Nonlinear Vibration Reduction
An Electromagnetically Tuned Mass Damper System
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Article
Periodic cutting motions in a vibration-assisted, regenerative, nonlinear Orthogonal turning system
In this paper, a mathematical model of 2-degrees-of-freedom (2-DOF), vibration-assisted, regenerative, nonlinear orthogonal turning system is developed. The period-1 motions of such a system are predicted thro...
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Chapter
Introduction
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Chapter
Discretization
In this chapter, a physical model of the tuned mass damper system will be presented. The discrete map** will be developed for periodic motions, and period-1 and period-m motions will be discussed and the cor...
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Chapter
Independent Period-12 Motions
Semi-analytical solutions, frequency-amplitude characteristics, and simulation results of one branch period-12 motions in the frequency range of $$\Om...
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Chapter
A Semi-analytical Method
Periodic motions in nonlinear dynamical systems will be obtained through the implicit map**s obtained from the nonlinear differential equations. If a nonlinear system has a periodic motion with a period of ...
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Chapter
Independent Period-9 Motions
Semi-analytical solutions, frequency-amplitude characteristics, and simulation results of one branch period-9 motions in the frequency range of $$\Ome...
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Chapter
On Complex Periodic Evolutions of a Periodically Diffused Brusselator
Complex periodic evolutions in a periodically Diffused Brusselator are presented through the generalized harmonic balance method, and the corresponding stability and bifurcations of the periodic evolutions are...
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Chapter
Independent Period-3 Motions
The semi-analytical solutions, frequency-amplitude characteristics, and simulation results of three branches independent period-3 motions in the frequency range of ...
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Book
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Chapter
Periodic Motions to Chaos in a Nonlinear Rotor System
In this chapter, a route of periodic motions to chaos in a nonlinear Jeffcott rotor system are studied through an implicit map** method. The continuous nonlinear rotor system is discretized to construct impl...
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Chapter
Periodic Motions and Bifurcations in a Double Pendulum
In this chapter, period-1 to period-4 motions and an independent period-3 motion of a periodically forced double-pendulum are predicted through a discrete implicit map** method. The corresponding stability a...
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Chapter
Period-1 Motion to Chaos
As in Guo and Luo [63, 64], the bifurcation trees of period-1 motion to chaos in the nonlinear electromagnetically tuned mass damper system will be presented. The harmonic frequency-amplitude characteristics a...
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Article
A Family of Periodic Motions to Chaos with Infinite Homoclinic Orbits in the Lorenz System
In this paper, the bifurcation dynamics of a family of \((n_{1},1,n_{2})\) -periodic motions to cha...
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Article
Symmetric and asymmetric periodic motions of a nonlinear oscillator with a tuned mass damper inerter
In this paper, periodic responses in a nonlinear oscillator with electromagnetic resonant shunt tuned mass damper inerter (ERS-TMDI) are studied. Symmetric and asymmetric periodic motions of such a system are ...
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Article
Periodic motions on bifurcation trees in an inverted pendulum with a periodically moving base
This paper studies periodic motions of an inverted pendulum with a periodically moving base. A bifurcation tree of period-1 to period-8 motions is predicted through a discrete implicit map** method. The stab...
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Article
Analytical periodic motions in a discontinuous system with a switching hyperbola
In this paper, studied are periodic motions in a discontinuous system with three vector fields switching through two branches of a hyperbola. The switchability conditions of flows at the discontinuous boundari...
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Article
On bifurcations and local stability in 1-D nonlinear discrete dynamical systems
In this paper, a theory of bifurcations and local stability of fixed-points (or period-1 solutions) in one-dimensional nonlinear discrete dynamical systems is presented. The linearized discrete dynamical syste...
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Chapter
Quadratic Nonlinear Functional Systems
In this chapter, the stability of equilibriums in 1-dimensional quadratic nonlinear functional systems are discussed. The upper-saddle-node and lower-saddle-node appearing and switching bifurcations with and with...
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Chapter
(2m+1)th-Degree Polynomial Functional Systems
In this chapter, the global stability and bifurcation of functional equilibriums in the (2m + 1)th-degree polynomial nonlinear functional dynamical systems.
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Chapter
Correction to: Two-Dimensional Quadratic Nonlinear Systems
This book was inadvertently published with few errors. This has now been amended in respective chapters.
