Nonlinear dynamics of parts in engineering systems
TL;DR: It is shown that chaotic vibrations arise from nonlinear deterministic physical systems or non-random differential or difference equations, and in numerous engineering systems there exist nonlinearities.
Abstract: By definition, chaotic vibrations arise from nonlinear deterministic physical systems or non-random differential or difference equations. In numerous engineering systems there exist nonlinearities ...
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TL;DR: In this paper, the authors analyzed the brake squeal data obtained from a full brake system on a noise dynamometer with nonlinear analysis techniques and showed that lower dimensional attractors are isolated and quantified by dynamic invariants such as correlation dimension estimates or Lyapunov exponents.
117 citations
Cites background from "Nonlinear dynamics of parts in engi..."
...It is unclear how nonlinear the behaviour of brake components is and how this nonlinearity influences the overall acoustic radiation properties (see also [42])....
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TL;DR: In this article, the correlation analysis between the time-averaged friction coefficient and peak sound pressure data is performed by applying a semblance analysis and a joint recurrence quantification analysis.
113 citations
TL;DR: In this article, a review of state-of-the-art studies on brake vibration and noise is presented, focusing on the still-open questions that appear crucial from the perspective of a leading brake manufacturer.
Abstract: Several state of the art papers and even books on brake vibration and/or noise have been presented in the literature. Many of them have analytically and sharply accounted for the impressive amount of research undertaken on this topic. This state of the art review focuses on the still-open questions that appear crucial from the perspective of a leading brake manufacturer. The paper deals with the phenomena of brake vibration and/or noise, the experimental and theoretical methods for studying such phenomena, and the actions that are identified to be necessary to definitely solve the addressed problem. Key topics are the modelling of friction, the modelling of the dynamics of the brake as a non-linear system subjected to deterministic or random (parametric) excitation, the proper modelling of the contact between the disc and the pad, and the experimental validation of the mathematical models.
86 citations
TL;DR: In this article, a new formulation for frictional elastic-plastic contact between two surfaces is developed to consider both frictional, oblique contact (of which normal, frictionless contact is a limiting case) and strain hardening effects.
80 citations
TL;DR: In this article, a concentrate spring between a beam and a rod at their contact point is simulated to simulate the deformability of impacting bodies at the interaction zones, and a reliable and convenient method for determining impact forces is also presented.
Abstract: Systems constituted by impacting beams and rods of non-negligible mass are often encountered in many applications of engineering practice. The impact between two rigid bodies is an intrinsically indeterminate problem due to the arbitrariness of the velocities after the instantaneous impact and implicates an infinite value of the contact force. The arbitrariness of after-impact velocities is solved by releasing the impenetrability condition as an internal constraint of the bodies and by allowing for elastic deformations at contact during an impact of finite duration. In this paper, the latter goal is achieved by interposing a concentrate spring between a beam and a rod at their contact point, simulating the deformability of impacting bodies at the interaction zones. A reliable and convenient method for determining impact forces is also presented. An example of engineering interest is carried out: a flexible beam that impacts on an axially deformable strut. The solution of motion under a harmonic excitation of the beam built-in base is found in terms of transverse and axial displacements of the beam and rod, respectively, by superimposition of a finite number of modal contributions. Numerical investigations are performed in order to examine the influence of the rigidity of the contact spring and of the ratio between the first natural frequencies of the beam and the rod, respectively, on the system response, namely impact velocity, maximum displacement, spring stretching and contact force. Impact velocity diagrams, nonlinear resonance curves and phase portraits are presented to determine regions of periodic motion with impacts and the appearance of chaotic solutions, and parameter ranges where the functionality of the non-structural element is at risk.
73 citations
References
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Book•
01 Jan 1991
TL;DR: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
Abstract: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
15,545 citations
21 Aug 1996
TL;DR: Unilateral Contact - Problem Formulation (A. Curnier).- Scalar Force Potentials in Rigid Multibody Systems (Ch. Glocker).
Abstract: THEORY. Multibody Kinematics. Dynamics of Rigid Body Systems. Contact Kinematics. Multiple Contact Configurations. Detachment and Stick-Slip Transitions. Frictionless Impacts by Newton's Law. Impacts with Friction by Poisson's Law. The Corner Law of Contact Dynamics. APPLICATIONS. Applications with Discontinuous Force Laws. Applications with Classical Impact Theory. Applications with Coulomb's Friction Law. Applications with Impacts and Friction. References. Index.
868 citations
TL;DR: In this article, a single-degree of freedom non-linear oscillator is considered and the nonlinearity is in the restoring force and is piecewise linear with a single change in slope.
802 citations
TL;DR: In this paper, a digital simulation technique and the method of harmonic balance were used to develop steady state solutions for the internal sinuosidal excitations in a spur gear pair.
538 citations
Book•
01 Jan 1992
TL;DR: A fascinating and timely look at the applications of chaotic dynamics in science and technology can be found in this paper, which reflects the collected research of the world's foremost physicists, chemists, mathematicians, engineers, and computer scientists.
Abstract: A fascinating and timely look at the applications of chaotic dynamics in science and technology, this volume reflects the collected research of the world's foremost physicists, chemists, mathematicians, engineers, and computer scientists. An outgrowth of the EPRI-sponsored International Workshop on Applications of Chaos, this work reveals how the concepts and language of chaos link these disparate fields together . Subjects covered include the dynamics of electrocardiograph data, the instability of conveyor belts, time series modelling, the control of chaos, and more. 1992 (0471-54453-1)450 pp.
492 citations