Time-domain simulation of damped impacted plates. I. Theory and experiments

Abstract

A time-domain formulation for the flexural vibrations in damped rectangular isotropic and orthotropic plates is developed, in order to investigate transient excitation of plates by means of sound synthesis. The model includes three basic mechanisms of damping (thermoelasticity, viscoelasticity and radiation) using a general differential operator. The four rigidity factors of the plate are modified by perturbation terms, each term corresponding to one specific damping mechanism. The first damping term is derived from the coupling between the thermoelastic stress-strain relations and the heat diffusion equation. The second term is obtained from the general differential formulation of viscoelasticity. The third term is obtained through a Pade approximation of the damping factor which governs the coupling of the plate with the surrounding air. The decay factors predicted by the model reproduce adequately the dependence on both dimensions and frequency of the decay factors measured on rectangular plates of various sizes and thicknesses made of four different materials (aluminum, glass, carbon fiber, and wood). The numerical resolution of the complete problem, including initial and boundary conditions, and the comparison between real and simulated sounds are presented in a companion paper.

Sound absorption of porous substrates covered by foliage: Experimental results and numerical predictions

“…15 The substrate is used to grow small plants. These plants develop into foliage which covers 16 densely the porous substrate and might affect its acoustic absorption properties. The substrates 17 typically used for wall vegetation exhibit high values of the absorption coefficient 3,4 and can be 18 adopted in noise abatement applications in an urban environment.…”

“…Therefore, the leaf was simply supported at three points so that we 14 were able to measure the influence of the leaf vibration and its acoustical shielding effect on the 15 acoustic absorption coefficient of the porous sample that was representing the soil. 16 When the pressure at two microphones in the impedance tube is recorded, the absorption …”

Wave turbulence in vibrating plates: The effect of damping

“…The damping is due to very different physical origins: thermoelasticity, acoustic radiation and dissipation at the boundaries in particular. In our case the coincidence frequency for acoustic radiation can be estimated in the vicinity of 20 kHz [18,20] and is thus not relevant for our frequency range. Thermal effects can be described by Zener model [21] which leads to a frequencyindependent [13,18,20] small value for the damping factor, roughly estimated at 0.8s −1 for our plate.…”

“…In our case the coincidence frequency for acoustic radiation can be estimated in the vicinity of 20 kHz [18,20] and is thus not relevant for our frequency range. Thermal effects can be described by Zener model [21] which leads to a frequencyindependent [13,18,20] small value for the damping factor, roughly estimated at 0.8s −1 for our plate. A part of the energy is also dissipated at the clamped boundary where two pieces of rubber are inserted in order to avoid a metallic contact between the plate and the clamp.…”

“…Concerning the latter phenomenum, weak turbulence theory requires dissipative scales to be widely separated from forcing scales to allow the conservation of the energy flux through the cascade. In solid plates, the dissipation has different origins and is in fact present at every scales [18], so that this property is highly questionable. The goal of this paper is therefore to quantify both experimentally and numerically the influence of the real dissipation on the turbulent spectra.…”