Thermal gradient effect on the free vibration of a cardioid cross-section cylindrical shell

References

• Chen, Y. N., Kempner, J. (1978). Modal method for free vibration of oval cylindrical shells with simply supported or clamped ends. Journal of Applied Mechanics 45:142–148.
   Web of Science ®Google Scholar
• Chung, H. (1981). Free vibration analysis of cylindrical shells. Journal of Sound and Vibration 74(3):331–350.
   Web of Science ®Google Scholar
• Culberson, L., Boyd, D. (1971). Free vibrations of freely supported oval cylinders. AIAA Journal 9(8):1474–1480.
   Web of Science ®Google Scholar
• El-Kaabazi, N., David, K. (2012). Calculation of natural frequencies and vibration modes of variable thickness cylindrical shells using the Wittrick-Williams algorithm. Computer Structures 104:4–12.
   Web of Science ®Google Scholar
• Flügge, W. (1973) Stress in Shells. New York: Springer-Verlag.
   Google Scholar
• Ganapathi, M., Patel, B. P., Patel, H. G., Pawargi, D. S. (2003). Vibration analysis of laminated cross-ply oval cylindrical shells. Journal of Sound and Vibration 262: 65–86.
   Web of Science ®Google Scholar
• Ganapathi, M., Patel, B. P., Patel, H. G. (2004). Free flexural vibration behavior of laminated angle-ply elliptical cylindrical shells. Computer Structures 82:509–518.
   Web of Science ®Google Scholar
• Gokhan, A., Burak, A. G. (2007). The effects of orthotropic materials on the vibration characteristics of structural systems. Mechanics Based Design of Structures and Machines 35:363–380.
   Web of Science ®Google Scholar
• Haddadpour, H., Mahmoudkhani, S., Navazi, H. M. (2007). Free vibration analysis of functionally graded cylindrical shells including thermal effects. Thin Wall Structures 45:591–599.
   Web of Science ®Google Scholar
• Joseph, W. T., Celal, N. K., Artur, K. (1987). Free vibration analysis of circular cylindrical shells. Computer Structures 25(5):677–685.
   Web of Science ®Google Scholar
• Khalifa, M. (2010). A study of free vibration of a circumferentially non-uniform cylindrical shell with a four-lobed cross-section. Journal of Vibration and Control 17(8):1158–1172.
   Web of Science ®Google Scholar
• Khalifa, M. (2011a). Exact solutions for the vibration of circumferentially stepped orthotropic circular cylindrical shells. Comptes Rendus Mecanique 339:708–718.
   Web of Science ®Google Scholar
• Khalifa, M. (2011b). Vibration and buckling approximation of an axially loaded cylindrical shell with a three lobed cross section having varying thickness. Applied Mathematics 2:329–342.
   Google Scholar
• Khalifa, M. (2011c). Simplified equations and solutions for the free vibration of an orthotropic oval cylindrical shell with variable thickness. Mathematical Methods in the Applied Sciences 34:1789–1800.
   Web of Science ®Google Scholar
• Khalifa, M. (2014). New approach for the vibrations of inhomogeneous orthotropic cylindrical shells resting on step-wise Winkler foundations. Inverse Problems in Science and Engineering. doi:10.1080/17415977.2014.97
   Web of Science ®Google Scholar
• Khalifa, M. (2015). Effects of non-uniform Winkler foundation and non-homogeneity on the free vibration of an orthotropic elliptical cylindrical shell. European Journal of Mechanics A/Solids 49:570–581.
   Web of Science ®Google Scholar
• Koumousis, V. K., Armenakas, A. E. (1983). Free vibrations of simply supported cylindrical shells of oval cross section. AIAA Journal 21(7):1017–1027.
   Web of Science ®Google Scholar
• Leissa, A. W. (1973) Vibration of Shells. NASA, SP-288: Washington.
   Google Scholar
• Liu, B., Xing, Y. F., Qatu, M. S., Ferreira, A. J. M. (2012). Exact characteristic equations for free vibrations of thin orthotropic circular cylindrical shells. Composite Structures 94:484–493.
   Web of Science ®Google Scholar
• Lu Dai Tiejun, Y., Jingtao, D., Li, W. L., Brennan, M. J. (2013). An exact series solution for the vibration analysis of cylindrical shells with arbitrary boundary conditions. Applied Acoustics 74:440–449.
   Web of Science ®Google Scholar
• Love, A. E. (1944). Mathematical Theory of Elasticity. Dover: New York.
   Google Scholar
• Malekzadeh, P., Fiouz, A. R, Sobhrouyan, M. (2012). Three-dimensional free Vibration of functionally graded truncated conical shells subjected to thermal environment. International Journal of Pressure Vessels and Piping 89:210–221.
   Web of Science ®Google Scholar
• Malekzadeh, P., Heydarpour, Y. (2012). Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment. Composite Structures 94:2971–2981.
   Web of Science ®Google Scholar
• Massalas, C., Dalamangas, A., Soldatos, K., Tzivanidis, G. (1981). Dynamic behaviour of a cylindrical shell subjected to a thermal gradient. Acta Mechanics 40:147–158.
   Web of Science ®Google Scholar
• Novozhilov, V. (1964). The theory of Thin Elastic Shells. Groningen: The Netherlands, P. Noordhoff Ltd.
   Google Scholar
• Parhi, A., Singh, B. N. (2014). Stochastic response of laminated composite shell panel in hygrothermal environment. Mechanics Based Design of Structures and Machines 42(4):454–482.
   Web of Science ®Google Scholar
• Parhi, A., Singh, B. N. (2015). Stochastic response of laminated composite shell panel in hygrothermal environment. Mechanics Based Design of Structures and Machines 43(3):314–341.
   Web of Science ®Google Scholar
• Rayleigh, L. (1945). The Theory of Sound. New York: Dover.
   Google Scholar
• Sewall, J. L., Pusey, C. G. (1971). Vibration study of clamped-free elliptical shells. AIAA Journal 9:1004–1011.
   Web of Science ®Google Scholar
• Sheng, G. G., Wang, X. (2010). Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells. Applied Mathematical Modelling 34:2630–2643.
   Web of Science ®Google Scholar
• Smith, B. L., Haft, E. E. (1968). Natural frequencies of clamped cylindrical shells. AIAA Journal 6(4):720–721.
   Web of Science ®Google Scholar
• Soldatos, K. P. (1999). Mechanics of cylindrical shells with noncircular cross section: a survey. Applied Mechanics Reviews 52:237–274.
   Google Scholar
• Tesar, A., Fillo, L. (1988). Transfer Matrix Method. Dordrecht: Kluwer Academic.
   Google Scholar
• Tomabene, F., Fantuzzi, N. (2013). General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels. Composite Structures 104:94–117.
   Web of Science ®Google Scholar
• Tomabene, F., Fantuzzi, N., Bacciocchi, M. (2014a). 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.
   Web of Science ®Google Scholar
• Tomabene, F., Fantuzzi, N., Bacciocchi, M. (2014b). The local GDQ method applied to general higher-order theories of doubly-curved laminated composite shells and panels: The free vibration analysis. Composite Structures 116:637–660.
   Web of Science ®Google Scholar
• Toorani, M. H., Lakis, A. A. (2004). Large amplitude vibrations of anisotropic cylindrical shells. Computer Structures 82:2015–2025.
   Web of Science ®Google Scholar
• Uhrig, R. (1973). Elastostatik und elastokinetik in matrizenschreibweise. Berlin: Springer.
   Google Scholar
• Xin, J., Wang, J., Yao, J., Han, Q. (2011). Vibration, buckling and dynamic stability of a cracked cylindrical shell with time-varying rotating speed. Mechanics Based Design of Structures and Machines 39(4):461–490.
   Web of Science ®Google Scholar
• Xuebin, L. I. (2008). Study on free vibration analysis of circular cylindrical shells using wave propagation. Journal of Sound and Vibration 311:667–682.
   Web of Science ®Google Scholar
• Yamada, G., Irie, T., Notoya, S. (1985). Natural frequencies of elliptical cylindrical shell. Journal of Sound and Vibration 101(1):133–139.
   Web of Science ®Google Scholar
• Yamada, G., Irie, T., Tagawa, Y. (1984). Free vibration of non-circular cylindrical shells with variable circumferential profile. Journal of Sound and Vibration 95(1):117–126.
   Web of Science ®Google Scholar
• Yuehua, C., Guoyong, J. N., Zhigang, L. (2013). Free vibration analysis of circular cylindrical shell with non-uniform elastic boundary constraints. International Journal of Mechanical Sciences 74:120–132.
   Web of Science ®Google Scholar
• Zhang, X. M., Liu, G. R., Lam, K. Y. (2001). Vibration analysis of thin cylindrical shells using wave propagation approach. Journal of Sound and Vibration 239: 397–403.
   Web of Science ®Google Scholar