Other affiliations: Technische Universität Darmstadt, Darmstadt University of Applied Sciences, Alstom ...read more
Bio: B. Ravindra is an academic researcher from Indian Institute of Technology, Jodhpur. The author has contributed to research in topic(s): Solar power & Photovoltaic system. The author has an hindex of 11, co-authored 30 publication(s) receiving 569 citation(s). Previous affiliations of B. Ravindra include Technische Universität Darmstadt & Darmstadt University of Applied Sciences.
TL;DR: In this paper, a non-linearity analysis of vibration isolators with symmetric and asymmetric restoring forces is performed under both force and base excitations, and linear stability analysis of the solutions is presented.
Abstract: Vibration isolators having non-linearity in both stiffness and damping terms are analyzed under harmonic excitations. Isolators with symmetric as well as asymmetric restoring forces are considered. The method of harmonic balance is used to obtain the steady state, harmonic response and transmissibility under both force and base excitations. The linear stability analysis of the solutions is presented. A parametric study indicating the effects of various types of damping is reported. The subharmonic and chaotic responses for the systems under investigation will be discussed in a subsequent paper.
17 Apr 1998-Archive of Applied Mechanics
TL;DR: In this paper, the dynamics of one-mode approximation of an axially moving continuum such as a moving magnetic tape is studied, where the system is modeled as a beam moving with varying speed, and the transverse vibration of the beam is considered.
Abstract: Nonlinear dynamics of one-mode approximation of an axially moving continuum such as a moving magnetic tape is studied. The system is modeled as a beam moving with varying speed, and the transverse vibration of the beam is considered. The cubic stiffness term, arising out of finite stretching of the neutral axis during vibration, is included in the analysis while deriving the equations of motion by Hamilton's principle. One-mode approximation of the governing equation is obtained by the Galerkin's method, as the objective in this work is to examine the low-dimensional chaotic response. The velocity of the beam is assumed to have sinusoidal fluctuations superposed on a mean value. This approximation leads to a parametrically excited Duffing's oscillator. It exhibits a symmetric pitchfork bifurcation as the axial velocity of the beam is varied beyond a critical value. In the supercritical regime, the system is described by a parametrically excited double-well potential oscillator. It is shown by numerical simulation that the oscillator has both period-doubling and intermittent routes to chaos. Melnikov's criterion is employed to find out the parameter regime in which chaos occurs. Further, it is shown that in the linear case, when the operating speed is supercritical, the oscillator considered is isomorphic to the case of an inverted pendulum with an oscillating support. It is also shown that supercritical motion can be stabilised by imposing a suitable velocity variation.
TL;DR: It is shown that a system exhibiting chaos can be driven to a desired periodic motion by designing a combination of feedforward controller and a time-varying controller.
Abstract: A general framework for local control of nonlinearity in nonautonomous systems using feedback strategies is considered in this work. In particular, it is shown that a system exhibiting chaos can be driven to a desired periodic motion by designing a combination of feedforward controller and a time-varying controller. The design of the time-varying controller is achieved through an application of Lyapunov–Floquet transformation which guarantees the local stability of the desired periodic orbit. If it is desired that the chaotic motion be driven to a fixed point, then the time-varying controller can be replaced by a constant gain controller which can be designed using classical techniques, viz. pole placement, etc. A sinusoidally driven Duffing's oscillator and the well-known Rossler system are chosen as illustrative examples to demonstrate the application.
01 Jun 1994-Physical Review E
TL;DR: It is shown that the bifurcation structure and the structure of the chaotic attractor are quite insensitive to the damping exponent p, however, the threshold values of the parameters, at which bIfurcations occur, depend both on the damped index and the damper coefficient.
Abstract: The effect of a strictly dissipative force (velocity to the pth power model) on the response and bifurcations of driven, soft Duffing oscillators is considered. The method of harmonic balance is used to obtain the steady state harmonic response. An anomalous jump in the harmonic response (signifying a break in the resonance curve), obtained in the case of linearly damped, soft Duffing oscillators, is shown to persist even in the presence of nonlinear damping. It is shown that the bifurcation structure and the structure of the chaotic attractor are quite insensitive to the damping exponent p. However, the threshold values of the parameters, at which bifurcations occur, depend both on the damping index and the damping coefficient. The Melinkov criterion and an analytical criterion for the period-doubling bifurcation have been obtained in the presence of combined linear and cubic damping.
TL;DR: In this article, the steady state, harmonic response of a vibration isolation system with a cubic, hard non-linear restoring force and combined Coulomb and viscous damping is presented by using the method of harmonic balance.
Abstract: The steady-state, harmonic response of a vibration isolation system with a cubic, hard non-linear restoring force and combined Coulomb and viscous damping is presented. The results have been obtained by using the method of harmonic balance. It has been assumed that the motion is continuous without any stop. An anomalous jump in the response, similar to the one obtained in earlier studies on certain soft systems, is observed when the isolation system is subjected to a base excitation. Linear stability analysis is carried out to determine the status of the anomalous jump. The effect of the damping parameters on the jump in the response is investigated. Transmissibility curves are plotted for various parameter values to study the performance characteristics. The obtained results extend the previous works of Den Hartog and Ruzicka who considered a linear restoring element.
01 Aug 2005-Nonlinear Dynamics
TL;DR: In this article, a different approach is adopted, and proper orthogonal decomposition is considered, and modes extracted from the decomposition may serve two purposes, namely order reduction by projecting high-dimensional data into a lower-dimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data.
Abstract: Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theory based on nonlinear normal modes is indubitably the most appealing. In this paper, a different approach is adopted, and proper orthogonal decomposition is considered. The modes extracted from the decomposition may serve two purposes, namely order reduction by projecting high-dimensional data into a lower-dimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data. The utility of the method for dynamic characterization and order reduction of linear and nonlinear mechanical systems is demonstrated in this study.
TL;DR: In this paper, a comprehensive assessment of recent developments of nonlinear isolators in the absence of active control means is presented, which highlights resolved and unresolved problems and recommendations for future research directions.
Abstract: The theory of nonlinear vibration isolation has witnessed significant developments due to pressing demands for the protection of structural installations, nuclear reactors, mechanical components, and sensitive instruments from earthquake ground motion, shocks, and impact loads. In view of these demands, engineers and physicists have developed different types of nonlinear vibration isolators. This article presents a comprehensive assessment of recent developments of nonlinear isolators in the absence of active control means. It does not deal with other means of linear or nonlinear vibration absorbers. It begins with the basic concept and features of nonlinear isolators and inherent nonlinear phenomena. Specific types of nonlinear isolators are then discussed, including ultra-low-frequency isolators. For vertical vibration isolation, the treatment of the Euler spring isolator is based on the post-buckling dynamic characteristics of the column elastica and axial stiffness. Exact and approximate analyses of axial stiffness of the post-buckled Euler beam are outlined. Different techniques of reducing the resonant frequency of the isolator are described. Another group is based on the Gospodnetic–Frisch-Fay beam, which is free to slide on two supports. The restoring force of this beam resembles to a great extent the restoring roll moment of biased ships. The base isolation of buildings, bridges, and liquid storage tanks subjected to earthquake ground motion is then described. Base isolation utilizes friction elements, laminated-rubber bearings, and the friction pendulum. Nonlinear viscoelastic and composite material springs, and smart material elements are described in terms of material mechanical characteristics and the dependence of their transmissibility on temperature and excitation amplitude. The article is closed by conclusions, which highlight resolved and unresolved problems and recommendations for future research directions.
TL;DR: The equivalence of the matrices for processing, the objective functions, the optimal basis vectors, the mean-square errors, and the asymptotic connections of the three POD methods are demonstrated and proved when the methods are used to handle the POD of discrete random vectors.
Abstract: In view of the increasing popularity of the application of proper orthogonal decomposition (POD) methods in engineering fields and the loose description of connections among the POD methods, the purpose of this paper is to give a summary of the POD methods and to show the connections among these methods. Firstly, the derivation and the performance of the three POD methods: Karhunen–Loeve decomposition (KLD), principal component analysis (PCA), and singular value decomposition (SVD) are summarized, then the equivalence problem is discussed via a theoretical comparison among the three methods. The equivalence of the matrices for processing, the objective functions, the optimal basis vectors, the mean-square errors, and the asymptotic connections of the three methods are demonstrated and proved when the methods are used to handle the POD of discrete random vectors.
01 Jan 2005-Annual Reviews in Control
TL;DR: A survey of the emerging field termed “control of chaos” is given, which includes traditional control engineering methods including linear, nonlinear and adaptive control, neural networks and fuzzy control, and applications in various fields of engineering.
Abstract: A survey of the emerging field termed “control of chaos” is given. Several major branches of research are discussed in detail: feedforward or “nonfeedback control” (based on periodic excitation of the system); “OGY method” (based on linearization of the Poincare map), “Pyragas method” (based on a time-delay feedback), traditional control engineering methods including linear, nonlinear and adaptive control, neural networks and fuzzy control. Some unsolved problems concerning the justification of chaos control methods are presented. Other directions of active research such as chaotic mixing, chaotization, etc. are outlined. Applications in various fields of engineering are discussed.
TL;DR: In this paper, the authors provide insights into the physical interpretation of the proper orthogonal modes using the singular value decomposition (SVD) in the field of structural dynamics.
Abstract: Proper orthogonal decomposition is a statistical pattern analysis technique for finding the dominant structures, called the proper orthogonal modes, in an ensemble of spatially distributed data. While the proper orthogonal modes are obtained through a statistical formulation, they can be physically interpreted in the field of structural dynamics. The purpose of this paper is thus to provide some insights into the physical interpretation of the proper orthogonal modes using the singular value decomposition