Tran Quoc Quan, Dao Huy Bich, Nguyen Dinh Duc

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Based on classical shell theory with the geometrical nonlinearity in von Karman-Donell sense and the Ilyushin nonlinear supersonic aerodynamic theory, this paper successfully formulated the equations of motion of the functionally graded cylindrical panel on elastic foundations under impact of a moving supersonic airflow and found the critical velocity of supersonic airflow that make the panel unstable. This paper also used the Bubnov-Galerkin and Runge – Kutta methods to solve the system of nonlinear vibration differential equations and illustrated effects of initial dynamical conditions, shape and geometrical parameters, material constituents and elastic foundations on aerodynamic response and instability of FGM cylindrical panel.

Keywords: Nonlinear flutter, the Ilyushin supersonic aerodynamic theory, functional graded cylindrical panel, elastic foundations.


[1] M. Koizumi, “The concept of FGM,” Ceram Trans Funct Grad Mater, 34, 3-10 (1993).
[2] Y. Miyamoto, W.A. Kaysser B.H. Rabin, A. Kawasaki, R.G. Ford, Functionally graded materials: design, processing and applications. London: Kluwer Academic Publisher (1999).
[3] H.H. Ibrahim, M. Tawfik, M. Al-Ajmi, “Thermal buckling and nonlinear flutter behavior of FGM panels,” Journal of Aircraft, 44,1610-1618 (2008).
[4] K.J. Sohn, J.H. Kim, “Nonlinear thermal flutter of functionally graded panels under a supersonic flow,” J. Composite Structures, 88, 380-387 (2009).
[5] T. Prakash, M.K. Singha, M.A. Ganapathi, “Finite element study on the large amplitude flexural vibration characteristics of FGM plates under aerodynamic load,” International Journal of Non-Linear Mechanics, 47, 439-447 (2012).
[6] T. Prakash, M. Ganapathi, “Supersonic flutter characteristics of functionally graded flat panels including thermal effects,” J. Composite Structures, 72,10-18, (2006).
[7] M.A. Ganapathi, M. Touratier, “Supersonic flutter analysis of thermally stressed laminated composite flat panels,” J. Composite Structures, 34,241-248, (1996).
[8] H. Haddadpour, S. Mahmoudkhani, H.M. Navazi, “Supersonic flutter prediction of functionally graded cylindrical shells,” J. Composite Structures, 83,391-398 (2008).
[9] M.K. Singha, M.A. Ganapathi, “Parametric study on supersonic flutter behavior of laminated composite skew flat panels,” J. Composite Structures, 69,55-63 (2005).
[10] S.H. Moon, S.J. Kim, “Suppression of nonlinear composite panel flutter with active/ passive hybrid piezoelectric networks using finite element method,” J. Composite Structures, 59, 525-533 (2003).
[11] L.I. Librescu, P.Marfocca, “Supersonic/ hypersonic flutter and post-flutter of geometrically imperfect circular cylindrical panels,” Journal of Spacecraft and Rockets, 39,802-823 (2002).
[12] A.A. Ilyushin, “The law of plane cross sections in supersonic aerodynamics,” Journal of Applied Mathematics and Mechanics, 20 (6), (1956).
[13] R.D. Stepanov, On the flutter problem of plates. Machinery and equipment, 2 (1960).
[14] P.M. Oghibalov, Problems of dynamics and stability of shells, Moscow University Press, (1963).
[15] D.D. Brush, B.O. Almroth, Buckling of bars, plates and shells, Mc. Graw-Hill (1975).
[16] A.S. Volmir, Nonlinear dynamics of plates and shells, Science edition. Moscow (1972).