Buckling and Thermomechanical Vibration Analysis of a Cylindrical Sandwich Panel with an Elastic Core Using Generalized Differential Quadrature Method

Journal of Solid Mechanics

مقاله 12، دوره 11، شماره 2، شهریور 2019، صفحه 409-424   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2019.665367

نویسندگان

A.R Pourmoayed^{* 1}؛ K Malekzadeh²؛ M Shahravi²؛ H Safarpour³

¹Department of Mechanical Engineering, Khatamul-Anbiya Air Defense University, Tehran, Iran

²Faculty of Structural Analysis and Simulation Centre, MalekAshtar University,Tehran, Iran

³Department of Mechanics, Imam Khomeini International University, Qazvin, Iran

چکیده

In this paper, the vibrational and buckling analysis of a cylindrical sandwich panel with an elastic core under thermo-mechanical loadings is investigated. The modeled cylindrical sandwich panel as well as its equations of motions and boundary conditions is derived by Hamilton’s principle and the first-order shear deformation theory (FSDT). For the first time in the present study, various boundary conditions is considered in the cylindrical sandwich panel with an elastic core. In order to obtain the temperature distribution in the cylindrical sandwich panel in the absence of a heat-generation source, temperature distribution is obtained by solving the steady-state heat-transfer equation. The accuracy of the presented model is verified using previous studies and the results obtained by the Navier analytical method. The novelty of the present study is considering thermo-mechanical loadings as well as satisfying various boundary conditions. The generalized differential quadrature method (GDQM) is applied to discretize the equations of motion. Then, some factors such as the influence of length-to-radius ratio, circumferential wave numbers, thermal loadings, and boundary conditions are examined on the dynamic and static behavior of the cylindrical sandwich panel.

کلیدواژه‌ها

Heat-transfer equation؛ Buckling and vibration behavior؛ GDQM؛ Cylindrical sandwich panel؛ Various boundary conditions

مراجع

[1] Lim C., Ma Y., Kitipornchai S., Wang C., Yuen R., 2003, Buckling of vertical cylindrical shells under combined end pressure and body force, Journal of Engineering Mechanics 129: 876-884.
[2] Librescu L., Marzocca P., 2003, Thermal Stresses, Virginia Polytechnic Institute and State University, Blacksburg.
[3] Noor A. K., Burton W. S., 1992, Computational models for high-temperature multilayered composite plates and shells, Applied Mechanics Reviews 45: 419-446.
[4] Lam K., Loy C., 1995, Effects of boundary conditions on frequencies of a multi-layered cylindrical shell, Journal of Sound and vibration 188: 363-384.
[5] Li X., Chen Y., 2002, Transient dynamic response analysis of orthotropic circular cylindrical shell under external hydrostatic pressure, Journal of Sound and Vibration 257: 967-976.
[6] Loy C., Lam K., 1999, Vibration of thick cylindrical shells on the basis of three-dimensional theory of elasticity, Journal of Sound and Vibration 226: 719-737.
[7] Young P., 2000, Application of a three-dimensional shell theory to the free vibration of shells arbitrarily deep in one direction, Journal of Sound and Vibration 238: 257-269.
[8] Shariyat M., 1997, Elastic, plastic, and creep buckling of imperfect cylinders under mechanical and thermal loading, Journal of Pressure Vessel Technology 119: 27-36.
[9] Eslami M., Ziaii A., Ghorbanpour A., 1996, Thermoelastic buckling of thin cylindrical shells based on improved stability equations, Journal of Thermal Stresses 19: 299-315.
[10] Radhamoman S., Enkataramana J., 1975,Thermal buckling of orthotropic cylindrical shells, AIAA Journal 13: 397-399.
[11] Alibeigloo A., 2014, Three-dimensional thermo-elasticity solution of sandwich cylindrical panel with functionally graded core, Composite Structures 107: 458-468.
[12] Thangaratnam R. K., Palaninathan R., Ramachandran J., 1990,Thermal buckling of laminated composite shells, AIAA Journal 28: 859-860.
[13] Bert C., 1993, Buckling and post-buckling of composite plates and shells subjected to elevated temperature, Journal of Applied Mechanics 60(2): 514-519.
[14] Mohammad-Abadi M., Daneshmehr A., 2015, Modified couple stress theory applied to dynamic analysis of composite laminated beams by considering different beam theories, International Journal of Engineering Science 87: 83-102.
[15] Dumir P., Nath J., Kumari P., Kapuria S., 2008, Improved efficient zigzag and third order theories for circular cylindrical shells under thermal loading, Journal of Thermal Stresses 31: 343-367.
[16] Kant T., Khare R., 1994, Finite element thermal stress analysis of composite laminates using a higher-order theory, Journal of Thermal stresses 17: 229-255.
[17] Khdeir A., Rajab M., Reddy J., 1992, Thermal effects on the response of cross-ply laminated shallow shells, International Journal of Solids and Structures 29: 653-667.
[18] Khare R. K., Kant T., Garg A. K., 2003, Closed-form thermo-mechanical solutions of higher-order theories of cross-ply laminated shallow shells, Composite Structures 59: 313-340.
[19] Sheng G., Wang X., 2007, Effects of thermal loading on the buckling and vibration of ring-stiffened functionally graded shell, Journal of Thermal Stresses 30: 1249-1267.
[20] Sheng G., Wang X., 2010, Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells, Applied Mathematical Modelling 34: 2630-2643.
[21] Shiau L.-C., Kuo S.-Y., 2004, Thermal postbuckling behavior of composite sandwich plates, Journal of Engineering Mechanics 130: 1160-1167.
[22] Jeng-Shian C., 1990, FEM analysis of buckling and thermal buckling of antisymmetric angle-ply laminates according to transverse shear and normal deformable high order displacement theory, Computers & Structures 37: 925-946.
[23] Rao K. M., 1985, Buckling analysis of anisotropic sandwich plates faced with fiber-reinforced plastics, AIAA Journal 23: 1247-1253.
[24] Noor A. K., Starnes Jr J. H., Peters J. M., 1997, Curved sandwich panels subjected to temperature gradient and mechanical loads, Journal of Aerospace Engineering 10: 143-161.
[25] Chang C.-C., 2012, Thermoelastic behavior of a simply supported sandwich panel under large temperature gradient and edge compression, Journal of the Aerospace Sciences 2012: 480.
[26] Huang H., 2003, The initial post-buckling behavior of face-sheet delaminations in sandwich composites, Journal of Applied Mechanics 70: 191-199.
[27] Huang H., Kardomateas G. A., 2002, Buckling and initial postbuckling behavior of sandwich beams including transverse shear, AIAA Journal 40: 2331-2335.
[28] Frostig Y., Thomsen O. T., 2008, Non-linear thermal response of sandwich panels with a flexible core and temperature dependent mechanical properties, Composites Part B: Engineering 39: 165-184.
[29] Khalili S., Mohammadi Y., 2012, Free vibration analysis of sandwich plates with functionally graded face sheets and temperature-dependent material properties: A new approach, European Journal of Mechanics-A/Solids 35: 61-74.
[30] Leonenko D., Starovoitov E., 2016, Vibrations of cylindrical sandwich shells with elastic core under local loads, International Applied Mechanics 52: 359-367.
[31] Malekzadeh F. K., Malek M. H., 2017, Free vibration and buckling analysis of sandwich panels with flexible cores using an improved higher order theory, Journal of Solid Mechanics 9(1): 39-53.
[32] Jabbari M., Zamani N. M., Ghannad M., 2017, Stress analysis of rotating thick truncated conical shells with variable thickness under mechanical and thermal loads, Journal of Solid Mechanics 9(1): 100-114.
[33] Saviz M., 2016, Coupled vibration of partially fluid-filled laminated composite cylindrical shells, Journal of Solid Mechanics 8: 823-839.
[34] Golpayegani I. F., 2018, Calculation of natural frequencies of bi-layered rotating functionally graded cylindrical shells, Journal of Solid Mechanics 10: 216-231.
[35] Saadatfar M., Aghaie K. M., 2015, On the magneto-thermo-elastic behavior of a functionally graded cylindrical shell with pyroelectric layers featuring interlaminar bonding imperfections rested in an elastic foundation, Journal of Solid Mechanics 7(3): 344-363.
[36] Ghasemi A., Hajmohammad M., 2017, Evaluation of buckling and post buckling of variable thickness shell subjected to external hydrostatic pressure, Journal of Solid Mechanics 9: 239-248.
[37] Hosseini-Hashemi S., Abaei A., Ilkhani M., 2015, Free vibrations of functionally graded viscoelastic cylindrical panel under various boundary conditions, Composite Structures 126: 1-15.
[38] Thinh T. I., Nguyen M. C., Ninh D. G., 2014, Dynamic stiffness formulation for vibration analysis of thick composite plates resting on non-homogenous foundations, Composite Structures 108: 684-695.
[39] Tauchert T. R., 1974, Energy Principles in Structural Mechanics, McGraw-Hill Companies.
[40] Reddy J. N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press.
[41] Ghadiri M., SafarPour H., 2017, Free vibration analysis of size-dependent functionally graded porous cylindrical microshells in thermal environment, Journal of Thermal Stresses 40: 55-71.
[42] Bellman R., Casti J., 1971, Differential quadrature and long-term integration, Journal of Mathematical Analysis and Applications 34: 235-238.
[43] Bellman R., Kashef B., Casti J., 1972, Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics 10: 40-52.
[44] Shu C., 2012, Differential Quadrature and its Application in Engineering, Springer Science & Business Media.
[45] Shu C., Richards B. E., 1992, Application of generalized differential quadrature to solve two‐dimensional incompressible Navier‐Stokes equations, International Journal for Numerical Methods in Fluids 15: 791-798.
[46] Loy C., Lam K., Shu C., 1997, Analysis of cylindrical shells using generalized differential quadrature, Shock and Vibration 4: 193-198.
[47] Loy C., Lam K., Reddy J., 1999, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences 41: 309-324.
[48] Matsunaga H., 2009, Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory, Composite Structures 88: 519-531.
[49] Rabani Bidgoli M., Saeed Karimi M., Ghorbanpour Arani A., 2016, Nonlinear vibration and instability analysis of functionally graded CNT-reinforced cylindrical shells conveying viscous fluid resting on orthotropic Pasternak medium, Mechanics of Advanced Materials and Structures 23: 819-831.