scholarly journals On the detection of a nonlinear damage in an uncertain nonlinear beam using stochastic Volterra series

2019 ◽  
Vol 19 (4) ◽  
pp. 1137-1150 ◽  
Author(s):  
Luis GG Villani ◽  
Samuel da Silva ◽  
Americo Cunha ◽  
Michael D Todd
Keyword(s):  
Volterra Series ◽  
Novelty Detection ◽  
Nonlinear Behavior ◽  
System Response ◽  
Baseline Model ◽  
Nonlinear Beam ◽  
Stochastic Version ◽  
Nonlinear Components ◽  
Baseline State ◽  
Data Variation

In the present work, two issues that can complicate a damage detection process are considered: the uncertainties and the intrinsically nonlinear behavior. To deal with these issues, a stochastic version of the Volterra series is proposed as a baseline model, and novelty detection is applied to distinguish the condition of the structure between a reference baseline state (presumed “healthy”) and damaged. The studied system exhibits nonlinear behavior even in the reference condition, and it is exposed to a type of damage that causes the structure to display a nonlinear behavior with a different nature than the initial one. In addition, the uncertainties associated with data variation are taken into account in the application of the methodology. The results confirm that the monitoring of nonlinear coefficients and nonlinear components of the system response enables the method to detect the presence of the damage earlier than the application of some linear-based metrics. Besides that, the stochastic treatment enables the specification of a probabilistic interval of confidence for the system response in an uncertain ambient, thus providing more robust and reliable forecasts.

Generalized Cause-and-Effect Analyses for the Prototypic Nonlinear Mass–Spring–Damper System Using Volterra Kernels

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Ashraf Omran ◽  
Brett Newman
Keyword(s):  
Parametric Study ◽  
Volterra Series ◽  
System Response ◽  
System Behavior ◽  
Volterra Kernels ◽  
Numerical Examples ◽  
Frequency Domains ◽  
Variational Expansion ◽  
Mass Spring ◽  
Bilinear Terms

This paper develops generalized analytical first and second Volterra kernels for the prototypic nonlinear mass–spring–damper system. The nonlinearity herein is mathematically considered in quadratic and bilinear terms. A variational expansion methodology, one of the most efficient analytical Volterra techniques, is used to develop an analytical two-term Volterra series. The resultant analytical first and second kernels are visualized in both the time and the frequency domains followed by a parametric study to understanding the influence of each nonlinear/linear term appearing in the kernel structure. An analytical nonlinear step and periodic responses are also conducted to characterize the overall system response from the fundamental components. The developed analytical responses provide an illumination for the source of differences between nonlinear and linear responses. Feasibility of the proposed implementation is assessed by numerical examples. The developed kernel-based model shows the ability to predict, understand, and analyze the system behavior beyond that attainable by the linear-based model.

Characterization of Nonlinear Rattling Behavior of a Gear Pair Through a Validated Torsional Model

2021 ◽  
Author(s):  
Ata Donmez ◽  
Ahmet Kahraman
Keyword(s):  
Piecewise Linear ◽  
Nonlinear Behavior ◽  
Severity Index ◽  
System Response ◽  
Gear Pair ◽  
Computationally Efficient ◽  
Linear Solution ◽  
Set Up ◽  
The Impact ◽  
Gear Rattle

Abstract Dynamic response of a gear pair subjected to input and output torque or velocity fluctuations is examined analytically. Such motions are commonly observed in various powertrain systems and identified as gear rattle or hammering motions with severe noise and durability consequences. A reduced-order torsional model is proposed along with a computationally efficient piecewise-linear solution methodology to characterize the system response including its sensitivity to excitation parameters. Validity of the proposed model is established through comparisons of its predictions to measurements from a gear rattle experimental set-up. A wide array of nonlinear behavior is demonstrated through presentation of periodic and chaotic responses in the forms of phase plots, Poincaré maps, and bifurcation diagrams. The severity of the resultant impacts on the noise outcome is also assessed through a rattle severity index defined by using the impact velocities.

Nonlinear Dynamic Analysis of Atomic Force Microscopy

2006 ◽  
Author(s):  
Hossein Nejat Pishkenari ◽  
Mehdi Behzad ◽  
Ali Meghdari
Keyword(s):  
Atomic Force Microscopy ◽  
Equations Of Motion ◽  
Basin Of Attraction ◽  
Nonlinear Dynamic Analysis ◽  
Nonlinear Behavior ◽  
Random Excitation ◽  
System Response ◽  
Force Microscopy ◽  
Atomic Force ◽  
Exciting Frequency

This paper is devoted to the analysis of nonlinear behavior of amplitude modulation (AM) and frequency modulation (FM) modes of atomic force microscopy. For this, the microcantilever (which forms the basis for the operation of AFM) is modeled as a single mode approximation and the interaction between the sample and cantilever is derived from a van der Waals potential. Using perturbation methods such as Averaging, and Fourier transform nonlinear equations of motion are analytically solved and the advantageous results are extracted from this nonlinear analysis. The results of the proposed techniques for AM-AFM, clearly depict the existence of two stable and one unstable (saddle) solutions for some of exciting parameters under deterministic vibration. The basin of attraction of two stable solutions is different and dependent on the exciting frequency. From this analysis the range of the frequency which will result in a unique periodic response can be obtained and used in practical experiments. Furthermore the analytical responses determined by perturbation techniques can be used to detect the parameter region where the chaotic motion is avoided. On the other hand for FM-AFM, the relation between frequency shift and the system parameters can be extracted and used for investigation of the system nonlinear behavior. The nonlinear behavior of the oscillating tip can easily explain the observed shift of frequency as a function of tip sample distance. Also in this paper we have investigated the AM-AFM system response under a random excitation. Using two different methods we have obtained the statistical properties of the tip motion. The results show that we can use the mean square value of tip motion to image the sample when the excitation signal is random.

Prediction of Periodic Response of Flexible Mechanical Systems With Nonlinear Characteristics

1990 ◽  
Vol 112 (4) ◽  
pp. 501-507 ◽  
Author(s):  
Ting-Nung Shiau ◽  
An-Nan Jean
Keyword(s):  
Nonlinear Differential Equations ◽  
System Response ◽  
Algebraic Equations ◽  
Nonlinear Characteristics ◽  
Periodic Response ◽  
Rotor Systems ◽  
Nonlinear Algebraic Equations ◽  
Numerical Analytical Method ◽  
Harmonic Components ◽  
Nonlinear Components

A numerical-analytical method for the prediction of steady state periodic response of large order nonlinear rotordynamic systems is addressed. Using this method, the set of nonlinear differential equations governing the motion of the rotor systems is transformed to a set of nonlinear algebraic equations. A condensation technique is proposed to reduce the nonlinear algebraic equations to those only related to the physical coordinates associated with nonlinear components. The method allows for the inclusion of searching for sub, super, ultra-sub and ultra-super harmonic components of the system response. Furthermore it can be used to locate limit cycles of an autonomous system. Three examples are employed to demonstrate the accuracy and the efficiency of the present method.

Dynamics of a Rotating System With a Nonlinear Eddy-Current Damper

1998 ◽  
Vol 120 (4) ◽  
pp. 848-853 ◽  
Author(s):  
Y. Kligerman ◽  
O. Gottlieb
Keyword(s):  
Nonlinear Dynamics ◽  
Eddy Current ◽  
Eddy Currents ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
System Response ◽  
Rotating System ◽  
Restoring Force ◽  
Rotating Systems ◽  
Eddy Current Damper

We investigate the nonlinear dynamics and stability of a rotating system with an electromagnetic noncontact eddy-current damper. The damper is modeled by a thin nonmagnetic disk that is translating and rotating with a shaft in an air gap of a direct current electromagnet. The damper dissipates energy of the rotating system lateral vibration through induced eddy-currents. The dynamical system also includes a cubic restoring force representing nonlinear behavior of rubber o-rings supporting the shaft. The equilibrium state of the balanced rotating system with an eddy-current damper becomes unstable via a Hopf bifurcation and exact solutions for the limit cycle radius and frequency of the self-excited oscillation are obtained analytically. Forced vibration induced by the rotating system mass imbalance is also investigated analytically and numerically. System response includes periodic and quasiperiodic solutions. Stability of the periodic solutions obtained from the balanced self-excited motion and the imbalance forced response is analyzed by use of Floquet theory. This analysis enables an explanation of the nonlinear dynamics and stability phenomena documented for rotating systems controlled by electromagnetic eddy-current dampers.

Application of Peak Distribution Method for Response Based Analysis of Mooring Lines Under Tropical Storms

2020 ◽  
Author(s):  
A. Ghasemi ◽  
Y. Drobyshevski ◽  
M. Kimiaei ◽  
M. Efthymiou
Keyword(s):  
Time Domain ◽  
Nonlinear Behavior ◽  
Extreme Value Distribution ◽  
Time Domain Analysis ◽  
System Response ◽  
Response Analysis ◽  
Tropical Storms ◽  
Mooring Lines ◽  
Distribution Method ◽  
Large Variability

Abstract Response based analysis (RBA) is a comprehensive approach for the prediction of extreme responses and design metocean conditions of offshore facilities. For RBA, the structural system needs to be modelled, and its behavior analyzed when subjected to large metocean datasets, usually comprising thousands of different sea states. Due to the dynamic and nonlinear behavior of mooring systems in floating structures, application of conventional time domain analysis for RBA of these systems is a computationally demanding process. Hence, investigation of faster solvers and more efficient methods for the RBA is inevitable. Peak distribution method (PDM), which has recently been introduced and used for response analysis of mooring systems under extreme design conditions, is a possible solution to reduce the computational efforts in RBA by reducing the number of simulations. This study explores the utilization of the PDM for RBA of the mooring system of a turret-moored large FPSO subjected to tropical storms. Large variability of metocean parameters within such storms limits the applicability of intuitive judgement for the selection of governing sea states. The results are compared through both time-domain and frequency-domain simulations and a computationally efficient methodology is proposed. It provides a general robust framework of computing the extreme value distribution of the system response. The proposed methodology can be used for RBA of mooring lines tension under storm conditions comprising large number of sea states.

Nonlinear analysis of VCO jitter generation using Volterra series

2018 ◽  
Vol 37 (2) ◽  
pp. 755-771
Author(s):  
Hadi Dehbovid ◽  
Habib Adarang ◽  
Mohammad Bagher Tavakoli
Keyword(s):  
Phase Noise ◽  
Volterra Series ◽  
Nonlinear Behavior ◽  
Voltage Controlled Oscillator ◽  
Degree Polynomial ◽  
Content Type ◽  
Practical Model ◽  
Oscillator Phase Noise ◽  
Oscillator Phase ◽  
Second Degree

PurposeCharge pump phase locked loops (CPPLLs) are nonlinear systems as a result of the nonlinear behavior of voltage-controlled oscillators (VCO). This paper aims to specify jitter generation of voltage controlled oscillator phase noise in CPPLLs, by considering approximated practical model for VCO. Design/methodology/approachCPPLL, in practice, shows nonlinear behavior, and usually in LC-VCOs, it follows second-degree polynomial function behavior. Therefore, the nonlinear differential equation of the system is obtained which shows the CPPLLs are a nonlinear system with memory, and that Volterra series expansion is useful for such systems. FindingsIn this paper, by considering approximated practical model for VCO, jitter generation of voltage controlled oscillator phase noise in CPPLLs is specified. Behavioral simulation is used to validate the analytical results. The results show a suitable agreement between analytical equations and simulation results. Originality/valueThe proposed method in this paper has two advantages over the conventional design and analysis methods. First, in contrast to an ideal CPPLL, in which the characteristic of the VCO’s output frequency based on the control voltage is linear, in the present paper, a nonlinear behavior was considered for this characteristic in accordance with the real situations. Besides, regarding the simulations in this paper, a behavior similar to the second-degree polynomial was considered, which caused the dependence of the produced jitter’s characteristic corner frequency on the jitter’s amplitude. Second, some new nonlinear differential equations were proposed for the system, which ensured the calculation of the produced jitter of the VCO phase noise in CPPLLs. The presented method is general enough to be used for designing the CPPLL.

Dynamics of a Rotating System With a Nonlinear Eddy-Current Damper

1997 ◽  
Author(s):  
Yuri Kligerman ◽  
Oded Gottlieb
Keyword(s):  
Nonlinear Dynamics ◽  
Eddy Current ◽  
Eddy Currents ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
System Response ◽  
Rotating System ◽  
Restoring Force ◽  
Rotating Systems ◽  
Eddy Current Damper

Abstract The investigation of nonlinear dynamics and stability of a rotating system with an electromagnetic non-contact eddy-current damper is carried out. The damper is modeled by a thin nonmagnetic disk that is translating and rotating with a shaft in an air gap of a direct current electromagnet. The damper dissipates energy of the rotating system lateral vibration through induced eddy-currents. The dynamical system also includes a cubic restoring force representing nonlinear behavior of rubber o-rings supporting the shaft. The equilibrium state of the balanced rotating system with an eddy-current damper becomes unstable via a Hopf bifurcation and exact solutions for the limit cycle radius and frequency of the self-excited oscillation are obtained analytically. Forced vibration induced by the rotating system mass imbalance is also investigated analytically and numerically. System response includes periodic and quasiperiodic solutions. Stability of the periodic solutions obtained from the balanced self-excited motion and the unbalance forced response is analyzed by use of Floquet theory. This analysis enables an explanation of the nonlinear dynamics and stability phenomena documented for rotating systems controlled by electromagnetic eddy-current dampers.

Nonlinearity Mode Theory Foundation Research of EMP Coupling by Volterra Series

2014 ◽  
Vol 511-512 ◽  
pp. 1022-1026
Author(s):  
Yong Sheng Gao ◽  
Sha Wu ◽  
Jiu He Ma ◽  
Jiu Liang Xiong
Keyword(s):  
Volterra Series ◽  
Electromagnetic Coupling ◽  
Nonlinear Behavior ◽  
Coupling Model ◽  
Kernel Functions ◽  
Volterra Kernel ◽  
Coupling Process ◽  
Electric System ◽  
Model Research ◽  
Theory Foundation

Strong Electromagnetic Pulses (EMP) as a new idea weapon has caused many effects like malfunctions, performance degradation, interferences, and destructions in electronic and electrical systems. EMP coupling model research is the foundation of effect evolution and protection. In this paper, a new modeling method on the base of combination system identification theory and Volterra series algorithm was utilized to analyze the electromagnetic coupling process from an external field to an inner electric system. First, we will analyze the theory foundation of non-parameters model evolution. And then, using input and output test data, we presented commonly Voleterra series expression of EMP electromagnetic coupling model. Then, we analyze coupling models several important characteristics in detail. Finally, we approach High Order Spectrum algorithms to identify Volterra kernel functions. Theoretical results show that the Volterra kernel function will be used as an efficient method in EMP coupling model research and can apply this method to character the nonlinear behavior of the EMP electromagnetic coupling. The model described above was assigned under certain assumptions, moreover describes the effects in theory only and does not consider the time variation of the parameters of the system. From this reason it appears as more convenient to characterize the electromagnetic coupling process, by a more universal mathematical approach.

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