Discrete Frequency Models: A New Approach to Temporal Analysis

2000 ◽  
Vol 123 (1) ◽  
pp. 98-103 ◽  
Author(s):  
Douglas E. Adams ◽  
Randall J. Allemang
Keyword(s):  
Dynamic Systems ◽  
Excitation Frequency ◽  
Temporal Analysis ◽  
Structural Vibrations ◽  
Single Degree Of Freedom ◽  
New Approach ◽  
Discrete Frequency ◽  
Nonlinear Responses ◽  
Vibration Responses ◽  
Continuous Frequency

Forced vibration responses of nonlinear systems contain harmonics of the excitation frequency. These harmonics are either directly forced or are subharmonic, superharmonic, or combination resonances. Nonlinear responses of this type have been modeled historically using continuous time, discrete time, and continuous frequency models. A new approach to dynamic systems analysis is introduced here that uses difference equations in the discrete frequency domain to describe the evolution of forced, single degree of freedom, steady state vibration responses in frequency instead of time. A variety of possible applications in nonlinear experimental structural vibrations are also discussed.

A new method of fluxgate signal extraction

2017 ◽  
Vol 2017 (45) ◽  
pp. 83-89
Author(s):  
A.A. Marusenkov ◽  
Keyword(s):  
High Frequency ◽  
Second Harmonic ◽  
Excitation Frequency ◽  
Low Noise ◽  
Measuring System ◽  
Signal Extraction ◽  
Fluxgate Magnetometer ◽  
New Approach ◽  
Average Value ◽  
The Time Domain

Using dedicated high-frequency measuring system the distribution of the Barkhausen jumps intensity along a reversal magnetization cycle was investigated for low noise fluxgate sensors of various core shapes. It is shown that Barkhausen (reversal magnetization) noise intensity is strongly inhomogeneous during an excitation cycle. In the traditional second harmonic fluxgate magnetometers the signals are extracted in the frequency domain, as a result, some average value of reversal magnetization noises is contributed to the output signals. In order to fit better the noise shape and minimize its transfer to the magnetometer output the new approach for demodulating signals of these sensors is proposed. The new demodulating method is based on information extraction in the time domain taking into account the statistical properties of cyclic reversal magnetization noises. This approach yields considerable reduction of the fluxgate magnetometer noise in comparison with demodulation of the signal filtered at the second harmonic of the excitation frequency.

Analytical and experimental study on Van der Pol-type and Rayleigh-type equations for modeling nonlinear aeroelastic instabilities

2021 ◽  
pp. 136943322110220
Author(s):  
Guangzhong Gao ◽  
Ledong Zhu ◽  
Hua Bai ◽  
Wanshui Han ◽  
Feng Wang
Keyword(s):  
Aerodynamic Force ◽  
Early Stage ◽  
Higher Order ◽  
Empirical Modeling ◽  
Identification Algorithm ◽  
Van Der Pol ◽  
Single Degree Of Freedom ◽  
Section Shape ◽  
Vibration Responses ◽  
Aerodynamic Parameters

An empirical modeling of nonlinear aerodynamic force during aeroelastic instabilities, that is, vortex-induced vibration (VIV), galloping and flutter, is necessary in the estimation of vibration responses. Previous works on single-degree-of-freedom (SDOF) models suggest that nonlinear forms (Van der Pol or Rayleigh types) differ from section to section, which causes difficulty in practical application. Analytical evidences in this study have clarified that Van der Pol-type and Rayleigh-type models are equivalent in the amplitude-dependent aerodynamic damping; their difference lies in the higher-order harmonic responses. An identification algorithm of aerodynamic parameters is proposed to improve the robustness of aerodynamic parameters and guarantee the equivalence of both model types. Wind-tunnel tests of typical aeroelastic instabilities indicate that higher-order harmonic responses are small for VIV, galloping, and early-stage flutter instability when compared with the fundamental components due to weak nonlinearity. Van der Pol-type and Rayleigh-type models are both applicable until the flutter amplitude grows excessively large. It is clear that both model types are suitable for any section shape when use the proposed method of aerodynamic identification, and thus can be treated as a universal model for estimating the vibration amplitudes of nonlinear aeroelastic instabilities.

scholarly journals A New Approach of Asymmetric Homoclinic and Heteroclinic Orbits Construction in Several Typical Systems Based on the Undetermined Padé Approximation Method

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Jingjing Feng ◽  
Qichang Zhang ◽  
Wei Wang ◽  
Shuying Hao
Keyword(s):  
Dynamic Systems ◽  
Approximation Method ◽  
Padé Approximation ◽  
Global Bifurcation ◽  
Heteroclinic Orbits ◽  
Symmetric System ◽  
Pade Approximation ◽  
New Approach ◽  
Homoclinic And Heteroclinic Orbits ◽  
Single Orbit

In dynamic systems, some nonlinearities generate special connection problems of non-Z2symmetric homoclinic and heteroclinic orbits. Such orbits are important for analyzing problems of global bifurcation and chaos. In this paper, a general analytical method, based on the undetermined Padé approximation method, is proposed to construct non-Z2symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z2heteroclinic orbits are analyzed in detail. An undetermined frequency coefficient and a corresponding new analytic expression are introduced to improve the accuracy of the orbit trajectory. The proposed method shows high precision results for the Nagumo system (one single orbit); general types of non-Z2symmetric nonlinear quintic systems (orbit with one cusp); and Z2symmetric system with high-order nonlinear terms (orbit with two cusps). Finally, numerical simulations are used to verify the techniques and demonstrate the enhanced efficiency and precision of the proposed method.

Two Groups of Chaotic Vibrations in a Single-Degree-of-Freedom Maglev System

1997 ◽  
Author(s):  
Zhixiang Xu ◽  
Hideyuki Tamura
Keyword(s):  
Magnetic Levitation ◽  
Excitation Frequency ◽  
Power Spectra ◽  
Period Doubling ◽  
Excitation Amplitude ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Moving Base ◽  
Period Doubling Bifurcations

Abstract In this paper, a single-degree-of-freedom magnetic levitation dynamic system, whose spring is composed of a magnetic repulsive force, is numerically analyzed. The numerical results indicate that a body levitated by magnetic force shows many kinds of vibrations upon adjusting the system parameters (viz., damping, excitation amplitude and excitation frequency) when the system is excited by the harmonically moving base. For a suitable combination of parameters, an aperiodic vibration occurs after a sequence of period-doubling bifurcations. Typical aperiodic vibrations that occurred after period-doubling bifurcations from several initial states are identified as chaotic vibration and classified into two groups by examining their power spectra, Poincare maps, fractal dimension analyses, etc.

Beating Effects in a Single Nonlinear Dynamical System in a Neighborhood of the Resonance

2016 ◽  
Vol 849 ◽  
pp. 76-83
Author(s):  
Jiří Náprstek ◽  
Cyril Fischer
Keyword(s):  
Harmonic Balance ◽  
Excitation Frequency ◽  
Nonlinear Dynamical System ◽  
Numerical Continuation ◽  
System Response ◽  
Algebraic Equations ◽  
Single Degree Of Freedom ◽  
Nonlinear Dynamical ◽  
The Difference ◽  
Eigen Frequency

The exact coincidence of external excitation and basic eigen-frequency of a single degree of freedom (SDOF) nonlinear system produces stationary response with constant amplitude and phase shift. When the excitation frequency differs from the system eigen-frequency, various types of quasi-periodic response occur having a character of a beating process. The period of beating changes from infinity in the resonance point until a couple of excitation periods outside the resonance area. Theabove mentioned phenomena have been identified in many papers including authors’ contributions. Nevertheless, investigation of internal structure of a quasi-period and its dependence on the difference of excitation and eigen-frequency is still missing. Combinations of harmonic balance and small parameter methods are used for qualitative analysis of the system in mono- and multi-harmonic versions. They lead to nonlinear differential and algebraic equations serving as a basis for qualitativeanalytic estimation or numerical description of characteristics of the quasi-periodic system response. Zero, first and second level perturbation techniques are used. Appearance, stability and neighborhood of limit cycles is evaluated. Numerical phases are based on simulation processes and numerical continuation tools. Parametric evaluation and illustrating examples are presented.

scholarly journals Characterization of laser Doppler vibrometers using acousto-optic modulators

ACTA IMEKO ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 361
Author(s):  
Michael Gaitan ◽  
Jon Geist ◽  
Benjamin J. Reschovsky ◽  
Ako Chijioke
Keyword(s):  
Frequency Shift ◽  
Excitation Frequency ◽  
Laser Doppler Vibrometer ◽  
Laser Doppler ◽  
New Approach ◽  
Frequency Reference ◽  
Discrete Velocity ◽  
Velocity Shift ◽  
Vibration Excitation

We report on a new approach to characterize the performance of a laser Doppler vibrometer (LDV). The method uses two acousto-optic modulators (AOMs) to frequency shift the light from an LDV by a known quantity to create a synthetic velocity shift that is traceable to a frequency reference. Results are presented for discrete velocity shifts and for sinusoidal velocity shifts that would be equivalent to what would be observed in an ideal accelerometer vibration calibration. The method also enables the user to sweep the synthetic vibration excitation frequency to characterize the bandwidth of an LDV together with its associated electronics.

scholarly journals Une nouvelle approche pour immuniser nos forêts contre l'incertitude (essai)

2018 ◽  
Vol 169 (4) ◽  
pp. 199-202 ◽  
Author(s):  
Christian Messier ◽  
Fanny Maure ◽  
Núria Aquilué
Keyword(s):  
Forest Management ◽  
Global Change ◽  
Conceptual Framework ◽  
Complexity Theory ◽  
Dynamic Systems ◽  
Spatial Network ◽  
New Approach ◽  
The World ◽  
Present Context ◽  
Monitoring And Forecasting

A new approach to immunizing our forests against uncertainty (essay) In the present context of global change, managing our forests is a major challenge, in particular because of the great uncertainty associated with this change. Faced with this new reality, our methods of monitoring and forecasting the developments in our forests are no longer effective enough, so we have to review how we manage our forests. Complexity theory provides a conceptual framework for our approach, which leads us to adopt a more holistic and flexible way of seeing the world when planning our forest management. We must therefore accept that forests are complex and dynamic systems, and for that reason, never completely predictable. By incorporating the functional properties of trees and the complex spatial network of their populations in our forest management, and encouraging greater functional diversity and connectivity, we can immunize the forests against present and future stresses.

scholarly journals Polymeric Bearings as a new base isolation system suitable for mitigating machine-induced vibrations

2018 ◽  
Vol 211 ◽  
pp. 17001 ◽  
Author(s):  
Tomasz Falborski ◽  
Robert Jankowski
Keyword(s):  
Base Isolation ◽  
Excitation Frequency ◽  
Hysteresis Loops ◽  
Shaking Table ◽  
Damping Properties ◽  
Structural Vibrations ◽  
Isolation System ◽  
Equivalent Damping ◽  
Flexible Polymer ◽  
Base Isolation System

The present paper summarizes the preliminary results of the experimental shaking table investigation conducted in order to verify the effectiveness of a new base isolation system consisting of Polymeric Bearings in reducing strong horizontal machine-induced vibrations. Polymeric Bearing considered in the present study is a prototype base isolation system, which was constructed with the use of a specially prepared flexible polymer with improved damping properties. Dynamic oscillatory tests, during which a concrete base slab supported by four Polymeric Bearings was subjected to horizonal sinusoidal excitations characterized by different frequencies and amplitudes, were conducted in order to determine the damping properties of Polymeric Bearings and their effectiveness in mitigating structural vibrations. Equivalent damping ratios for every excitation frequency considered were determined using the experimentally obtained hysteresis loops. Final conclusions are presented and the results discussed.

Support Vector Regression Modeling for Design and Analysis of Mechanical Snubbing

2010 ◽  
Author(s):  
Sudhir Kaul
Keyword(s):  
Theoretical Model ◽  
Support Vector Regression ◽  
Dynamic Systems ◽  
Hysteretic Behavior ◽  
Model Complexity ◽  
Computational Time ◽  
Support Vector ◽  
Isolation System ◽  
Single Degree Of Freedom ◽  
Design Cycle

This paper discusses the application of Support Vector Regression (SVR) for modeling the non-linear and hysteretic behavior exhibited by mechanical snubbing systems. Though the discussion in this paper is limited to the application of SVR to snubbing in elastomeric isolators, the approach is generic and can be applied to other dynamic systems or to systems exhibiting hysteretic behavior. A theoretical model that represents the coupled dynamics of an isolation system with the corresponding snubbing system for a single degree-of-freedom system is proposed. The theoretical model is experimentally validated and is subsequently used to build a metamodel using SVR. The results of the metamodel are compared to the theoretical model for a simulation example and are found to be comparable, thereby reducing the computational time for the design and analysis of the snubbing system by orders of magnitude. The SVR based metamodel can, therefore, be used to substitute the computationally intense theoretical model for performing design iterations and design optimization of the snubbing system, significantly reducing model complexity as well as computational time during the design cycle.

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