A fifth-order multiple-scale solution for Hopf bifurcations

Hassard, 1981 Dowell, 1995 Dowell, 1988 Lee BHK, Jiang L, Wong YS. Flutter of an airfoil with a cubic nonlinear restoring force. AIAA-98-1725, 1998. p. 237–57 Tang, 1992, Flutter and stall response of helicopter blade with structural nonlinearity, J. Aircraft, 29, 953, 10.2514/3.46268 Carcaterra, 2000, Shock spectral analysis of elastic systems impacting on the water surface, J. Sound Vib., 229, 579, 10.1006/jsvi.1999.2517 Dessi, 2002, Limit-cycle stability reversal near a Hopf bifurcation with aeroelastic applications, J. Sound Vib., 347, 10.1006/jsvi.2001.4212 Poincaré, 1929 Bruno AD. Local method in nonlinear differential equations: Part I: The local method of nonlinear analysis of differential equations; Part II: The sets of analyticity of normalizing transformation. Soviet Mathematics. Springer, 1989 Deprit, 1969, Canonical transformation depending on a small parameter, Celestial Mech., 1, 12, 10.1007/BF01230629 Kamel, 1970, Perturbation method in the theory of nonlinear oscillations, Celestial Mech., 3, 90, 10.1007/BF01230435 Kryloff, 1947 Cole, 1963, Uniformly valid asymptotic approximation for certain nonlinear differential equations, vol. 9 Sandri, 1963, The foundations of nonequilibrium statistical mechanics, Ann. Phys., 24, 332, 10.1016/0003-4916(63)90076-9 Frieman, 1963, On a new method in the theory of irreversible process, J. Math. Phys., 4, 410, 10.1063/1.1703968 Nayfeh, 1965, A perturbation method for treating nonlinear oscillation problems, J. Math. Phys., XLIV, 368, 10.1002/sapm1965441368 Nayfeh, 1973 Nayfeh, 1979 Morino, 1969, A perturbation method for treating nonlinear panel flutter problems, AIAA J., 7, 405, 10.2514/3.5121 Smith, 1976, Stability analysis of nonlinear differential autonomous system with applications to flutter, AIAA J., 14, 333, 10.2514/3.61370 Morino L, Kuo C. Detailed Extension of Perturbation Methods for Nonlinear Panel Flutter. ASRL TR 164-2, Massachusetts Institute of Technology, Cambridge MA, 1971 Chow, 1982 Mastroddi F. Aeroservoelasticità: Problematiche Nonlineari. PhD thesis, Department of Aerospace Engineering and Astronautics, University of Rome La Sapienza, 1994 Nayfeh, 1995 Lacabanne M. An experimental analysis of the aeroelastic behaviour with a freeplay in a control surface. In: Proceedings of the CEAS International Forum of Aeroelasticity and Structural Dynamics, vol. 3, Rome, 1999. p. 239–46 Matsushita H, Saitoh K, Granasy P. Wind tunnel investigation of transonic limit cycle flutter. AIAA-98-1728, 1998. p. 267–73 Chen PC, Sarhaddi D, Liu DD. Limit-cycle-oscillations studies of a fighter with external stores. AIAA-98-1727, 1998. p. 258–66