Abstract
The incremental harmonic balance method was extended to analyze the flutter of systems with multiple structural strong nonlinearities. The strongly nonlinear cubic plunging and pitching stiffness terms were considered in the flutter equations of two-dimensional airfoil. First, the equations were transferred into matrix form, then the vibration process was divided into the persistent incremental processes of vibration moments. And the expression of their solutions could be obtained by using a certain amplitude as control parameter in the harmonic balance process, and then the bifurcation, limit cycle flutter phenomena and the number of harmonic terms were analyzed. Finally, numerical results calculated by the Runge-Kutta method were given to verify the results obtained by the proposed procedure. It has been shown that the incremental harmonic method is effective and precise in the analysis of strongly nonlinear flutter with multiple structural nonlinearities.
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References
Woolston D S, Runyan H L, Andrews R E. An investigation of effects of certain types of structural nonlinearities on wing and control surface flutter[J]. Journal of the Aeronautical Sciences, 1957, 24(1):57–63.
Shen S F. An approximate analysis of nonlinear flutter problem[J]. Journal of the Aeronautical Sciences, 1959, 28(1):25–32,45.
Breitbach E. Flutter Analysis of an Airplane with Multiple Structural Nonlinearities in the Control System[M]. National Aeronautics and Space Administration, Hampton, Virginia, NASA TN-1620, 1980.
Liu J K, Zhao L C. Bifurcation analysis of airfoils in incompressible flow[J]. Journal of Sound and Vibration, 1992, 154(1):117–124.
Yang Y R, Zhao L C. Subharmonic bifurcation analysis of wing with store flutter[J]. Journal of Sound and Vibration, 1992, 157(3):477–484.
Lee C L. An iterative procedure for nonlinear analysis[J]. American Institute of Aeronautics and Astronautics Journal, 1986, 24(5):833–840.
Lau S L, Cheung Y K. Amplitude incremental variational principle for nonlinear vibration of elastic system[J]. ASME Journal of Applied Mechanics, 1981, 48(4):959–964.
Cheung Y K, Chen S H, Lau S L. Application of the incremental harmonic balance method to cubic non-linearity systems[J]. Journal of Sound and Vibration, 1990, 140(2):273–286.
Wong C W, Zhang W S, Lau S L. Periodic forced vibration of unsymmetrical piecewise linear systems by incremental harmonic balance method[J]. Journal of Sound and Vibration, 1991, 149(1):91–105.
Zhang W Y, Huseyin K. Complex formulation of the IHB technique and its comparison with other methods[J]. Applied Mathematical Modelling, 2001, 26(1):53–75.
Cai M, Liu J K, Yang Y. Incremental harmonic balance method for strongly nonlinear flutter of airfoils[J]. Mechanical Science and Technology, 2004, 23(6):742–744 (in Chinese).
Zhao L C, Yang Z C. Chaotic motion of an airfoil with nonlinear stiffness in incompressible flow[J]. Journal of Sound and Vibration, 1990, 138(2):245–254.
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Communicated by HUANG Xiao-qing
Project supported by the Ph. D. Programs Foundation of Ministry of Education of China (No. 20050558032); the Natural Science Foundation of Guangdong Province of China (No. 05003295); the Foundation of Sun Yat-sen University Advanced Research Center (No.06M8); the Young Teacher Scientific Research Foundation of Sun Sat-sen University (No.1131011)
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Cai, M., Liu, Jk. & Li, J. Incremental harmonic balance method for airfoil flutter with multiple strong nonlinearities. Appl Math Mech 27, 953–958 (2006). https://doi.org/10.1007/s10483-006-0711-y
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DOI: https://doi.org/10.1007/s10483-006-0711-y