A. Le Bot

Comparison of an integral equation on energy and the ray-tracing technique in room acoustics.

This paper deals with a comparison of two room acoustic models. The first one is an integral formulation stemming from power balance and the second is the ray-tracing technique with a perfectly diffuse reflection law. The common assumptions to both models are the uncorrelated wave hypothesis and the perfectly diffuse reflection law. The latter allows the use of these methods for nondiffuse fields beyond the validity domain of Sabines formula. Comparisons of numerical simulations performed with the softwares RAYON and CeReS point out that these results are close to each other and finally, a formal proof is proposed showing that both methods are actually equivalent.

Review of statistical energy analysis hypotheses in vibroacoustics

This paper is a discussion of the equivalence between rain-on-the-roof excitation, diffuse field and modal energy equipartition hypotheses when using statistical energy analysis (SEA). A first example of a simply supported plate is taken to quantify whether a field is diffuse or the energy is equally distributed among modes. It is shown that the field can be diffuse in a certain region of the frequency-damping domain with a single point force but without energy equipartition. For a rain-on-the-roof excitation, the energy becomes equally distributed, and the diffuse field is enforced in all regions. A second example of two plates coupled by a light spring is discussed. It is shown that in addition to previous conclusions, the power exchanged between plates agrees with the statistical prediction of SEA if and only if the field is diffuse. The special case of energy equipartition confirms this observation.

Friction-Induced Vibration by Stribeck's Law: Application to Wiper Blade Squeal Noise

This paper is concerned with the squeal noise of a wiper/windscreen contact. It is shown that squeal noise stems from friction-induced self-excited vibrations in the context of Stribeck’s law for friction coefficient. The study is specifically focussed on the instability range of velocities and not on the amplitude of limit cycles. The studied dynamic system consists of a single degree-of-freedom mass-spring-damper oscillator submitted to a velocity-dependent frictional force which follows the Stribeck law. The local stability is analyzed by the first Lyapunov method and results in a stability criterion. Experiments have been performed on a glass/elastomer contact lubricated with water. The tribometer ‘LUG’ provides measurements of the vibrational velocity and friction force versus sliding speed. It is found that the instability appears during the transition between boundary and elastohydrodynamic regimes where the negative gradient of the friction versus velocity curve is steep. The apparition and vanishing of instability are correctly predicted by the steady-state stability criterion.

A functional equation for the specular reflection of rays

This paper aims to generalize the “radiosity method” when applied to specular reflection. Within the field of thermics, the radiosity method is also called the “standard procedure.” The integral equation for incident energy, which is usually derived for diffuse reflection, is replaced by a more appropriate functional equation. The latter is used to solve some specific problems and it is shown that all the classical features of specular reflection, for example, the existence of image sources, are embodied within this equation. This equation can be solved with the ray-tracing technique, despite the implemented mathematics being quite different. Several interesting features of the energy field are presented.

Energy flow analysis for curved beams

This paper presents an energy model for the medium- and high-frequency analysis of Love–Kirchhoff curved beams. This model introduced by Nefske and Sung [Statistical Energy Analysis NCA 3, 47–54 (1987)] for straight beams and investigated further by other authors, is developed for curved rods (tangential or longitudinal waves), and then for curved beams (radial or flexural waves). The exact-energy solution for curved rods or beams is shown to consist of a smooth spatial variation, which the energy model represents, and a spatially oscillating solution, which can be represented by an energy envelope. Finally, a complete energy model is proposed for curved components including both longitudinal and flexural waves. Boundary conditions are also given in this paper. It is shown that this method, which is numerically attractive in the mid- and high-frequency range, predicts the arithmetic mean value of the energy variables.

Liquefaction of immersed granular media under isotropic compression

We report an observation of the spontaneous liquefaction of glass beads immersed in water and compacted by external isotropic stress. We show that during compression, loose granular samples exhibit a series of sudden rearrangements accompanied by a transient overpressure of interstitial fluid. Ultimately, spontaneous liquefaction with large deformation of the sample is observed. By contrast, denser samples do not show a liquefaction by maintaining its shape integrity. We then discuss the potential mechanisms which could explain this unexpected liquefaction.

Specular and diffuse reflections of rays in coupled thin plates at high frequencies

The flexural energy distribution in two right-angled point-excited thin plates at high frequencies is investigated by means of an integral energy flow approach. The fields of energy averaged over time and frequency are described by the superposition of uncorrelated cylindrical waves stemming from both boundaries and direct sources. Specular and diffuse laws are considered for the reflection and transmission of rays, giving rise to two kinds of energy equations. The diffuse law leads to a Fredholm integral equation over the boundary sources while the specular law is shown to allow an image source solution when the plates have identical propagation properties. The algorithm for computing the image position, magnitude and directivities is described. Then, some comparisons between the results from the both energy formulations and also from the statistical energy analysis and the numerical solution of the equations of motion are performed with two damped plates at high frequency. The non-diffuse pattern of the averaged flexural energy fields is well described by the energy flow approaches.

Entropy in sound and vibration: towards a new paradigm

This paper describes a discussion on the method and the status of a statistical theory of sound and vibration, called statistical energy analysis (SEA). SEA is a simple theory of sound and vibration in elastic structures that applies when the vibrational energy is diffusely distributed. We show that SEA is a thermodynamical theory of sound and vibration, based on a law of exchange of energy analogous to the Clausius principle. We further investigate the notion of entropy in this context and discuss its meaning. We show that entropy is a measure of information lost in the passage from the classical theory of sound and vibration and SEA, its thermodynamical counterpart.

Analytical Model and Experimental Validation of Friction Laws for Composites Under Low Loads

In order to account for interfacial friction of composite materials, an analytical model based on contact geometry and local friction is proposed. A contact area includes several types of microcontacts depending on reinforcement materials and their shape. A proportion between these areas is defined by in-plane contact geometry. The model applied to a fibre-reinforced composite results in the dependence of friction on surface fibre fraction and local friction coefficients. To validate this analytical model, an experimental study on carbon fibre-reinforced epoxy composites under low normal pressure was performed. The effects of fibre volume fraction and fibre orientation were studied, discussed and compared with analytical model results.

EXPERIMENTAL STUDY ON FRICTION NOISE OF DRY ROUGH SURFACES

This paper presents an experimental study of the friction noise, between two rough and dry surfaces. Two different geometries of contact have been studied: flat - flat contact and sphere - flat contact. The domain of interest is the dry contact under light pressure where the roughness is the dominant cause of noise. In agreement with some other studies, it has been observed that the sound pressure level Lp (dB) is a logarithmic function of the surface roughness and the sliding speed. However, the exponent of the logarithmic law between sound pressure level and surface roughness largely depends on the topography of the sliding surfaces. On the other hand, the exponent of the law between sound pressure level and sliding speed depends on the contact geometry.