Abstract
The free thermal vibration of functionally graded material (FGM) cylindrical shells containing porosities is investigated. Both even distribution and uneven distribution are taken into account. In addition, three thermal load types, i.e., uniform temperature rise (UTR), nonlinear temperature rise (NLTR), and linear temperature rise (LTR), are researched to explore their effects on the vibration characteristics of porous FGM cylindrical shells. A modified power-law formulation is used to describe the material properties of FGM shells in the thickness direction. Love’s shell theory is used to formulate the strain-displacement equations, and the Rayleigh-Ritz method is utilized to calculate the natural frequencies of the system. The results show that the natural frequencies are affected by the porosity volume fraction, constituent volume fraction, and thermal load. Moreover, the natural frequencies obtained from the LTR have insignificant differences compared with those from the NLTR. Due to the calculation complexity of the NLTR, we propose that it is reasonable to replace it by its linear counterpart for the analysis of thin porous FGM cylindrical shells. The present results are verified in comparison with the published ones in the literature.
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References
KOIZUMI, M. FGM activities in Japan. Composites Part B: Engineering, 28, 1–4 (1997)
WANG, Y. and ZU, J. W. Nonlinear oscillations of sigmoid functionally graded material plates moving in longitudinal direction. Applied Mathematics and Mechanics (English Edition), 38(11), 1533–1550 (2017) https://doi.org/10.1007/s10483-017-2277-9
WAN, Z. and LI, S. Thermal buckling analysis of functionally graded cylindrical shells. Applied Mathematics and Mechanics (English Edition), 38(8), 1059–1070 (2017) https://doi.org/10.1007/s10483-017-2225-7
WANG, Y. Q. and ZU, J. W. Nonlinear steady-state responses of longitudinally traveling functionally graded material plates in contact with liquid. Composite Structures, 164, 130–144 (2017)
DUNG, D. V., NGA, N. T., and HOA, L. K. Nonlinear stability of functionally graded material (FGM) sandwich cylindrical shells reinforced by FGM stiffeners in thermal environment. Applied Mathematics and Mechanics (English Edition), 38(5), 647–670 (2017) https://doi.org/10.1007/s10483-017-2198-9
ZHANG, W., YANG, J., and HAO, Y. Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory. Nonlinear Dynamics, 59, 619–660 (2010)
ZHANG, W., HAO, Y., GUO, X., and CHEN, L. Complicated nonlinear responses of a simply supported FGM rectangular plate under combined parametric and external excitations. Meccanica, 47, 985–1014 (2012)
WANG, Y. Q., HUANG, X. B., and LI, J. Hydroelastic dynamic analysis of axially moving plates in continuous hot-dip galvanizing process. International Journal of Mechanical Sciences, 110, 201–216 (2016)
LOY, C. T., LAM, K. Y., and REDDY, J. N. Vibration of functionally graded cylindrical shells. International Journal of Mechanical Sciences, 41, 309–324 (1999)
PATEL, B., GUPTA, S., LOKNATH, M., and KADU, C. Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory. Composite Structures, 69, 259–270 (2005)
SHAH, A. G., MAHMOOD, T., and NAEEM, M. N. Vibrations of FGM thin cylindrical shells with exponential volume fraction law. Applied Mathematics and Mechanics (English Edition), 30(5), 607–615 (2009) https://doi.org/10.1007/s10483-009-0507-x
MATSUNAGA, H. Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory. Composite Structures, 88, 519–531 (2009)
ARSHAD, S. H., NAEEM, M. N., SULTANA, N., SHAH, A. G., and IQBAL, Z. Vibration analysis of bi-layered FGM cylindrical shells. Archive of Applied Mechanics, 81, 319–343 (2011)
DING, H., TAN, X., and DOWELL, E. H. Natural frequencies of a super-critical transporting Timoshenko beam. European Journal of Mechanics-A/Solids, 66, 79–93 (2017)
TAN, X., MAO, X. Y., DING, H., and CHEN, L. Q. Vibration around non-trivial equilibrium of a supercritical Timoshenko pipe conveying fluid. Journal of Sound and Vibration, 428, 104–118 (2018)
CARRERA, E., BRISCHETTO, S., CINEFRA, M., and SOAVE, M. Effects of thickness stretch-ing in functionally graded plates and shells. Composites Part B: Engineering, 42, 123–133 (2011)
BICH, D. H. and XUAN, N. N. Nonlinear vibration of functionally graded circular cylindrical shells based on improved Donnell equations. Journal of Sound and Vibration, 331, 5488–5501 (2012)
STROZZI, M. and PELLICANO, F. Nonlinear vibrations of functionally graded cylindrical shells. Thin-Walled Structures, 67, 63–77 (2013)
TORNABENE, F., FANTUZZI, N., and BACCIOCCHI, M. Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories. Composites Part B: Engineering, 67, 490–509 (2014)
BHANGALE, R. K., GANESAN, N., and PADMANABHAN, C. Linear thermoelastic buckling and free vibration behavior of functionally graded truncated conical shells. Journal of Sound and Vibration, 292, 341–371 (2006)
HADDADPOUR, H., MAHMOUDKHANI, S., and NAVAZI, H. Free vibration analysis of func-tionally graded cylindrical shells including thermal effects. Thin-Walled structures, 45, 591–599 (2007)
ZHAO, X., LEE, Y., and LIEW, K. M. Thermoelastic and vibration analysis of functionally graded cylindrical shells. International Journal of Mechanical Sciences, 51, 694–707 (2009)
KIANI, Y., SHAKERI, M., and ESLAMI, M. Thermoelastic free vibration and dynamic behaviour of an FGM doubly curved panel via the analytical hybrid Laplace-Fourier transformation. Acta Mechanica, 223, 1199–1218 (2012)
ZHANG, W., HAO, Y. X., and YANG, J. Nonlinear dynamics of FGM circular cylindrical shell with clamped-clamped edges. Composite Structures, 94, 1075–1086 (2012)
DU, C., LI, Y., and JIN, X. Nonlinear forced vibration of functionally graded cylindrical thin shells. Thin-Walled Structures, 78, 26–36 (2014)
LIU, Y. Z., HAO, Y. X., ZHANG, W., CHEN, J., and LI, S. B. Nonlinear dynamics of initially imperfect functionally graded circular cylindrical shell under complex loads. Journal of Sound and Vibration, 348, 294–328 (2015)
DUC, N. D. Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylin-drical shells surrounded on elastic foundations using the Reddy’s third-order shear deformation shell theory. European Journal of Mechanics-A/Solids, 58, 10–30 (2016)
SHENG, G. G. and WANG, X. The non-linear vibrations of rotating functionally graded cylin-drical shells. Nonlinear Dynamics, 87, 1095–1109 (2017)
ZHU, J., LAI, Z., YIN, Z., JEON, J., and LEE, S. Fabrication of ZrO2-NiCr functionally graded material by powder metallurgy. Materials Chemistry and Physics, 68, 130–135 (2001)
WATTANASAKULPONG, N. and CHAIKITTIRATANA, A. Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method. Meccanica, 50, 1331–1342 (2015)
EBRAHIMI, F., GHASEMI, F., and SALARI, E. Investigating thermal effects on vibration be-havior of temperature-dependent compositionally graded Euler beams with porosities. Meccanica, 51, 223–249 (2016)
WANG, Y. Q. and ZU, J. W. Vibration characteristics of moving sigmoid functionally graded plates containing porosities. International Journal of Mechanics and Materials in Design (2017) https://doi.org/10.1007/s10999-017-9385-2
WANG, Y. Q. Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state. Acta Astronautica, 143, 263–271 (2018)
WANG, Y. Q. and ZU, J. W. Nonlinear dynamics of a translational FGM plate with strong mode interaction. International Journal of Structural Stability and Dynamics, 18, 1850031 (2018)
JAVAHERI, R. and ESLAMI, M. Thermal buckling of functionally graded plates. AIAA journal, 40, 162–169 (2002)
AMABILI, M. Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, Cambridge (2008)
PELLICANO, F. Vibrations of circular cylindrical shells: theory and experiments. Journal of Sound and Vibration, 303, 154–170 (2007)
REDDY, J. N. and CHIN, C. D. Thermomechanical analysis of functionally graded cylinders and plates. Journal of Thermal Stresses, 21, 593–626 (1998)
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Project supported by the National Natural Science Foundation of China (No. 11672071) and the Fundamental Research Funds for the Central Universities (No.N170504023)
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Wang, Y., Ye, C. & Zu, J.W. Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities. Appl. Math. Mech.-Engl. Ed. 39, 1587–1604 (2018). https://doi.org/10.1007/s10483-018-2388-6
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DOI: https://doi.org/10.1007/s10483-018-2388-6
Key words
- functionally graded material (FGM)
- cylindrical shell
- porosity
- free vibration
- thermal load
- Rayleigh-Ritz method