Detection of gases and vapours concentration from resonance curve of interdigital system

The influence of the electromagnetic parameters on the torsional dynamics of the electric vehicle powertrain is studied by considering the electromechanical coupling effect. By adding the electromagnetic torque on the drive side, the powertrain is simplified as nonlinear drive-shaft model. The number, stability, and bifurcation conditions of the equilibrium points of the nonlinear drive-shaft model are deduced. Based on the averaged equations and the amplitude-frequency response equation, the stability and bifurcation conditions, such as fold bifurcation and Hopf bifurcation, of the resonance curve are discussed. The influence of electromagnetic parameters on the torsional dynamics is studied by simulation. It is shown that with the change of the parameters, the number as well as the stability of the equilibrium points may be changed which is affected by fold bifurcation. It is also shown that the resonance curve may lose its stability when fold bifurcation happens. By limiting the parameters in the region without fold bifurcation, the unstable dynamics of the resonance curve can be controlled.

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Nonlinear Resonance Curve: Electrical

Laboratory Manual for Nonlinear Physics with Maple for Scientists and Engineers ◽

10.1007/978-1-4612-2438-9_18 ◽

1997 ◽

pp. 87-91

Author(s):

Richard H. Enns ◽

George McGuire

Keyword(s):

Nonlinear Resonance ◽

Resonance Curve

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Nonlinear Resonance Curve: Magnetic

Nonlinear Physics with Maple for Scientists and Engineers ◽

10.1007/978-1-4612-1322-2_33 ◽

2000 ◽

pp. 589-592

Author(s):

Richard H. Enns ◽

George C. McGuire

Keyword(s):

Nonlinear Resonance ◽

Resonance Curve

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Associated equations and their corresponding resonance curve

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/9996 ◽

1999 ◽

Vol 21 (3) ◽

pp. 147-155

Author(s):

Nguyen Van Dinh

Keyword(s):

Numerical Method ◽

Analytical Method ◽

Nonlinear Oscillations ◽

Resonance Curve ◽

Practical Case ◽

High Harmonics

In the theory of nonlinear oscillations, in order to identify the resonance curve we usually try to eliminate the diphase Ѳ in the equations of stationary oscillations. We obtain thus a certain frequency-amplitude relationship. In simple cases when the mentioned equations contain only and linearly the first harmonics (sin Ѳ, cos Ѳ) the elimination of Ѳ is elementary, by using the trigono-metrical identity sin2 Ѳ+ cos2 Ѳ = 1. In general, high harmonics (sin2 Ѳ, cos2 Ѳ, etc.) are present. Consequently the expressions of sin Ѳ, cos Ѳ are cumbersome or do not exist and the analytical elimination of Ѳ is quite inconvenient or impossible. For this reason, to identify the resonance curve of complicated systems, we use the numerical method. Below, intending to develop the analytical method, we shall propose a procedure enabling us to transform the "original" complicated equations of stationary oscillations into the so-called associated ones, only and linearly containing sin Ѳ, cos Ѳ. The equivalence of the original and associated equations will be treated and the associated resonance 'curve-that is determined by the associated equations-will be analyzed The discussion will be restricted to a simple practical case in which, beside sin Ѳ and cos Ѳ, only sin2 Ѳ and cos2 Ѳ are present. Nevertheless, the method proposed and the results obtained can be generalized.

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Prediction of Isolated Resonance Curves Using Nonlinear Normal Modes

Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

10.1115/detc2015-46301 ◽

2015 ◽

Cited By ~ 1

Author(s):

R. J. Kuether ◽

L. Renson ◽

T. Detroux ◽

C. Grappasonni ◽

G. Kerschen ◽

...

Keyword(s):

Normal Modes ◽

Resonance Curve ◽

Element Model ◽

Nonlinear Normal Modes ◽

Initial Guess ◽

Forced Response ◽

Numerical Continuation ◽

Continuation Algorithm ◽

Resonance Curves ◽

Nonlinear Normal

Isolated resonance curves are separate from the main nonlinear forced-response branch, so they can easily be missed by a continuation algorithm and the resonant response might be underpredicted. The present work explores the connection between these isolated resonances and the nonlinear normal modes of the system and adapts an energy balance criterion to connect the two. This approach provides new insights into the occurrence of isolated resonances as well as a method to find an initial guess to compute the isolated resonance curve using numerical continuation. The concepts are illustrated on a finite element model of a cantilever beam with a nonlinear spring at its tip. This system presents jumps in both frequency and amplitude in its response to a swept sinusoidal excitation. The jumps are found to be the result of a modal interaction that creates an isolated resonance curve that eventually merges with the main resonance branch as the excitation force increases. Excellent insight into the observed dynamics is provided with the NNM theory, which supports that NNMs can also be a useful tool for predicting isolated resonance curves and other behaviors in the damped, forced response.

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Exact Optimization of a Three-Element Dynamic Vibration Absorber: Minimization of the Maximum Amplitude Magnification Factor

Journal of Vibration and Acoustics ◽

10.1115/1.4040575 ◽

2018 ◽

Vol 141 (1) ◽

Cited By ~ 6

Author(s):

Osamu Nishihara

Keyword(s):

Maximum Amplitude ◽

Resonance Curve ◽

Element Model ◽

Optimality Criteria ◽

Simultaneous Equations ◽

Vibration Absorber ◽

Magnification Factor ◽

Dynamic Vibration Absorber ◽

Dynamic Vibration ◽

Numerical Computing

In this study, the maximum amplitude magnification factor for a linear system equipped with a three-element dynamic vibration absorber (DVA) is exactly minimized for a given mass ratio using a numerical approach. The frequency response curve is assumed to have two resonance peaks, and the parameters for the two springs and one viscous damper in the DVA are optimized by minimizing the resonance amplitudes. The three-element model is known to represent the dynamic characteristics of air-damped DVAs. A generalized optimality criteria approach is developed and adopted for the derivation of the simultaneous equations for this design problem. The solution of the simultaneous equations precisely equalizes the heights of the two peaks in the resonance curve and achieves a minimum amplitude magnification factor. The simultaneous equations are solvable using the standard built-in functions of numerical computing software. The performance improvement of the three-element DVA compared to the standard Voigt type is evaluated based on the equivalent mass ratios. This performance evaluation is highly accurate and reliable because of the precise formulation of the optimization problem. Thus, the advantages of the three-element type DVA have been made clearer.

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