Document Type : Research Paper

Authors

Faculty of Materials & Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran.

Abstract

In this paper, the free vibrations of multi-layered composite cylindrical shells with rectangular cutout are analyzed analytically. Cylindrical shell equilibrium equations are derived based on classical shell theory (CST) and using Newton's method. Boundary conditions of the two-headed shell are considered simply supported. According to the boundary conditions, the displacement components are written as double Fourier series expansions. Relationships of the strain-displacement and curvature displacement are considered based on Love’s approximation theory. Modeling of the cutout by distribution function (Heaviside) is considered based on the equilibrium equations of the composite cylindrical shell. In order to obtain the natural frequency of the rectangular cutout composite cylindrical shell, the equations of motion have been solved using the Galerkin method. For validation, firstly, the results of the composite cylindrical shell have been compared with the Abaqus finite element software and the Previous literature in this field, that there is a good match between them. Finally, the effect of the geometrical parameters of the composite cylindrical shell with cutout, such as the length, radius, thickness and layering of the cylindrical shell, as well as the dimensions, direction and location of the cutout, on the natural frequency of the structure was investigated, that the results show that with increasing The dimensions of the cutout increase the reduction of the natural frequency of the structure.

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Main Subjects

[1]  Shahani, A. and Kiarasi, F., “Numerical and Experimental Investigation on Post-Buckling Behavior of Stiffened Cylindrical Shells with Cutout subject to Uniform Axial Compression”, Journal of Applied and Computational Mechanics, pp. 1–20, 2020.
[2]  Lee, H. and Kwak, M. K., “Free vibration analysis of a circular cylindrical shell using the Rayleigh-Ritz method and comparison of different shell theories”, J. Sound Vib., Vol. 353, pp. 344–377, 2015.
[3]  Ghorbani, K., Mohammadi, K., Rajabpour, A. and Ghadiri, M., “Surface and size-dependent effects on the free vibration analysis of cylindrical shell based on Gurtin-Murdoch and nonlocal strain gradient theories”, J. Phys. Chem. Solids., Vol. 129, pp. 140–150, 2019.
[4]  Takabatake, H., “Static analayses of elastic plates with voids”, Int. J. Solids. Struct., Vol. 28, pp. 179–196, 1991.
[5]  Azhari, M., Shahidi, A. R. and Saadatpour, M. M., “Local and post local buckling of stepped and perforated thin plates”, Appl. Math. Modelling., Vol. 29, pp. 633–652, 2005.
[6]  Li, G. and Cheng, J., “A Generalized Analytical Modeling of Grid Stiffened Composite Structures”, Compos. Struct., Vol. 94, pp. 1117–1127, 2007.
[7]  Zhang, Z., Chen, H. and Ye, L., “A stiffened plate element model for advanced grid stiffened composite plates/shells”, J. Compos. Mater., Vol. 45, 2011.
[8]  Wilson, A. J. and Rajasekaran, S., “Elastic stability of all edges simply supported, stepped and stiffened rectangular plate under Biaxial loading”, Appl. Math. Modelling., Vol. 38, pp. 479–495, 2014.
[9]  Huang, L., Sheikh, A. H., Ng, C. T. and Griffith, M. C., “An efficient finite element model for buckling analysis of grid stiffened laminated composite plates”, Compos. Struct., Vol. 122, pp. 41–50, 2015.
[10] Omidvaran, C., “Free vibration of grid-stiffened plates”, J. Sound. Vib., Vol. 19, pp. 463-472, 1971.
[11] Kalita, K. and Haldar, S., “Free vibration analysis of rectangular plates with Central cutout”, Cogent. Eng., 2016.
[12] Soleimanian, S., Davar, A., Azarafza, R., Jam, J. E. and Zamani, M. R., “Theoretical, numerical, and experimental analyses of free vibrations of glass fiber reinforced polymer plates with central cutouts and free boundaries”, Mechanics of Advanced Composite Structures., Vol. 5, pp. 67-74, 2018.
[13] Li, G. and Cheng, J., “A Generalized Analytical Modeling of Grid Stiffened Composite Structures”, Journal of Composite Materials., Vol. 41, 2007.
[14] Azarafza, R., Golkar, A. H. and Davar, A., “Analytical investigation of Low-Velocity Oblique Impact on Composite Cylindrical Shells”, Journal of Science and Technology of Composites., Vol. 3, pp. 1106-1119, 2020.
[15] Chaudhuri, P. B., Mitra, A. and Sahoo, S., “Free vibration analysis of antisymmetric angle ply laminated composite stiffened hyper shell with cut out”, in Materials Today: Proceedings., Vol. 5, pp. 5563–5572, 2018.
[16] Zhi-yuan, C. and Hua-ning, W., “Free vibration of FGM cylindrical shells with holes under various boundary conditions”, J. Sound Vib., Vol. 306, pp. 227–237, 2007.
[17] Azarafza, R., Davar, A. and Baghani, H., “Investigation of Free Vibration of Laminated Composite Conical Shell with Local Attached Mass”, Mechanics of Advanced Composite Structures., Vol. 9, pp. 173-184, 2022.
[18] Talezadehlari, A., “Free vibration analysis of perforated composite cylindrical shell using Generalized Differential Quadrature Method”, In Persian, Journal of Science and Technology of Composites, Vol. 7, No. 3, pp. 1120-1132, 2020.
[19] Y. Ansaryan, Y. Jafari, A. A., “Investigation of Free and Forced Vibration of a Composite Circular Cylindrical Shell with Internal Fluid”, In Persian, Journal of Solid and Fluid Mechanics, Vol. 7, No. 2, pp. 93-109, 2017.
[20] Talezadehlari, A. and Rahimi, G. H., “Buckling Analysis of Perforated Composite Cylindrical Shell Using Generalized Differential Quadrature Method (Gdqm)”, In Persian, Modares Mechanical Engineering, Vol. 17, No. 11, pp. 385-396, 2018.
[21] Khalili, S.M.R. Sedigh, Y. and Hossein Ahari, S.M. M. M., “Experimental and numerical study of the buckling of semi-cylindrical composite lattice”, In Persian, Journal of Science and Technology of Composites, Vol. 3, No. 3, pp. 269-276, 2016.
[22] Khalili, S. M. R. Ahari, S. M. M. M. Sedigh, Y., “Experimental and numerical investigation on semi-cylindrical compositelatticereinforced with triangular cellssubjected to high velocity impact”, In Persian, Journal of Science and Technology of Composites, Vol. 05, No. 02, pp. 208-217, 2018
[23] Fereidoon, A., Kolasangiani, K. et al., “Study on buckling of steel cylindrical shells with an elliptical cutout under combined loading”, JCARME., Vol. 3, pp. 13-25, 2013.
[24] Poore, A. L., Barut, A. and Madenci, E., “Free vibration of laminated cylindrical shells with a circular cutout”, J. Sound Vib., Vol. 312, pp. 55–73, 2008.
[25] Khalili, S. M. R., Azarafza, R. and Davar, A., “Transient dynamic response of initially stressed composite circular cylindrical shells under radial impulse load”, Compos. Struct., vol. 89, pp. 275–284, 2009.
[26] Azarafza, R., Khalili, S. M. R., Jafari, A. A. and Davar, A., “Analysis and optimization of laminated composite circular cylindrical shell subjected to compressive axial and transverse transient dynamic loads”, Thin-Walled Struct., vol. 47, pp. 970–983, 2009.
[27] Tong, B., Li, Y., Zhu, X. and Zhang, Y., “Three-dimensional vibration analysis of arbitrary angle-ply laminated cylindrical shells using differential quadrature method”, Applied Acoustics., vol. 146, pp. 390–397, 2019.
[28] Ghasemi, A. R. and Mohandes, M., “Comparison between the frequencies of FML and composite cylindrical shells using beam modal function model”, JCAMECH., vol. 50, pp. 239-245, 2019.