Titlebook: Nonlinear Vibration Reduction; An Electromagnetical Albert C. J. Luo,Chuan Guo Book 2022 The Editor(s) (if applicable) and The Author(s), u

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A Semi-analytical Method,a nonlinear system has a periodic motion with a period of ., then such a periodic motion can be expressed by discrete points through discrete mappings of continuous corresponding systems. The method is presented through the following theorem. From Luo [51, 66], we have the following theorem.

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Discretization,period-1 and period-m motions will be discussed and the corresponding stability and bifurcation criteria will be presented. The finite Fourier series of periodic motions will be discussed from the corresponding discrete nodes.

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Period-1 Motion to Chaos,esented. The harmonic frequency-amplitude characteristics are presented for vibration reduction and energy harvesting, which can help one better understand nonlinear dynamics of the tuned mass damper systems. Period-1, period-2 and period-4 motions are illustrated through phase trajectories and harmonic amplitude spectrum.