Bernard Laulagnet

Finite Element Simulation of Dynamic Instabilities in Frictional Sliding Contact

This paper describes tools for numerical modelisation which enable the understanding of the appearance of the vibration of structure generated by the frictional contact between two bodies (the excitation source being friction). The dynamic finite element code PLASTD is used to reproduce transitory phenomena generated at the contact interface. This code includes contact and friction algorithms based upon the formulation of Lagrange multipliers. A numerical study of the dynamic response of a 2D mechanical model composed of a deformable plane in relative translation and unilateral contact with Coulomb friction with a rigid surface is presented. The steady sliding solution is generically unstable and leads to a dynamic response which leads to the generation of instabilities characterized by the appearance of sliding-sticking or sliding-sticking-separation waves. It is important to notice that those instabilities appear even with a constant friction coefficient. These simulations have permitted to obtain the local contact conditions (kinematics, tribological state, contact stresses, etc). The kinematics shows the existence of local impacts and sliding at high frequencies. Furthermore, local normal pressure is much higher than that expected for a smooth surface. Finally, a 3D simulation of braking is carried out. We focused on the vibration of the disc and the brake pad which caused noises due to the generation of interface instabilities.© 2003 ASME

Nearfield acoustic holography using a laser vibrometer and a light membrane.

This paper deals with a measurement technique for planar nearfield acoustic holography (NAH) applications. The idea is to use a light tensionless membrane as a normal acoustic velocity sensor, whose response is measured by using a laser vibrometer. The main technical difficulty is that the used membrane must be optically reflective but acoustically transparent. The latter condition cannot be fully satisfied because of the membrane mass, which has to be minimized to reduce acoustic reflections. A mass correction operator is proposed in this work, based on a two-dimensional discrete Fourier transform of the membrane velocity field. An academic planar NAH experiment is finally reported, illustrating qualitatively and quantitatively the feasibility of the method and the pertinence of the mass correction operator.

Vibroacoustics of orthotropic plates ribbed in both directions: Application to stiffened rectangular wood panels

This paper is focused on the vibroacoustic behavior of a rectangular ribbed wood panel. This is done by developing an analytical model based on a variational approach, taking into account the kinetic and strain energies of a special orthotropic plate, 11 ribs oriented in a first direction and 1 other strong stiffener oriented in the perpendicular direction, which are considered as beams tied to the plate. A modal decomposition is adopted on the basis of the simply supported orthotropic plate. This allows calculating the modes of the wood panel (ribbed modes) in the frequency range 0-5000 Hz. The acoustical radiation of the baffled panel is also calculated. The radiation coefficients of the ribbed modes are presented and compared, when possible, to similar unribbed plate modes. Finally, the vibroacoustic analysis of the structure shows that an excitation placed on the hard point makes the panel particularly radiative and decreases the apparent critical frequency.

A modal approach to piano soundboard vibroacoustic behavior

This paper presents an analytical method for modeling the vibro-acoustic behavior of ribbed non-rectangular orthotropic clamped plates. To do this, the non-rectangular plate is embedded in an extended rectangular simply supported plate on which a spring distribution is added, blocking the extended part of the surface, and allowing the description of any inner surface shapes. The acoustical radiation of the embedded plate is ensured using the radiation impedances of the extended rectangular simply supported plate. This method is applied to an upright piano soundboard: a non-rectangular orthotropic plate ribbed in both directions by several straight stiffeners. A modal decomposition is adopted on the basis of the rectangular extended simply supported plate modes, making it possible to calculate the modes of a piano soundboard in the frequency range [0;3000] Hz, showing the different associated mode families. Likewise, the acoustical radiation is calculated using the radiation impedances of a simply supported baffled plate, demonstrating the influence of the string coupling point positions on the acoustic radiated power. The paper ends with the introduction of indicators taking into account spatial and spectral variations of the excitation depending on the notes, which add to the accuracy of the study from the musical standpoint. A parametrical study, which includes several variations of soundboard design, highlights the complexity of rendering high-pitched notes homogeneous.

Semi-analytical modeling of ground/plate interaction for general elastic boundary conditions

This letter introduces ground/plate interaction using the concept of ground cross-modal impedance in the case of general elastic boundary conditions. Navier equations are generally used to account for ground vibration with two propagating waves, the dilatational wave and the shear wave. The plate equation of motion follows the Kirchhoff-Love hypothesis, where shear and rotational inertia are neglected in the plate thickness. The general elastic boundary conditions are expressed analytically through a two-dimensional Fourier series in the plate displacement solution. This study shows that the plate general boundary conditions have a small influence on the plate velocity. However, two categories of boundary conditions could be implemented, especially at low frequency.

Vibroacoutsic Modelling of Piano Soundboards through Analytical Approaches in Frequency and Time Domains

The vibratory behavior and radiation of complex structures are a real challenge for many industrial domains. The increasing requirements of users and manufacturers justify the interest of the scientific community about this subject, particularly about ribbed structures. Initially, the design of such a structure is led by structural reasons and offers in the same time the possibility to reduce the weight and to reinforce the conception. Thus, they are common in many industrial domains, but also building and crafting sector. Among them, mention automotive, shipbuilding and aerospace industries or musical instruments too (see Fig. 8.1).

Sound radiation from cylinders: Modal analysis effect of curvature, and guidelines of noise reduction

The paper will present a review of works by the authors in sound radiation from a cylindrical shell including theoretical predictions and experimental results. The present analysis of shell vibroacoustic behavior essentially deals with global quantities like power radiation, shell quadratic velocity, and radiation factor; however, the farfield directivity pattern and nearfield pressure, velocity, or intensity can be calculated. The theoretical model is a finite baffled cylindrical shell, immersed in light or heavy fluid, excited by driving point forces. Ring stiffeners and the viscoelastic coating layer can be taken into account. The calculations use the in‐vacuo modal basis of the shell without stiffeners to expand shell displacements and boundary pressure, and the fluid loading is introduced by modal radiation impedances. Numerical implementation requires truncation of modal expansion, and criteria are necessary to select the modes governing vibroacoustic phenomena. This was established [B. Laulagnet an...