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The tuned mass damper is one of the classic dynamic vibration absorbers with effective devices for energy dissipation and vibration reduction. The electromagnetically tuned mass damper system is extensively used for vibration reduction in engineering. A better understanding of the nonlinear dynamics of the electromagnetically tuned mass damper system is very important to optimize the parameters of such systems for vibration reduction. However, until now, one cannot fully understand complex periodic motions in such a nonlinear, electromagnetically tuned mass damper system. In this book, the semi-analytical solutions of periodic motions are presented through period-1, period-3, period-9, and period-12 motions. The corresponding stability and bifurcations of periodic motions are determined. The frequency-amplitude characteristics for bifurcation routes of such higher-order periodic motions are presented. This book helps people better understand the dynamical behaviors of an electromagnetically tuned mass damper system for the new development and design of vibration reduction and energy harvesting systems.
About the Authors
A Semi-analytical Method
Discretization
A Tuned Mass Damper System
Period-1 Motions
Period-m Motion
Finite Fourier Series of Periodic Motions
Period-1 Motion to Chaos
Bifurcation Routes of Period-1 Motion to Chaos
Frequency-Amplitude Characteristics
Period-1 and Period-2 Motions Illustrations
Independent Period-3 Motions
Analytical Period-3 Motions
Frequency-Amplitude Characteristics
Period-3 Motion Illustrations
Independent Period-9 Motions
A Semi-analytical Solution
Frequency-Amplitude Characteristics
Period-9 Motion Illustrations
Independent Period-12 Motions
A Semi-analytical Solution
Frequency-Amplitude Characteristics
Period-12 Motion Illustrations