Mathematical Model in Studying the Stability of Dynamic Systems
Main Article Content
Abstract
In this paper, the author investigated the phenomenon of flutter, which may be the cause of instability of construction structure when it is affected by aerodynamics. By analyzing the effect of aerodynamic on the structure via mathematical analysis, the author has established a mathematical model to study the stability of the structure in the aerodynamic flux that moves supersonically.
Keywords:
Aerodynamics, flutter, stability
References
[1] F.Sabri, A.A. Lakis, (2013) Efficient Hybrid Finite Element Method for Flutter Prediction of Functionally Graded Cylindrical Shells, Journal of Vibration and Acoustics 136. First published as doi: 10.1115/1.4025397.
[2] McNamara J.J., Friedmann P.P., Powell K.G., Thuruthimattam B.J. (2005), “ Three- dimensional Aeroelastic and Aerothermoelastic behavior in Hypersonic Flow”, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Material Conference 18-21 April 2005, Texas.
[3] Barbero E. J, Reddy J. N. (1990). “Nonlinear analysic of composite laminated plates using a generalized laminate plate theory”, AIAA Journal, Vol. 28, No.1, pp 1987-1994.
[4] Beldica C. E., Hilton H.H. and Kubair D. (2001). “Viscoelastic panel flutter-stability, probabilities of failure and survival times”, Submitted to The 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Material Conference 16-19 April 2001, Seattle, W.A.
[5] Dey P. and Singha M. K. (2006). “Dynamic stability analysis of composite skew plates subjected to periodic in- plane load”, Thin-Walled Structures 44, pp. 937 - 942.
[6] Singha M. K and Ganapathi M. (2005). “ A parametric study on supersonic flutter behaviour of laminated composite skew flat panels”, Composite Structures 69, pp. 55-63.
[7] Bich D. H., Dung D. V., Nam V. H. (2012) “Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels”, Composite Structures 94(8): 2465-73.
[8] Long N. V., Quoc T. H., Tu T. M. (2016) “Bending and free vibration analysis ò functionally graded plates using new eight- unknown shear deformation theory by finite element method”, Journal of Science and Technology 54 (3), 402-415.
[2] McNamara J.J., Friedmann P.P., Powell K.G., Thuruthimattam B.J. (2005), “ Three- dimensional Aeroelastic and Aerothermoelastic behavior in Hypersonic Flow”, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Material Conference 18-21 April 2005, Texas.
[3] Barbero E. J, Reddy J. N. (1990). “Nonlinear analysic of composite laminated plates using a generalized laminate plate theory”, AIAA Journal, Vol. 28, No.1, pp 1987-1994.
[4] Beldica C. E., Hilton H.H. and Kubair D. (2001). “Viscoelastic panel flutter-stability, probabilities of failure and survival times”, Submitted to The 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Material Conference 16-19 April 2001, Seattle, W.A.
[5] Dey P. and Singha M. K. (2006). “Dynamic stability analysis of composite skew plates subjected to periodic in- plane load”, Thin-Walled Structures 44, pp. 937 - 942.
[6] Singha M. K and Ganapathi M. (2005). “ A parametric study on supersonic flutter behaviour of laminated composite skew flat panels”, Composite Structures 69, pp. 55-63.
[7] Bich D. H., Dung D. V., Nam V. H. (2012) “Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels”, Composite Structures 94(8): 2465-73.
[8] Long N. V., Quoc T. H., Tu T. M. (2016) “Bending and free vibration analysis ò functionally graded plates using new eight- unknown shear deformation theory by finite element method”, Journal of Science and Technology 54 (3), 402-415.