3.4 Time-Delayed, Nonlinear Vibration Systems
In this section, the analytical solutions of periodic motion in time-delayed, nonlinear vibration systems are presented because of extensive application in vibration control, and the local stability and bifurcation theory will be applied to determine the stability and bifurcation of approximate solutions of time-delayed, nonlinear vibration systems.
3.4.1 Time-Delayed, Free Vibration Systems
Periodic flows in time-delayed, nonlinear vibration systems will be discussed herein. If such a time-delayed, vibration system has periodic flows with period 
, then such a periodic motion can be expressed by the Fourier series.
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