Modal Techniques for Remote Identification of Nonlinear Reactions at Gap-Supported Tubes Under Turbulent Excitation

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Xavier Delaune ◽  
José Antunes ◽  
Vincent Debut ◽  
Philippe Piteau ◽  
Laurent Borsoi
Keyword(s):  
Transfer Functions ◽  
Contact Forces ◽  
Modal Parameters ◽  
Continuous Systems ◽  
Nonlinear Dynamical ◽  
Impact Forces ◽  
Vibratory Response ◽  
Imperfect Knowledge ◽  
Active Research ◽  
Remote Identification

Predictive computation of the nonlinear dynamical responses of gap-supported tubes subjected to flow excitation has been the subject of very active research. Nevertheless, experimental results are still very important, for validation of the theoretical predictions as well as for asserting the integrity of field components. Because carefully instrumented test tubes and tube-supports are seldom possible, due to space limitations and to the severe environment conditions, there is a need for robust techniques capable of extracting, from the actual vibratory response data, information that is relevant for asserting the components integrity. The dynamical contact/impact (vibro-impact) forces are of paramount significance, as are the tube/support gaps. Following our previous studies in this area using wave-propagation techniques (De Araújo, Antunes, and Piteau, 1998, “Remote Identification of Impact Forces on Loosely Supported Tubes: Part 1—Basic Theory and Experiments,” J. Sound Vib., 215, pp. 1015–1041; Antunes, Paulino, and Piteau, 1998, “Remote Identification of Impact Forces on Loosely Supported Tubes: Part 2—Complex Vibro-Impact Motions,” J. Sound Vib., 215, pp. 1043–1064; Paulino, Antunes, and Izquierdo, 1999, “Remote Identification of Impact Forces on Loosely Supported Tubes: Analysis of Multi-Supported Systems,” ASME J. Pressure Vessel Technol., 121, pp. 61–70), we apply modal methods in the present paper for extracting such information. The dynamical support forces, as well as the vibratory responses at the support locations, are identified from one or several vibratory response measurements at remote transducers, from which the support gaps can be inferred. As for most inverse problems, the identification results may prove quite sensitive to noise and modeling errors. Therefore, topics discussed in the paper include regularization techniques to mitigate the effects of nonmeasured noise perturbations. In particular, a method is proposed to improve the identification of contact forces at the supports when the system is excited by an unknown distributed turbulence force field. The extensive identification results presented are based on realistic numerical simulations of gap-supported tubes subjected to flow turbulence excitation. We can thus confront the identified dynamical support contact forces and vibratory motions at the gap-support with the actual values stemming from the original nonlinear computations. The important topic of dealing with the imperfect knowledge of the modal parameters used to build the inverted transfer functions is thoroughly addressed elsewhere (Debut, Delaune, and Antunes, 2009, “Identification of Nonlinear Interaction Forces Acting on Continuous Systems Using Remote Measurements of the Vibratory Responses,” Proceedings of the Seventh EUROMECH Solids Mechanics Conference (ESMC2009), Lisbon, Portugal, Sept. 7–11). Nevertheless, identifications are performed in this paper based on both the exact modes and also on randomly perturbed modal parameters. Our results show that, for the system addressed here, deterioration of the identifications is moderate when realistic errors are introduced in the modal parameters. In all cases, the identified results compare reasonably well with the real contact forces and motions at the gap-supports.

Modal Techniques for Remote Identification of Nonlinear Reactions at Gap-Supported Tubes Under Turbulent Excitation

2009 ◽  
Author(s):  
Xavier Delaune ◽  
Jose´ Antunes ◽  
Vincent Debut ◽  
Philippe Piteau ◽  
Laurent Borsoi
Keyword(s):  
Transfer Functions ◽  
Contact Forces ◽  
Modal Parameters ◽  
Nonlinear Dynamical ◽  
Vibratory Response ◽  
Robust Techniques ◽  
Regularization Techniques ◽  
Imperfect Knowledge ◽  
Active Research ◽  
Remote Identification

Predictive computation of the nonlinear dynamical responses of gap-supported tubes subjected to flow excitation has been the subject of very active research. Nevertheless, there is a need for robust techniques capable of extracting, from the actual vibratory response data, information which is relevant for asserting the components integrity. The dynamical contact/impact (vibro-impact) forces are of paramount significance, as are the tube/support gaps. Following our previous studies in this field using wave-propagation techniques [1–3], we apply modal methods in the present paper for extracting such information. The dynamical support forces, as well as the vibratory responses at the support locations, are identified from one or several vibratory response measurements at remote transducers, from which the support gaps can be inferred. As for most inverse problems, the identification results prove quite sensitive to noise and modeling error problems. Therefore, topics discussed in the paper include regularization techniques to mitigate the effects of non-measured noise perturbations. In particular, a method is proposed to improve the identification of contact forces at the supports when the system is excited by an unknown distributed turbulence force field. The important topic of dealing with the imperfect knowledge of the modal parameters used to build the inverted transfer functions is addressed elsewhere [4]. Here, the extensive identifications presented are based on the exact modal parameters and performed on realistic numerical simulations of gap-supported tubes subjected to flow excitation. We can thus confront the identified dynamical support contact forces and vibratory motions at the gap-support with the actual values stemming from the original nonlinear computations, with overall satisfying results.

An implicit class of continuous dynamical system with data-sample outputs: a robust approach

2019 ◽  
Vol 37 (2) ◽  
pp. 589-606
Author(s):  
Raymundo Juarez ◽  
Vadim Azhmyakov ◽  
A Tadeo Espinoza ◽  
Francisco G Salas
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Models ◽  
Differential Algebraic Equations ◽  
Linear Feedback ◽  
Continuous Systems ◽  
Algebraic Equations ◽  
Nonlinear Dynamical ◽  
Ellipsoid Method ◽  
Invariant Ellipsoid

Abstract This paper addresses the problem of robust control for a class of nonlinear dynamical systems in the continuous time domain. We deal with nonlinear models described by differential-algebraic equations (DAEs) in the presence of bounded uncertainties. The full model of the control system under consideration is completed by linear sampling-type outputs. The linear feedback control design proposed in this manuscript is created by application of an extended version of the conventional invariant ellipsoid method. Moreover, we also apply some specific Lyapunov-based descriptor techniques from the stability theory of continuous systems. The above combination of the modified invariant ellipsoid approach and descriptor method makes it possible to obtain the robustness of the designed control and to establish some well-known stability properties of dynamical systems under consideration. Finally, the applicability of the proposed method is illustrated by a computational example. A brief discussion on the main implementation issue is also included.

scholarly journals Comparison of Linear and Nonlinear Behavior of Track Elements in Contact-Impact Models

2018 ◽  
Author(s):  
Jabbar Ali Zakeri ◽  
Mosab Reza Tajalli
Keyword(s):  
Linear Model ◽  
3D Model ◽  
Linear Models ◽  
Wave Length ◽  
Short Wave ◽  
Contact Forces ◽  
Reliable Estimate ◽  
Impact Forces ◽  
Linear Behavior ◽  
Non Linear

Existence of short wave length irregularities and discontinuities in the rail, such as corrugation, isolated rail joints, crossings and rail breakage, result in impact forces and an increase in wheel-rail contact force. Extreme forces in such could result in non-linear behavior of ballast and pads, and as a result, employing common linear models mihgt over/under estimate contact forces. A 3D model of wheel and rail is developed in this paper, and by considering rail breakage, validity of linear models and considering non-linear behavior of materials are studied. Wheel-rail interactions are studied for two common pads with high stiffness (HDPE) and low stiffness (Studded) for speeds of 20 to 160 km/h. Three behavioral patterns are considered for the developed 3D model: linear pad and ballast (LP-LB), nonlinear pad and linear ballast (NLP, LB), and nonlinear pad and ballast (NLP, NLB), and results are compared. According to the results, for HDPE pads and impact forces of up to 30 tons, linear model for material could estimate acceptable results. Yet for studded pads, linear model estimates forces that are comparably less than those estimated by non-linear model. Moreover employing NLP-LB model overestimates pad and wheel-rail contact forces by a rather small margin, compared to those estimated by NLP-NLB model, and hence, could be a suitable replacement for it. It is also observed that in order to have a reliable estimate of ballast forces, using non-linear ballast models are mandatory, and neither LP-LB nor NLP-LB could be acceptable replacements.

Modeling Expected Wear in Revolute Joints With Clearance in Multibody Mechanical Systems

2007 ◽  
Author(s):  
P. Flores ◽  
J. Ambro´sio ◽  
J. C. P. Claro ◽  
H. M. Lankarani
Keyword(s):  
Research Work ◽  
Contact Forces ◽  
Joint Surface ◽  
Force Model ◽  
Wear Model ◽  
Continuous Contact ◽  
Revolute Joints ◽  
Sliding Motion ◽  
Impact Forces ◽  
Contact Impact

The main goal of this work is to develop a methodology for studying and quantifying the wear phenomenon in revolute clearance joints. In the process, a simple model for a revolute joint in the framework of multibody systems formulation is presented. The evaluation of the contact forces developed is based on a continuous contact force model that accounts for the geometrical and materials properties of the colliding bodies. The friction effects due to the contact in the joints are also represented. Then, these contact-impact forces are used to compute the pressure field at the contact zone, which ultimately is employed to quantify the wear developed and caused by the relative sliding motion. In this work, the Archard’s wear model is used. A simple planar multibody mechanical system is used to perform numerical simulations, in order to discuss the assumptions and procedures adopted throughout this work. Different results are presented and discussed throughout this research work. From the main results obtained, it can be drawn that the wear phenomenon is not uniformly distributed around the joint surface, owing to the fact that the contact between the joint elements is wider and more frequent is some specific regions.

scholarly journals Small nanoparticles, surface geometry and contact forces

2018 ◽  
Vol 474 (2211) ◽  
pp. 20170723 ◽  
Author(s):  
Yoichi Takato ◽  
Michael E. Benson ◽  
Surajit Sen
Keyword(s):  
Contact Force ◽  
Contact Forces ◽  
Spherical Nanoparticles ◽  
Hertz Contact ◽  
Surface Geometry ◽  
Impact Forces ◽  
Nonlinear Contact ◽  
Amorphous Surface ◽  
The Impact ◽  
Small Nanoparticles

In this molecular dynamics study, we examine the local surface geometric effects of the normal impact force between two approximately spherical nanoparticles that collide in a vacuum. Three types of surface geometries—(i) crystal facets, (ii) sharp edges, and (iii) amorphous surfaces of small nanoparticles with radii R <10 nm—are considered. The impact forces are compared with their macroscopic counterparts described by nonlinear contact forces based on Hertz contact mechanics. In our simulations, edge and amorphous surface contacts with weak surface energy reveal that the average impact forces are in excellent agreement with the Hertz contact force. On the other hand, facet collisions show a linearly increasing force with increasing compression. Our results suggest that the nearly spherical nanoparticles are likely to enable some nonlinear dynamic phenomena, such as breathers and solitary waves observed in granular materials, both originating from the nonlinear contact force.

scholarly journals Nonlinear Dynamics and Motion Bifurcations of the Rotor Active Magnetic Bearings System with a New Control Scheme and Rub-Impact Force

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1502
Author(s):  
Nasser Abul-Fadeel Saeed ◽  
Emad Mahrous ◽  
Emad Abouel Nasr ◽  
Jan Awrejcewicz
Keyword(s):  
Control Method ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Rotating Disc ◽  
Nonlinear Dynamical ◽  
Dynamic Friction Coefficient ◽  
Impact Forces ◽  
Control Scheme ◽  
The Impact ◽  
First Time

This article is dedicated to investigating the nonlinear dynamical behaviors of the 8-pole rotor active magnetic bearing system. The rub and impact forces between the rotating disc and the pole-legs are included in the studied model for the first time. A new control scheme based on modifying the 8-pole positions has been introduced. The proposed control methodology is designed such that four poles only are located in the horizontal and vertical directions (i.e., in +X,+Y,−X,−Y directions), while the other four poles are inserted in a way such that each pole makes 45° with two of the axes +X,+Y,−X,−Y. The control currents in the horizontal and vertical poles are suggested to be proportional to both the velocity and displacement of the rotor in the horizontal and vertical directions, respectively, while the control currents in the inclined poles are proposed to be dependent on the combination of both the displacement and velocity of the rotor in the horizontal and vertical directions. Accordingly, the whole-system mathematical model is derived. The derived discontinuous dynamical system is analyzed employing perturbation methods, Poincare maps, bifurcation diagrams, whirling orbits, and frequency spectrum. The obtained results demonstrated that the controller proportional control gain can play a significant role in changing the vibratory behaviors of the system, where the proposed control method can behave either as a cartesian control strategy or as a radial control one depending on the magnitude of the proportional gain. In addition, it is found that the rotor system can vibrate with periodic, periodic-n, quasiperiodic, or chaotic motion when the rub and/or impact forces occur. Moreover, it is reported for the first time that the rotor-AMB can oscillate symmetrically in X and Y directions either in full annular rub mode or quasiperiodic partial rub mode depending on the impact stiffness coefficient and the dynamic friction coefficient.

scholarly journals Stability of conditionally invariant sets and controlled uncertain dynamic systems on time scales

1995 ◽  
Vol 1 (1) ◽  
pp. 1-10 ◽  
Author(s):  
V. Lakshmikantham ◽  
Z. Drici
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Invariant Sets ◽  
Continuous Systems ◽  
Stability Properties ◽  
Closed Sets ◽  
Controlled Systems ◽  
Uncertain Dynamic Systems ◽  
Imperfect Knowledge ◽  
The Stability

A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built which incorporates both continuous and discrete times, namely, time as an arbitrary closed sets of reals, and allows us to handle both systems simultaneously [1], [2], [12], [13]. This theory permits one to get some insight into and better understanding of the subtle differences between discrete and continuous systems. We shall, in this paper, utilize the framework of the theory of dynamic systems on time scales to investigate the stability properties of conditionally invariant sets which are then applied to discuss controlled systems with uncertain elements. For the notion of conditionally invariant set and its stability properties, see [14]. Our results offer a new approach to the problem in question.

scholarly journals Investigating the Effect of Some Train and Track Parameters on Contact-impact Forces in the Vicinity of a Rail Breakage

2019 ◽  
Author(s):  
Mosab Reza Tajalli ◽  
Jabbar Ali Zakeri
Keyword(s):  
Interaction Model ◽  
Element Model ◽  
Contact Forces ◽  
Railway Track ◽  
Dynamic Impact ◽  
Impact Forces ◽  
Risk Increase ◽  
Length Increase ◽  
Train Speed ◽  
Contact Impact

Broken rails or welds are the main causes of derailment in railway networks. Therefore, a wheel-rail interaction model, which precisely estimates contact-impact forces in the presence of broken rails, can have a significant effect on derailment risk reduction. This paper attempts to present contact-impact forces in the vicinity of broken rails by employing a detailed 3D finite element model. The model is verified using a field test carried out on a ballasted railway track. Effects of train speed, gap length, axle load and railpad and ballast characteristics are studied on rail-wheel contact forces as well as on railpad and ballast forces. Results suggest that increasing the train speed from 60 km/h to 110 km/h would increase dynamic impact force from 2.46 to 4.11. It is also observed that increasing axle load results in an increase in the wheel-rail impact forces and in railpad and ballast forces, while leading to a reduced dynamic impact factor. Furthermore, investigating the effect of the track parameters demonstrates that ballast stiffness is the most important characteristic of the track, which has a reverse effect on dynamic impact forces. Moreover, unloading length increase and consequently derailment risk increase is highly sensitive to increasing train speed.

Semi-Explicit Composition Methods in Memcapacitor Circuit Simulation

2019 ◽  
Vol 10 (2) ◽  
pp. 37-52 ◽  
Author(s):  
Denis N. Butusov ◽  
Valerii Y. Ostrovskii ◽  
Artur I. Karimov ◽  
Valery S. Andreev
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Circuit Simulation ◽  
Simulation Software ◽  
Continuous Systems ◽  
Implicit Midpoint Rule ◽  
Nonlinear Dynamical ◽  
Composition Methods ◽  
The Stability ◽  
New Generation ◽  
Embedded Applications

Composition algorithms make up a prospective class of methods for solving ordinary differential equations. Their main advantage is an ability to retain some properties of the simulated continuous systems, e.g. phase space volume. Meanwhile, computational costs of composition solvers for non-Hamiltonian systems are high because the implicit midpoint rule should be used as a basic method. This also complicates the development of embedded applications based on the numerical solution of ODEs, such as hardware chaos generators. In this article, a new semi-explicit composition methods are proposed. The stability regions for different composition algorithms were plotted and a memcapacitor circuit was studied as a test problem. Computational experiments reveal the superior properties of semi-explicit composition algorithms as a hardware-targeted ODE solvers. The obtained results imply that the development of semi-explicit composition algorithms is a step towards construction a new generation of simulation software for nonlinear dynamical systems and embedded chaos generators.

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