Analytical Investigation of the Vibrational and Dynamic Response of Nano-Composite Cylindrical Shell Under Thermal Shock and Mild Heat Field by DQM Method




In this paper, the vibrations and dynamic response of an orthotropic thin-walled composite cylindrical shell with epoxy graphite layers reinforced with carbon nanotubes under heat shock and heat field loading are investigated. the carbon nanotubes were uniformly distributed along the thickness of the composite layer. The problem is that at first there is a temperature change due to the thermal field in the cylinder and the cylinder is coincident with the thermal field, then the surface temperature of the cylinder rises abruptly. Partial derivative equations of motion are coupled to heat equations. The differential quadrature method (DQM) is used to solve the equations. In this study, the effects of length, temperature, thickness and radius parameters on the natural frequencies and mid-layer displacement are investigated. The results show that increasing the outside temperature reduces the natural frequency and increases the displacement of the system. Radial displacement results were also compared with previous studies and were found to be in good agreement with previous literature. Increasing the percentage of carbon nanotubes also increased the natural frequency of the system and decreased the mobility of the middle layer.


Heat shock, DQM, natural frequency, composite, carbon nanotubes


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<p>[1] McQuillen, E. J., Brull, M. A., Dynamic thermoelastic response of cylindrical shells, Journal of applied Mechanics 37(3): 661-670, 1970. ‏</p>
<p>[2] M.R. Eslami, H. Vahedi, a general finite element stress formulation of dynamic thermoelastic problems using Galerkin method, J. Therm. Stresses 14 (1991) (in Persian).</p>
<p>[3] M.R. Eslami, M. Shakeri, R. Sedaghati, Coupled thermoelasticity of axially symmetric cylindrical shell, J. Therm. Stresses 17 (1), 115–135, 1994(in Persian).</p>
<p>[4] M.R. Eslami, M. Shakeri, A.R. Ohadi, B. Shiari, coupled thermoelasticity of shells, effect of normal stress and coupling, AIAA J. 37 (4), 496–504, 1999 (in Persian).</p>
<p>[5] Hakimelahi, B., Soltani, N., A solution for the coupled dynamic thermoelastic problems of thin cylindrical shells under pressure shear and temperature shocks using finite element methods, J. Fac. Eng. Univ. Tehran 33 (3): 73–86, 1999 (in Persian).</p>
<p>[6] Eslami, M. R., Mousavi, S. M., Dynamic analysis of conical shells under mechanical and thermal loading by Galerkin finite element method, in: Second Conference of Aerospace Engineering in Iran: 535–543, 1998 (in Persian).</p>
<p>[7] Tarn, J. Q., Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads, International Journal of Solids and Structures 38(46-47): 8189-8206, 2001. ‏</p>
<p>[8] Alibeigloo, A., Thermoelastic solution for static deformations of functionally graded cylindrical shell bonded to thin piezoelectric layers, Composite Structures 93(2): 961-972, 2011(in Persian). ‏</p>
<p>[9] Ansari, R., Torabi, J., Faghih Shojaei, M., Free vibration analysis of embedded functionally graded carbon nanotube-reinforced composite conical/cylindrical shells and annular plates using a numerical approach. Journal of Vibration and Control, 24 (6): 1123-1144, 2016 (in Persian).</p>
<p>[10] Alibeigloo, A., Elasticity solution of functionally graded carbon nanotube-reinforced composite cylindrical panel subjected to thermo mechanical load, Composites Part B: Engineering 87: 214-226, 2016 (in Persian). ‏</p>
<p>[11] Wang, Y. Z., et al. "Thermoelastic interaction in functionally graded thick hollow cylinder with temperature-dependent properties."&nbsp;Journal of Thermal Stresses&nbsp;41.4, 399-417, 2018.</p>
<p>[12] Esmaeili H.R., Arvin H., Kiani Y., Axisymmetric nonlinear rapid heating of FGM cylindrical shells, Journal of Thermal Stresses <strong>42</strong>(4): 490-505, 2019 (in Persian).</p>
<p>[13] Keibolahi A., Kiani Y., Eslami M.R., Dynamic snap-through of shallow arches under thermal shock, Aerospace Science and Technology 77: 545-554, 2018 (in Persian).</p>
<p>[14] Javani M., Kiani Y., Eslami M.R., Geometrically nonlinear rapid surface heating of temperature-dependent FGM arches, Aerospace Science and Technology 90: 264-274, 2019 (in Persian).</p>
<p>[15] Javani M., Kiani Y., Eslami M.R., Large amplitude thermally induced vibrations of temperature dependent annular FGM plates, Composites Part B: Engineering 163: 371-383, 2019 (in Persian).</p>
<p>[16] S.A.Mousavi., M. Rahmani, M. Kaffash Mirzarahimi, and S. Mahjoub Moghadas. "The Dynamic and Vibration Response of Composite Cylindrical Shell Under Thermal Shock and Mild Heat Field."&nbsp;Journal of Solid Mechanics, 2020 (in Persian).</p>
<p>[17] P. Zhu, Z.X. Lei, K.M. Liew, Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory, Composite Structures,450-1460, 2012.</p>
<p>[18] Chang, J. S., Shyong, J. W., Thermally induced vibration of laminated circular cylindrical shell panels, Composites science and technology 51(3): 419-427, 1994.</p>
<p>[19] Bert, C. W., Kumar, M., Vibration of cylindrical shells of bimodulus composite materials, Journal of Sound and Vibration 81(1):107-121, 1982.</p>
<p>&nbsp;[20] Eslami, M., Vahedi, H., Galerkin finite element displacement formulation of coupled thermoelasticity spherical problems. Journal of pressure vessel technology 114(3): 380-384, 1992 (in Persian).</p>
<p>[21] Shiari, B., Eslami, M. R., Shaker, M., Thermomechanical shocks in composite cylindrical shells: a coupled thermoelastic finite element analysis. Scientia Iranica 10(1): 13-22, 2003 (in Persian). ‏</p>
<p>[22] A. Ghorbanpour Arani, V. Atabakhshian, A. Loghman, A.R. Shajari, S. Amir, Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method, Phisy. 2549-2555, 2012 (in Persian).</p>
<p>[23] T. Murmu, S.C. Pradhan, buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Phisy. E 41,1232-1239, 2009.</p>
<p>[24] O. Civalek, Harmonic differential quadrature-finite differences coupled approaches for geometrically nonlinear static and dynamic analysis of rectangular plates on elastic foundation, J. Sound. Vib. 294, 966–980, 2006.</p>






Research Article

How to Cite

M. Rahmani and A. Moslemi Petrudi, “Analytical Investigation of the Vibrational and Dynamic Response of Nano-Composite Cylindrical Shell Under Thermal Shock and Mild Heat Field by DQM Method”, J. Mod. Sim. Mater., vol. 3, no. 1, pp. 22-36, Mar. 2020.