Analysis of a Nonlinear Friction Damping Mechanism in a Fluid-Structure Interaction System

Analysis of a nonlinear friction damping mechanism in a fluid-structure interaction system is performed by combining a generalized averaging procedure with a recently developed identification algorithm based on the Hilbert transform. The system considered includes a nonlinear restoring force and a nonlinear dissipation force incorporating both viscous and structural damping. Frequency and damping response backbone curves obtained from simulated data are compared with analytical and approximate solutions and are found to be accurate. An example large scale experiment exhibiting viscous and Coulomb damping is also analyzed resulting in identification of system parameters.

Self-Excited Oscillations in Sliding With a Constant Friction Coefficient

The sliding of two surfaces with respect to each other involves many interacting phenomena. In this paper a simple model is presented for the dynamic interaction of two dry sliding surfaces. This model consists of a beam on elastic foundation acted upon by a series of moving linear springs, where the springs represent the asperities on one of the surfaces. The coefficient of friction is constant. Although a nominally steady-state solution exists, an analysis of the dynamic problem indicates that the steady solution is dynamically unstable for any finite speed. Eigenvalues with positive real parts give rise to self-excited motion which continues to increase with time. The mechanism responsible for the instability is a result of the interaction of certain complex modes of vibration (which result from the moving springs) with the friction force of the moving springs. It is expected that these vibrations play a role in the behavior of sliding members with dry friction.

Impacts With Friction

Mechanically impacts with friction include questions of relative kinematics and of constraint dynamics both in normal and in tangential directions. In addition both directions are of course coupled because impulses in one direction influence the behaviour in the other direction, especially when considering the normal impulses stored at the end of the compression phase. Together with the stored tangential impulses it governs the expansion phase. Paper presents a model of such impacts with friction considering a compression and an expansion phase. Some examples illustrate the practical relevancy of the theory.

Nonlinear Combination Resonances in Cantilever Composite Plates

We experimentally investigated nonlinear combination resonances in a graphite-epoxy cantilever plate having the configuration (–75/75/75/ – 75/75/ – 75)s. As a first step, we compared the natural frequencies and mode shapes obtained from the finite-element and experimental modal analyses. The largest difference in the obtained frequencies was 2.6%. Then, we transversely excited the plate and obtained force-response and frequency-response curves, which were used to characterize the plate dynamics. We acquired time-domain data for specific input conditions using an A/D card and used them to generate time traces, power spectra, pseudo-state portraits, and Poincaré maps. The data were obtained with an accelerometer monitoring the excitation and a laser vibrometer monitoring the plate response. We observed the external combination resonance Ω≈12(ω2+ω5) and the internal combination resonance Ω≈ω8≈12(ω2+ω13), where the ωi are the natural frequencies of the plate and Ω is the excitation frequency. The results show that a low-amplitude high-frequency excitation can produce a high-amplitude low-frequency motion.

Identification of Nonlinear Systems Parameters Using Polyspectral Measurements and Analysis

Experimental and analytical techniques that characterize nonlinear modal interactions in structures are used to quantify parameters in representative nonlinear systems. The subject of the experimental study is a three-beam frame. Subharmonic resonances and interaction between widely spaced modes are exploited to determine nonlinear parameters in models that represent these interactions. The phases of the auto-bispectra of the response of this structure appear in the analytical solutions of the representative models. Values of these phases could thus aid in determining other unknown parameters of nonlinear systems.

Applications of Time-Frequency Analysis to Structures With Internal Resonance

Time-frequency analysis is an approach to characterizing the nature of signals whose frequency content changes over time. Although the primary applications of this field have, to date, been in the area of communications and signal analysis, it is becoming known in the field of structural dynamics. This paper explores the application of two straightforward time-frequency techniques to several structures that exhibit internal resonance. In particular, the systems analyzed exhibit simple modal interactions and, in one case, a transition to chaos. While other methods exist for analysis of these types of behaviors, larger systems with more complex resonances maybe better analyzed with time-frequency techniques.

A Study of the Effects of Negative Friction-Speed Slope on Brake Squeal

Brake squeal is caused by friction-induced vibration of brake systems. It may take place due to several possible mechanisms. The inverse variation of friction coefficient with relative sliding speed, also called negative μ-v slope, is one of them. Although it has been demonstrated in many articles that negative μ-v slope can cause unstable vibration for systems with a single degree of freedom (d.o.f.), its effects on multi-d.o.f. brake systems are not yet well understood. Since almost all types of friction materials for automotive brakes exhibit negative μ-v slope under certain conditions, it is important to clarify its role in brake squeal. The current study incorporates the negative μ-v slope friction law into a Finite element model for disc brake systems. The rotor and pads are modeled by beam elements, and the caliper is represented by a rigid body with two degrees of freedom. The effects of negative μ-v slope on the vibration stability of a brake system are studied along with several parameters including friction level, lining compression modulus, and steelback thickness.

Nonlinear Transient Analysis of Aircraft Landing Gear Brake Whirl and Squeal

The feasibility of computing non-linear transient finite element simulations of aircraft landing gear brake whirl and squeal is demonstrated and discussed. Methodology to conduct the high frequency brake transient analysis is developed using an explicit integration finite element approach. Results indicate the approach has the capability to simulate brake dynamic behavior in dynamometer and aircraft landing gear installations — thus enabling evaluation of modifications to braking systems that lead to more stable and robust designs. A simple multi-disk brake model is developed and described. Modeling techniques for including the dynamometer road wheel and runway in the simulations are given. Issues such as piston housing hydraulic fluid stiffness and damping effects, and parametric friction modeling are discussed.

Pattern Changes of Time-Shifted Vibration Signals on Wavelet Time-Scale Maps

As a multi-resolution signal decomposition and analysis technique, the wavelet transforms have been already introduced to vibration signal processing. In this paper, a comparison on the time-scale map analysis is made between the discrete and the continuous wavelet transform. The orthogonal wavelet transform decomposes the vibration signal onto a series of orthogonal wavelet functions and the number of wavelets on one wavelet level is different from those on the other levels. Since the grids are unevenly distributed on the time-scale map, it is shown that a representation pattern of a vibration component on the map may be significantly altered or even be broken down into pieces when the signal has a shift along the time axis. On contrary, there is no such uneven distribution of grids on the continuous wavelet time-scale map, so that the representation pattern of a vibration signal component will not change its shape when the signal component shifts along the time axis. Therefore, the patterns in the continuous wavelet time-scale map are more easily recognised by human visual inspection or computerised automatic diagnosis systems. Using a Gaussian enveloped oscillation wavelet, the wavelet transform is capable of retaining the frequency meaning used in the spectral analysis, while making the interpretation of patterns on the time-scale maps easier.

Experimental Investigation of the Dynamics and Bifurcations of an Impacting Spherical Pendulum

An experimental investigation was performed to determine the dynamics of an inverted, impacting spherical pendulum with large deflection and vertical parametric forcing. The pendulum system was studied with nine different bob and two different base configurations, for twenty times the natural frequency at shaker powers of 0 to 125 mm-hz. It was found that sustained conical motions did not naturally occur. The spherical pendulum system was analyzed to determine under what conditions the onset of Type I and sustainable Type II responses occurred.