Hopf bifurcation of an oscillator with quadratic and cubic nonlinearities and with delayed velocity feedback

摘要: This paper studies the local dynamics of an SDOF system with quadratic and cubic stiffness terms, linear delayed velocity feedback. The analysis indicates that for a sufficiently large feedback gain, equilibrium may undergo number stability switches increase time delay, then becomes unstable forever. At each critical value delay which changes its stability, generic Hopf bifurcation occurs periodic motion emerges in one-sided neighbourhood delay. method Fredholm alternative is applied to determine bifurcating motions their stability. It stresses on effect parameters stable regions amplitudes solutions.