Adnan Akay

Acoustics of friction

This article presents an overview of the acoustics of friction by covering friction sounds, friction-induced vibrations and waves in solids, and descriptions of other frictional phenomena related to acoustics. Friction, resulting from the sliding contact of solids, often gives rise to diverse forms of waves and oscillations within solids which frequently lead to radiation of sound to the surrounding media. Among the many everyday examples of friction sounds, violin music and brake noise in automobiles represent the two extremes in terms of the sounds they produce and the mechanisms by which they are generated. Of the multiple examples of friction sounds in nature, insect sounds are prominent. Friction also provides a means by which energy dissipation takes place at the interface of solids. Friction damping that develops between surfaces, such as joints and connections, in some cases requires only microscopic motion to dissipate energy. Modeling of friction-induced vibrations and friction damping in mechanical systems requires an accurate description of friction for which only approximations exist. While many of the components that contribute to friction can be modeled, computational requirements become prohibitive for their contemporaneous calculation. Furthermore, quantification of friction at the atomic scale still remains elusive. At the atomic scale, friction becomes a mechanism that converts the kinetic energy associated with the relative motion of surfaces to thermal energy. However, the description of the conversion to thermal energy represented by a disordered state of oscillations of atoms in a solid is still not well understood. At the macroscopic level, friction interacts with the vibrations and waves that it causes. Such interaction sets up a feedback between the friction force and waves at the surfaces, thereby making friction and surface motion interdependent. Such interdependence forms the basis for friction-induced motion as in the case of ultrasonic motors and other examples. Last, when considered phenomenologically, friction and boundary layer turbulence exhibit analogous properties and, when compared, each may provide clues to a better understanding of the other.

Dynamic response of a revolute joint with clearance

The response of a revolute joint in a four-bar mechanism with a clearance is investigated. Motion of a rocker-arm pin at the ground connection is modelled using a Lagrangian approach. When the resulting equations of motion are solved numerically, they show non-linear dependence on both the size of the clearance and the coefficient of friction between the pin and bearing. The results, given in terms of pin trajectories and Poincare maps, show that the motion of the pin can range from simple periodic to periodic motions with periods that are multiples of the crank revolution, and in some cases pin motion becomes chaotic. It is of note that at moderately high values of coefficient of friction, the pin response is simple periodic, with a period same as that of the crank rotation.

A numerical model of friction between rough surfaces

This paper describes a computational method to calculate the friction force between two rough surfaces. In the model used, friction results from forces developed during elastic deformation and shear resistance of adhesive junctions at the contact areas. Contacts occur between asperities and have arbitrary orientations with respect to the surfaces. The size and slope of each contact area depend on external loads, mechanical properties and topographies of surfaces. Contact force distribution is computed by iterating the relationship between contact parameters, external loads, and surface topographies until the sum of normal components of contact forces equals the normal load. The corresponding sum of tangential components of contact forces constitutes the friction force. To calculate elastic deformation in three dimensions, we use the method of influence coefficients and its adaptation to shear forces to account for sliding friction. Analysis presented in Appendix A gives approximate limits within which influence coefficients developed for flat elastic half-space can apply to rough surfaces. Use of the method of residual correction and a successive grid refinement helped rectify the periodicity error introduced by the FFT technique that was used to solve for asperity pressures. The proposed method, when applied to the classical problem of a sphere on a half-space as a benchmark, showed good agreement with previous results. Calculations show how friction changes with surface roughness and also demonstrate the methods efficiency.

A review of impact noise

In this paper, available literature concerned with impact noise generation and control is reviewed with emphasis on generation mechanisms. Basic research studies are considered under five different classes according to the mechanism of sound generation. These are air ejection, rigid body radiation, radiation due to rapid surface deformations, pseudo-steady-state radiation, and sound radiation due to material fracture. A brief characterization of impact sounds in addition to a description of efforts to standardize impact noise exposure criteria is given in the Introduction. A bibliography on impact noise control is included in order to permit assessment of the state of the art.

Theoretical foundations of apparent-damping phenomena and nearly irreversible energy exchange in linear conservative systems

This paper discusses a class of unexpected irreversible phenomena that can develop in linear conservative systems and provides a theoretical foundation that explains the underlying principles. Recent studies have shown that energy can be introduced to a linear system with near irreversibility, or energy within a system can migrate to a subsystem nearly irreversibly, even in the absence of dissipation, provided that the system has a particular natural frequency distribution. The present work introduces a general theory that provides a mathematical foundation and a physical explanation for the near irreversibility phenomena observed and reported in previous publications. Inspired by the properties of probability distribution functions, the general formulation developed here is based on particular properties of harmonic series, which form the common basis of linear dynamic system models. The results demonstrate the existence of a special class of linear nondissipative dynamic systems that exhibit nearly irreversible energy exchange and possess a decaying impulse response. In addition to uncovering a new class of dynamic system properties, the results have far-reaching implications in engineering applications where classical vibration damping or absorption techniques may not be effective. Furthermore, the results also support the notion of nearly irreversible energy transfer in conservative linear systems, which until now has been a concept associated exclusively with nonlinear systems.

Stick-slip oscillations: Dynamics of friction and surface roughness

While its classical model is relatively simple, friction actually depends on both the interface properties of interacting surfaces and on the dynamics of the system containing them. At a microscopic level, the true contact area changes as the surfaces move relative to each other. Thus at a macroscopic level, total friction and normal forces are time-dependent phenomena. This paper introduces a more detailed friction model, one that explicitly considers deformation of and adhesion between surface asperities. Using probabilistic surface models for two nominally flat surfaces, the stick–slip model sums adhesive and deformative forces over all asperities. Two features distinguish this approach from more traditional analyses: (i) Roughness distributions of the two interacting surfaces are considered to be independent, (ii) Intersurface contacts occur at both asperity peaks, as in previous models, and on their slopes. Slope contacts, in particular, are important because these oblique interactions produce motion...

Transient energy exchange between a primary structure and a set of oscillators: Return time and apparent damping

In this paper we examine the conditions that influence the return time, the time it takes before energy returns from a set of satellite oscillators attached to a primary structure. Two methods are presented to estimate the return time. One estimate is based on an analysis of the reaction force on a rigid base by a finite number of oscillators as compared with an infinite number of continuously distributed oscillators. The result gives a lower-bound estimate for the return time. A more accurate estimation results from considering the dynamic behavior of a set of oscillators as waves in a waveguide. Such an analogy explains energy flow between a primary structure and the oscillators in terms of pseudowaves and shows that a nonlinear frequency distribution of the oscillators leads to pseudodispersive waves. The resulting approximate expressions show the influence of the natural frequency distribution within the set of oscillators, and of their number, on the return time as compared with the asymptotic case of a continuous set with infinite oscillators. In the paper we also introduce a new method based on a Hilbert envelope to estimate the apparent damping loss factor of the primary structure during the return time considering transient energy flow from the primary structure before any energy reflects back from the attached oscillators. The expressions developed for return time and damping factor show close agreement with direct numerical simulations. The paper concludes with a discussion of the return time and its relation to apparent damping and optimum frequency distribution within a set of oscillators that maximize these quantities.

Energy sinks: Vibration absorption by an optimal set of undamped oscillators

This presentation offers the concept of energy sinks as an alternative to conventional methods of vibration absorption and damping. A prototypical energy sink envisioned here consists of a set of oscillators attached to, or an integral part of, a vibrating structure. The oscillators that make up an energy sink absorb vibratory energy from a structure and retain it in their phase‐space. In principle, energy sinks do not dissipate vibratory energy as heat in the classical sense. The absorbed energy remains in an energy sink permanently so that the flow of energy from the primary structure appears to it as damping. This paper demonstrates that a set of linear oscillators can collectively absorb and retain vibratory energy with near irreversibility when they have a particular distribution of natural frequencies. The approach to obtain such a frequency response is based on an optimization that minimizes the energy retained by the structure as a function of frequency distribution of the oscillators in the set.

Near-irreversibility in a conservative linear structure with singularity points in its modal density

Through two complementary approaches, using modal response and wave propagation, the analyses presented here show the conditions under which a decaying impulse response, or a nearly irreversible energy trapping, takes place in a linear conservative continuous system. The results show that the basic foundation of near-irreversibility or apparent damping rests upon the presence of singularity points in the modal density of dynamic systems or, analogously, in the wave-stopping properties associated with these singularities. To illustrate the concept of apparent damping in detail, a simple undamped beam is modified to introduce a singularity point in its modal density distribution. Simulations show that a suitable application of a compressive axial force to an undamped beam placed on an elastic foundation attenuates its impulse response with time and develops the characteristics of a nearly irreversible energy trap.

Sound radiation from an impact‐excited clamped circular plate in an infinite baffle

Sound radiation from most mechanical systems results from impact forces of various kinds. In this paper, transient sound radiation from impact‐excited circular plates is studied both analytically and experimentally. First, the contact force developed during the inelastic collision of a ball with a flexible plate was obtained. The plate vibrations were then obtained using normal mode analysis. The sound radiation waveforms in the time domain were obtained by numerical integration of the Rayleigh integral. Both analytical and experimental results show the radiation of a sound pulse during the contact which is a result of the forced deformation of the plate. Quantitative relationships are given for the plate vibration response and acoustic radiation.