Albert C. J. Luo - Nonlinear Vibration Reduction: An Electromagnetically Tuned Mass Damper System

This series publishes short books in mechanical engineering (ME), the engineering branch that combines engineering, physics and mathematics principles with materials science to design, analyze, manufacture, and maintain mechanical systems. It involves the production and usage of heat and mechanical power for the design, production and operation of machines and tools. This series publishes within all areas of ME and follows the ASME technical division categories.

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The vibration reduction of machines and structures is an important issue in engineering. Once the vibration reduction of machines and structures can be achieved, the usage lives of the machines and structures will be extended. On other hands, in recent years, one is more interested in harvesting energy from the vibrating structures and machines. Both vibration reduction and energy harvesting systems have the similar physical and mechanical mechanisms. Thus, this book will present how to determine periodic responses in vibration reduction systems and energy harvesting systems through a nonlinear, electromagnetically tuned mass damper. 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. The 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, there are seven chapters. The brief literature survey will be presented for the vibration reduction through the tuned mass damper systems. The semi-analytical methods are presented for stable and unstable periodic motions, and the corresponding stability and bifurcations are discussed in Chap. , independent period-12 motions are discussed, and the periodic motions become more and more complex. Such higher-order complex motions have their corresponding bifurcation trees to chaos through the period-doubling bifurcations. 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 frequencyamplitude characteristics for bifurcation routes of such higher-order periodic motions are presented. The unstable periodic motions are analytically determined. To keep such unstable periodic motions, some control schemes can be embedded in such vibration reductions and energy harvesting systems.

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. The authors hope this book can provide a way to look into nonlinear vibration reduction and energy harvesting in engineering systems.