96)00095-9.
[24] Soldatos, K. P., and Shu, X. P. ‘On the stress analysis of cross-ply laminated plates and shallow shell panels’, Composites Structure, vol. 46, pp. 333–44, 1999. https://doi.org/10.1016/S0263-8223(99)00061-6.
[25] Reddy, J. N. ‘Mechanics of laminated composite plates and shells: theory and analysis. 2nd’, CRC Press, 2004. https://doi.org/10.1201/b12409.
[26] Qatu, M. S. ‘Vibration of laminated shells and plates’, San Diego: Elsevier, 2004.
[27] Ferreira, AJM., Castro, L. M., Bertoluzza, S. ‘A wavelet collocation approach for the analysis of laminated shells’, Compos Part B: Eng., vol. 42, pp. 99-04, 2011. https://doi.org/10.1016/j.compositesb.2010.06.003.
[28] Ferreira, AJM., Carrera, E., Cinefra, M., and Roque, CMC. ‘Analysis of laminated doubly curved shells by a layerwise theory and radial basis functions collocation, accounting for through-the-thickness deformations’, Compute Mech., vol. 48, pp. 13-25, 2011. https://doi.org/10.1007/s00466-011-0579-4.
[29] Qatu, M. S., and Asadi, E. ‘Vibration of doubly curved shallow shells with arbitrary boundaries’, Appl. Acoustic., vol. 73, pp. 21–7, 2012. https://doi.org/10.1016/j.apacoust.2011.06.013.
[30] Sayan, B. and Bhavani, V. ‘Mechanical properties of hybrid composites using finite element method-based micromechanics’, composites: part B, vol. 58, pp. 318-327, 2014.
[31] Guoyong, J., Shuangxia S., Zhu S., Shouzuo, L. and Zhigang, L. ‘A modified Fourier-Ritz approach for free vibration analysis of laminated functionally graded shallow shells with general boundary conditions’, International Journal of Mechanical Sciences, http://dx.doi.org/10.1016 j ijmecsci...02.006, 2015.
[32] Qingshan, W., Dongyan, S., Fuzhen, P., and Qian L. ‘Vibrations of composite laminated circular panels and shells of revolution with general elastic boundary conditions via fourier-ritz method’, http://dx.doi.org/10.1515/cls accepted, 2016.
[33] Wang, Q., Cui, X., Qin, B., and Liang, Q. ‘Vibration analysis of the functionally graded carbon nanotube reinforced composite shallow shells with arbitrary boundary conditions, composite structures’, http://doi.org/10.1016/j. compstruct, vol. 9, p.p. 43, 2017.
[34] Guoyong, J., Tiangui, Y., and Zhu S. ‘Structural Vibration: A Uniform Accurate Solution for Laminated Beams, Plates and Shells with General Boundary Conditions’, Science Press, Beijing and Springer-Verlag Berlin Heidelberg, 2015.
[35] Singiresu, S. R. ‘Mechanical Vibrations’, Fifth Edition, Pearson Education, Inc., publishing as Prentice Hall, 1 Lake Street, Upper Saddle River, NJ 07458, 2004.
[36] Wang ‘vibration of thin skew fiber reinforced composite laminated’, Journal of Sound and Vibration, vol. 201, pp. 335–352, 1997. https://doi.org/10.1006/jsvi.1996.0745.
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How to Cite
Adnan Yaseen, A., S. Alansari, L., Hussain Alnajem, M., & S. Al-anssari, Q. (2018). Calculating the frequency of composite plate and composite spherical shell with different boundary conditions. International Journal of Engineering & Technology, 7(4), 5007-5017. https://doi.org/10.14419/ijet.v7i4.25887Received date: 2019-01-14
Accepted date: 2019-02-04
Published date: 2018-11-05