Frequency domain analysis of a dimensionless cubic nonlinear damping system subject to harmonic input
TL;DR: In this article, the effects of cubic nonlinear damping on the system output spectrum are theoretically studied through a dimensionless mass-spring damping system model subject to a harmonic input, based on the Volterra series approximation.
Abstract: The effects of cubic nonlinear damping on the system output spectrum are theoretically studied through a dimensionless mass–spring damping system model subject to a harmonic input, based on the Volterra series approximation. It is theoretically shown that the cubic nonlinear damping has little effect on the system output spectrum at high or low frequencies but drives the system output spectrum to be an alternative series at the natural frequency 1 such that the system output spectrum can be suppressed by the cubic damping.
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TL;DR: A review of the vibration isolation theory and/or methods which were developed, mainly over the last decade, specifically for or potentially could be used for, micro-vibration control can be found in this paper.
311 citations
TL;DR: The magnetorheological fluid dampers could offer an outstanding capability in semiactive vibration control due to excellent dynamical features such as fast response, environmentally robust characteristics, large force capacity, low power consumption, and simple interfaces between electronic input and mechanical output as mentioned in this paper.
Abstract: Magnetorheological fluid technology has gained significant development during the past decades. The application of magnetorheological fluids has grown rapidly in civil engineering, safety engineering, transportation, and life science with the development of magnetorheological fluid–based devices, especially magnetorheological fluid dampers. The magnetorheological fluid dampers could offer an outstanding capability in semiactive vibration control due to excellent dynamical features such as fast response, environmentally robust characteristics, large force capacity, low power consumption, and simple interfaces between electronic input and mechanical output. To address the fast growing demand on magnetorheological fluid damping technology in extensive engineering practices, the state-of-the-art development is presented in this article, which provides a comprehensive review on the structure design and its analysis of magnetorheological fluid dampers (or systems). This can be regarded as a useful complement to...
298 citations
Cites background from "Frequency domain analysis of a dime..."
...…systems indicate that noticeable advantages could be produced by the nonlinearity in system vibration control compared with linear viscous damping (Gao and Cheng, 2004, 2005; Ibrahim, 2008; Jing et al., 2008a, 2008b, 2011a, 2011b; Jing and Lang, 2009; Lang et al., 2009; Marouze and Cheng, 2002)....
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TL;DR: In this paper, the authors consider a doubly clamped micromechanical beam oscillator, which exhibits nonlinearity in both elastic and dissipative properties, and show that nonlinear dissipation effects can have a significant impact on the dynamics of micro-empowered systems, and develop a continuous model of a geometrically nonlinear beam-string with a linear Voigt-Kelvin viscoelastic constitutive law.
Abstract: Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). A Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast, nonlinear dissipation effects in micromechanical oscillators are often overlooked. In this work, we consider a doubly clamped micromechanical beam oscillator, which exhibits nonlinearity in both elastic and dissipative properties. The dynamics of the oscillator is measured in both frequency and time domains and compared to theoretical predictions based on a Duffing-like model with nonlinear dissipation. We especially focus on the behavior of the system near bifurcation points. The results show that nonlinear dissipation can have a significant impact on the dynamics of micromechanical systems. To account for the results, we have developed a continuous model of a geometrically nonlinear beam-string with a linear Voigt–Kelvin viscoelastic constitutive law, which shows a relation between linear and nonlinear damping. However, the experimental results suggest that this model alone cannot fully account for all the experimentally observed nonlinear dissipation, and that additional nonlinear dissipative processes exist in our devices.
183 citations
TL;DR: In this article, the authors proposed a novel vibration isolator with 3D quasi-zero-stiffness (QZS) property, which applied symmetrically scissor-like structures in the horizontal directions, together with a traditional spring-mass-damper system assembled vertically with positive stiffness.
159 citations
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TL;DR: In this article, the authors consider a doubly clamped micromechanical beam oscillator, which exhibits nonlinearity in both elastic and dissipative properties, and the dynamics of the oscillator is measured in frequency domain and time domain and compared to theoretical predictions based on Duffing-like model with nonlinear dissipation.
Abstract: Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast, nonlinear dissipation effects in micromechanical oscillators are often overlooked. In this work, we consider a doubly clamped micromechanical beam oscillator, which exhibits nonlinearity in both elastic and dissipative properties. The dynamics of the oscillator is measured in frequency domain and time domain and compared to theoretical predictions based on Duffing-like model with nonlinear dissipation. We especially focus on the behavior of the system near bifurcation points. The results show that nonlinear dissipation can have a significant impact on the dynamics of micromechanical systems. To account for the results, we have developed a continuous model of a nonlinear viscoelastic string with Voigt-Kelvin dissipation relation, which shows a relation between linear and nonlinear damping. However, the experimental results suggest that this model alone cannot fully account for all the experimentally observed nonlinear dissipation, and that additional nonlinear dissipative processes exist in our devices.
146 citations
Cites background from "Frequency domain analysis of a dime..."
...For example, the effect of nonlinear damping for the case of strictly dissipative force, being proportional to the velocity to the nth power, on the response and bifurcations of driven Duffing [55–58] and other types of nonlinear oscillators [45, 57, 59–61] has been studied extensively....
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References
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Book•
25 Oct 1985
TL;DR: The history of the theory of averaging can be found in this paper, where a 4-dimensional example of Hopf Bifurcation is presented. But the history of averaging is not complete.
Abstract: Basic Material and Asymptotics.- Averaging: the Periodic Case.- Methodology of Averaging.- Averaging: the General Case.- Attraction.- Periodic Averaging and Hyperbolicity.- Averaging over Angles.- Passage Through Resonance.- From Averaging to Normal Forms.- Hamiltonian Normal Form Theory.- Classical (First-Level) Normal Form Theory.- Nilpotent (Classical) Normal Form.- Higher-Level Normal Form Theory.- The History of the Theory of Averaging.- A 4-Dimensional Example of Hopf Bifurcation.- Invariant Manifolds by Averaging.- Some Elementary Exercises in Celestial Mechanics.- On Averaging Methods for Partial Differential Equations.
1,765 citations
"Frequency domain analysis of a dime..." refers methods in this paper
..., the describing function and harmonic balance in the frequency domain [22, 23] and the averaging method in the time domain [24–27], etc....
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Book•
01 Aug 1981
969 citations
Additional excerpts
...The generalized frequency response function (GFRF) is defined as [13] ∫ ∫ ∞ ∞ − ∞ ∞ − + + − = n n n n n n n d d j h j j H τ τ τ ω τ ω τ τ ω ω L L L L L 1 1 1 1 1 )) ( exp( ) , , ( ) , , ( (3) which provides a basis for the frequency domain analysis of nonlinear systems....
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TL;DR: In this article, it was shown that any time-invariant continuous nonlinear operator with fading memory can be approximated by a Volterra series operator, and that the approximating operator can be realized as a finite-dimensional linear dynamical system with a nonlinear readout map.
Abstract: Using the notion of fading memory we prove very strong versions of two folk theorems. The first is that any time-invariant (TI) continuous nonlinear operator can be approximated by a Volterra series operator, and the second is that the approximating operator can be realized as a finite-dimensional linear dynamical system with a nonlinear readout map. While previous approximation results are valid over finite time intervals and for signals in compact sets, the approximations presented here hold for all time and for signals in useful (noncompact) sets. The discretetime analog of the second theorem asserts that any TI operator with fading memory can be approximated (in our strong sense) by a nonlinear moving- average operator. Some further discussion of the notion of fading memory is given.
923 citations
TL;DR: While the main emphasis is on Linear-Quadratic optimal control and active suspensions, the paper also addresses a number of related subjects including semi-active suspensions; robust, adaptive and nonlinear control aspects and some of the important practical considerations.
779 citations
"Frequency domain analysis of a dime..." refers background in this paper
...Keywords: Cubic nonlinear damping, Output frequency response, Alternative series 1 Introduction Suppression of system output vibration covers a wide range of applications such as active control or isolation of the foundation vibration in many engineering systems [5]....
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