Vibration Control Of Mechanical Systems Research Articles

Algebraic estimation for fractional integrals of noisy acceleration based on the behaviour of fractional derivatives at zero

In this paper, non-asymptotic and robust estimation for fractional integrals of noisy acceleration is considered for a class of fractional linear systems based on the study of the behaviour of fractional derivatives at zero. Particularly, the position and velocity can be estimated from the noisy acceleration via the designed estimators. Such estimates can be of value for health monitoring, reliability assessment, and vibration control of mechanical systems. Based on the existing numerical approaches addressing the proper fractional integrals, our attention is primarily restricted to estimating the unknown initial values. For completing the estimation, two methods based on classical modulating functions and generalized modulating functions are proposed, respectively. Via the results on fractional derivatives at zero, the initial values of the considered systems are discussed, and the corresponding estimator simplifications are performed. In addition, constructions of the required modulating functions are discussed. Finally, some numerical simulations are provided, which demonstrate the validity of the theoretical results and the efficiency of the proposed estimators.

Passive vibration damping of a cantilever plate

Vibration control of mechanical systems divided into two types active and passive, this case study illustrates other approach of passive control of the cantilever plate by using double layers of the viscoelastic material (Dyad 606) one in the upper face of the Al substrate (5051) and the second one in the lower face. This layers are affected by axial uniform distributed force by applying tension load, the damping level depend on the value of this axial force where the vertical component of this force consistently the other way of the vibrating element that reduce vibration amplitude in this direction by about (95%) of the original amplitude without damping layers. Computational analysis using ANSYS program are used firstly to verify that the results from the software are compatible with that obtained from analytical and experimental evaluation by comparing the values of natural frequencies. Then using ANSYS model to calculate the reduction occurs in the lateral vibration with changing of the axial loads on the viscoelastic plates. The benefits of this model are enhancing the reliability and reducing the cost.

ON AN INTEGRATED DYNAMIC CHARACTERIZATION OF VISCOELASTIC MATERIALS BY FRACTIONAL DERIVATIVE AND GHM MODELS

Abstract The passive vibration control of mechanical systems under unwanted vibrations can be accomplished in a very effective way by using devices incorporating viscoelastic materials. The design of such devices requires a broad knowledge of the dynamic properties of the employed viscoelastic material, usually supplied by adequate mathematical models. Among the available mathematical models, the fractional derivative (FD) model and the Golla-Hughes-McTavish (GHM) model, along with either the Williams-Landel-Ferry (WLF) equation or the Arrhenius equation, are now very prominent. The current work investigates the use of these models in a wide and integrated dynamic characterization of a typical and thermorheologically simple viscoelastic material. It focuses on experimental data collected from 0.1 to 100 Hz and -40 °C to 50 °C, which are simultaneously manipulated to raise both the frequency and the temperature dependencies of the material. In fitting the models, a hybrid approach - combining techniques of genetic algorithms and nonlinear optimization - is adopted. The ensuing results are evaluated by means of objective function values, comparative experimental-predicted data plots, and the Akaike’s Information Criterion (AIC). It is shown that the four-parameter fractional derivative model presents excellent curve fitting results. As for the GHM model, its modified version is the most adequate, although a higher number of terms is required for a satisfactory goodness-of-fit. None the less the fractional derivative model stands out.

A CWT-based methodology for piston slap experimental characterization

Noise and vibration control in mechanical systems has become ever more significant for automotive industry where the comfort of the passenger compartment represents a challenging issue for car manufacturers. The reduction of piston slap noise is pivotal for a good design of IC engines. In this scenario, a methodology has been developed for the vibro-acoustic assessment of IC diesel engines by means of design changes in piston to cylinder bore clearance. Vibration signals have been analysed by means of advanced signal processing techniques taking advantage of cyclostationarity theory. The procedure departs from the analysis of the Continuous Wavelet Transform (CWT) in order to identify a representative frequency band of piston slap phenomenon. Such a frequency band has been exploited as the input data in the further signal processing analysis that involves the envelope analysis of the second order cyclostationary component of the signal. The second order harmonic component has been used as the benchmark parameter of piston slap noise. An experimental procedure of vibrational benchmarking is proposed and verified at different operational conditions in real IC engines actually equipped on cars. This study clearly underlines the crucial role of the transducer positioning when differences among real piston-to-cylinder clearances are considered. In particular, the proposed methodology is effective for the sensors placed on the outer cylinder wall in all the tested conditions.

Connections among several chaos feedback control approaches and chaotic vibration control of mechanical systems

This study reveals the essential connections among several popular chaos feedback control approaches, such as delayed feedback control (DFC), stability transformation method (STM), adaptive adjustment method (AAM), parameter adjustment method, relaxed Newton method, and speed feedback control method (SFCM), etc. Meanwhile, the generality and practical applicability of these approaches are evaluated and compared. It is shown that for discrete chaotic maps, STM can be regarded as a kind of predictive feedback control, and AAM is actually a special case of STM which is merely effective for a particular dynamical system. The parameter adjustment method is only a different expression of the relaxed Newton method, and both of them represent just one search direction of STM, i.e., the gradient direction. Moreover, the intrinsic relation between the STM and SFCM for controlling the equilibrium of continuous autonomous systems is investigated, indicating that STM can be viewed as a special form of the SFCM. Finally, both the STM and SFCM are extended to control the chaotic vibrations of non-autonomous mechanical systems effectively.

1C13 Active/semi-active hybrid control framework for vibration control of mechanical systems(The 12th International Conference on Motion and Vibration Control)

1C13 Active/semi-active hybrid control framework for vibration control of mechanical systems(The 12th International Conference on Motion and Vibration Control)

Active Vibration Control in Mechanical Systems

1 School of Astronautics, Harbin Institute of Technology, P.O. Box 3015, Yikuang Street No. 2, Nangang District, Harbin 150001, China 2Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway 3 Institute of Automation and Complex Systems, University of Duisburg-Essen, 47057 Duisburg, Germany 4Department of Applied Mathematics III, Universitat Politecnica de Catalunya (UPC), 08242 Manresa, Spain

Adaptive‐Like Vibration Control in Mechanical Systems with Unknown Paramenters and Signals

AbstractThis paper describes the application of an on‐line algebraic identification methodology for parameter and signal estimation in vibrating mechanical systems. An important property of the algebraic identification is that the parameter identification is not asymptotic but algebraic, that is, the parameters are computed as fast as the system dynamics are being excited by some external input or by changes in the initial conditions. The algebraic identification is then employed to estimate mass, stiffness, and viscous damping in simple mechanical systems using only position measurements. This approach is also used in the identification of frequency, phase, and amplitude of exogenous vibrations affecting a mechanical system. The algebraic identification is then combined with a certainty equivalence controller to asymptotically stabilize the system response and, simultaneously, cancel harmonic vibrations. The proposed adaptive‐like control scheme is fast and robust against unknown parameters and frequency variations. Some numerical and experimental results illustrate the dynamic and robust performance of the algebraic identification and the active vibration controller.

The analytical model of rheological fluid for vibration and noise control

Rheological fluids (RF) also known as a controllable viscosity fluids (CVF) introduced in the area of vibration control of mechanical systems made possible a more efficient control of both: transient and continuous vibration. They are also used in design of sound barriers to control noise transmission loss and diaphragms for modification of noise absorption characteristics of sound absorbing materials. Their apparent viscosity is controllable by the use of external (electrical in electro-rheological ER or electromagnetic in magneto-rheological MR fluids) field. In the absence of applied external field, the RF exhibits Newtonian-like behavior. Applied external field changes this behavior and the RF shows in addition a yield shear stress which depends on strength of this field. In proposed model, the shear stress is expressed as a superposition of two components. One of them is proportional to the viscosity and relative velocity of a base fluid, and the second one, which depends on strength of applied external field. Modification of external field strength according to selected design parameter (velocity or time or distance—combination of them) allows to develop family of vibration or sound attenuating devices, which were not achievable before.

Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State‐Derivative Feedback

The motivation for the use of state‐derivative feedback instead of conventional state feedback is due to its easy implementation in some mechanical applications, for example, in vibration control of mechanical systems, where accelerometers have been used to measure the system state. Using linear matrix inequalities (LMIs) and a parameter‐dependent Lyapunov functions (PDLF) allowed by Finsler’s lemma, a less conservative approach to the controller design via state‐derivative feedback, is proposed in this work, with and without decay rate restriction, for continuous‐time linear systems subject to polytopic uncertainties. Finally, numerical examples illustrate the efficiency of the proposed method.

Vibration Control of Flexible Structures Based on Impedance Matching Index

AbstractThis paper is concerned with a new feedback control design methodology for vibration control of flexible structures by the wave control. In the wave control, controllers are usually designed to minimize the reflection coefficient based on the wave analysis. However, because the method utilizes the wave analysis directly, it has been mainly applied to simple uniform structures, and control design method with some other control objectives has not been established yet. In this paper, aiming to establish a control design method for more complex systems and more complex control design, we propose a method based on the impedance matching index, which represents the difference of the transfer functions between the closed system and the controller. The index is motivated by the wave analysis and control for the uniformly varying ladder networks, an electric circuit analogy of a class of mechanical systems. As a design example for vibration control of mechanical systems, optimal tuning of the passive damper and the dynamic absorber by the index is conducted in the numerical example.

Vibration control of mechanical systems using semi-active MR-damper

The concept of structural vibration control is to absorb vibration energy of the structure by introducing auxiliary devices. Various types of structural vibration control theories and devices have been recently developed and introduced into mechanical systems. One of such devices is damper employing controllable fluids such as ElectroRheological (ER) or MagnetoRheological (MR) fluids. MagnetoRheological (MR) materials are suspensions of fine magnetizable ferromagnetic particles in a non-magnetic medium exhibiting controllable rheological behaviour in the presence of an applied magnetic field. This paper presents the modelling of an MR-fluid damper. The damper model is developed based on Newtonian shear flow and Bingham plastic shear flow models. The geometric parameters are varied to get the optimised damper characteristics. The numerical analysis is carried out to estimate the damping coefficient and damping force. The analytical results are compared with the experimental results. The results confirm that MR damper is one of the most promising new semi-active devices for structural vibration control.

Statistical Dynamics and Reliability Theory for Mechanical Structures

3R3. Statistical Dynamics and Reliability Theory for Mechanical Structures. - VA Svetlitsky (Dept of Appl Mech, Bauman Moscow State Tech Univ, 2-nd Baumanskaya St 5, Moscow, 107005, Russia). Springer-Verlag, Berlin. 2003. 446 pp. ISBN 3-540-44297-9. $169.00.Reviewed by AM Vinogradov (Dept of Mech Eng, Montana State Univ, 220 Roberts Hall, Bozeman MT 59717).The book deals with the subject of random vibrations of mechanical systems. In addition, it contains a brief outline of reliability theory, focusing on the response of structural members subjected to random loads. The book represents a translation of Russian text, based primarily on course lectures taught by the author at the Moscow Bauman Technical University. In the introduction, the author demonstrates that it is often impossible to correctly determine the response of dynamic systems based on deterministic formulations due to various oversimplifications of reality required to implement the deterministic approach. In particular, examples illustrate that it is impossible to solve deterministically such problems as the vibration response of structures to wind gusts or vehicles traveling on rough roads. The book consists of ten chapters and four appendices. Chapter 1 provides the fundamentals of probability theory, which is expanded in Chapters 2 and 3 to characterize non-stationary and stationary stochastic processes. A brief description of Markov processes is given in Chapter 4. In general, Chapters 1-4 contains reference material intended to establish the background necessary for understanding the content of the following sections. The presentation of this material is brief. It is assumed that the reader should have prior knowledge of probability theory. Chapter 5 concerns random vibration analysis of single degree of freedom (SDOF) systems, the motion of which is characterized by a single coordinate. The main focus of this chapter is on random vibrations of linear systems, including such problems as free vibrations under stochastic initial conditions, and non-stationary and stationary forced vibration analyses. In addition, Chapter 5 deals with random vibrations of SDOF systems with nonlinear stiffness characteristics. Chapter 6 deals with the stochastic response of linear multiple degree of freedom (MDOF) systems characterized in terms of a limited number of coordinates. Both free and forced random vibration responses of linear MDOF systems are considered, including stationary and non-stationary problems involving random excitations. Chapters 7 and 8 concern stochastic vibration analysis of continuous systems, focusing on the response of elastic rods. Initially, the random vibration problem under consideration is formulated in general terms, aiming at nonlinear analyses. However, certain approximations introduced in the subsequent sections reduce the problem to the analysis of linear MDOF systems. The material presented in Chapters 9 and 10 is largely independent of the preceding text. Thus, Chapter 9 discusses some aspects of reliability theory using probabilistic approach. Chapter 10 considers special cases of random excitations of structural members and some issues of passive vibration control of mechanical systems. Appendices 1-4 contain information that appears redundant since it is either common knowledge or of little practical value in terms of the technical content of the book. In general, Statistical Dynamics and Reliability Theory for Mechanical Systems is of certain interest, however, several factors tend to undermine its quality. In particular, the technical translation of the Russian text leaves much to be desired. The book is difficult to read and in many instances its technical content is either distorted or lost in translation. Besides, the text contains a number of typographic errors. Figures and illustrations appear adequate, but no figure captions are provided. The list of references is outdated and incomplete. It contains primarily Russian publications with little demonstrated knowledge of the Western literature. In view of the indicated deficiencies it is hard to identify a potential reader that would benefit from or express compelling interest in this book.

Theoretical and Numerical Experiences on a Test Rig for Active Vibration Control of Mechanical Systems with Moving Constraints

Active control of vibrations in mechanical systems has recently benefited of the remarkable development of robust control techniques. These control techniques are able to guarantee performances in spite of unavoidable modeling errors. They have been successfully codified and implemented for vibrating structures whose uncertain parameters could be assumed to be time-invariant. Unfortunately a wide class of mechanical systems, such as machine tools with carriage motion realized by a ball-screw, are characterized by time varying modal parameters. The focus of this paper is on modeling and controlling the vibrations of such systems. A test rig for active vibration control is presented. An analytical model of the test rig is synthesized starting by design data. Through experimental modal analysis, parametric identification and updating procedures, the model has been refined and a control system has been synthesized.

Optimal Design of Piezoelectric Materials for Vibration Damping in Mechanical Systems

This paper examines two different techniques for vibration control in mechanical systems using piezoceramics: the first one is based on a pure collocated damping control and the second uses resonant circuit shunting. Optimization techniques are used to determine the best design parameters with respect to performance indexes, which are associated with the dynamical behavior of the system, when several natural frequencies are present in the frequency band. The methodology presented in this paper is focused on the design aspects of vibration control devices and it can be extended to more complex structures.

Arbitrary Assignment of Eigenvectors With State Feedback

Conditions under which eigenvectors of linear multivariable systems can be arbitrarily assigned using state feedback are derived. A procedure for obtaining the required feedback gain matrix is also given. Embedded within the procedure is the freedom to minimize the gain matrix as well as select eigenvalues associated with the assigned eigenvectors. Consequently, arbitrary shaping of the system transient response is possible by concentrating system energy in specific modes. This technique is well suited for applications in the active vibration control of mechanical systems.