Radiation efficiency of a distribution of baffled pistons with arbitrary phases.

The radiation resistance and efficiency of a collection of circular pistons, randomly placed on a plane and vibrating with arbitrary phases, are expressed as a combination of the self- and mutual-radiation components. We use the first product or bridge theorem to construct the directivity pattern of this type of arrangement and the radiation properties are calculated according to Bouwkamp's impedance theorem. To illustrate the versatility of our approach, we refer to special cases for symmetric arrangements, for example, to compare with the modal radiation efficiency in structures having "regular" modal patterns.

A transverse isotropic equivalent fluid model combining both limp and rigid frame behaviors for fibrous materials.

Due to the manufacturing process, some fibrous materials like glasswool may be transversely isotropic (TI): fibers are mostly parallel to a plane of isotropy within which material properties are identical in all directions whereas properties are different along the transverse direction. The behavior of TI fibrous material is well described by the TI Biot's model, but it requires one to measure several mechanical parameters and to solve the TI Biot's equations. This paper presents an equivalent fluid model that can be suitable for TI materials under certain assumptions. It takes the form of a classical wave equation for the pressure involving an effective density tensor combining both limp and rigid frame behaviors of the material. This scalar wave equation is easily amenable to analytical and numerical treatments with a finite element method. Numerical results, based on the proposed model, are compared with experimental results obtained for two configurations with a fibrous material. The first concerns the absorption of an incident plane wave impinging on a fibrous slab and the second corresponds to the transmission loss of a splitter-type silencer in a duct. Both configurations highlight the effect of the sample orientation and give an illustration of the unusual TI behavior for fluids.

Effectiveness of nonporous windscreens for infrasonic measurements.

This paper deals with nonporous windscreens used for reducing noise in infrasonic measurements. A model of sound transmission using a modal approach is derived. The system is a square plate coupled with a cavity. The model agrees with finite element simulations and measurements performed on two windscreens: a cubic windscreen using a material recommended by Shams, Zuckerwar, and Sealey [J. Acoust. Soc. Am. 118, 1335-1340 (2005)] and an optimized flat windscreen made out of aluminum. Only the latter was found to couple acoustical waves below 10 Hz without any attenuation. Moreover, wind noise reduction measurements show that nonporous windscreens perform similarly as a pipe array by averaging the pressure fluctuations. These results question the assumptions of Shams et al. and Zuckerwar [J. Acoust. Soc. Am. 127, 3327-3334 (2010)] about compact nonporous windscreens design and effectiveness.

A homogenization method used to predict the performance of silencers containing parallel splitters.

An analytical model based on a homogenization process is used to predict and understand the behavior of finite length splitter/baffle-type silencers inserted axially into a rigid rectangular duct. Such silencers consist of a succession of parallel baffles made of porous material and airways inserted axially into a rigid duct. The pore network of the porous material in the baffle and the larger pores due to the airway can be considered as a double porosity (DP) medium with well-separated pore sizes. This scale separation leads by homogenization to the DP model, widely used in the porous material community. This alternative approach based on a homogenization process sheds physical insight into the attenuation mechanisms taking place in the silencer. Numerical comparisons with a reference method are used to show that the theory provides good results as long as the pressure wave in the silencer airways propagates as a plane wave parallel to the duct axis. The explicit expression of the axial wavenumber in the DP medium is used to derive an explicit expression for the optimal resistivity value of the porous material, ensuring the best dissipation for a given silencer geometry.

Static model of a violin bow: influence of camber and hair tension on mechanical behavior.

Experienced bow makers empirically know the influence of wood, tapering, and camber on the playing and tonal qualities of a bow. However, the way each parameter affects the bow mechanical behavior is not clearly established. An in-plane finite element model is developed to highlight the link between the adjustable design parameters and the mechanical behavior of a bow. This model takes into account geometric nonlinearity as well as compliance of the hair. Its validity is discussed from measurements on a bow. Results from simulations are compared to experimental results from previous studies. The consequences of adjusting hair tension and camber are then investigated.

Ironless transducer for measuring the mechanical properties of porous materials.

This paper presents a measurement setup for determining the mechanical properties of porous materials at low and medium frequencies by extending toward higher frequencies the quasistatic method based on a compression test. Indeed, classical quasistatic methods generally neglect the inertia effect of the porous sample and the coupling between the surrounding fluid and the frame; they are restricted to low frequency range (<100 Hz) or specific sample shape. In the present method, the porous sample is placed in a cavity to avoid a lateral airflow. Then a specific electrodynamic ironless transducer is used to compress the sample. This highly linear transducer is used as actuator and sensor; the mechanical impedance of the porous sample is deduced from the measurement of the electrical impedance of the transducer. The loss factor and the Young's modulus of the porous material are estimated by inverse method based on the Biot's model. Experimental results obtained with a polymer foam show the validity of the method in comparison with quasistatic method. The frequency limit has been extended from 100 Hz to 500 Hz. The sensitivity of each input parameter is estimated in order to point out the limitations of the method.

On the use of a loudspeaker for measuring the viscoelastic properties of sound absorbing materials.

This paper investigates the feasibility to use an electrodynamic loudspeaker to determine viscoelastic properties of sound-absorbing materials in the audible frequency range. The loudspeaker compresses the porous sample in a cavity, and a measurement of its electrical impedance allows one to determine the mechanical impedance of the sample: no additional sensors are required. Viscoelastic properties of the material are then estimated by inverting a 1D Biot model. The method is applied to two sound-absorbing materials (glass wool and polymer foam). Results are in good agreement with the classical compression quasistatic method.

Validity of the limp model for porous materials: a criterion based on the Biot theory.

The validity of using the limp model for porous materials is addressed in this paper. The limp model is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. Being an equivalent fluid model accounting for the motion of the frame, it has fewer limitations than the usual equivalent fluid model assuming a rigid frame. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the frame stiffness influence (FSI), based on porous material properties. The critical values of FSI under which the limp model can be used are determined using a one-dimensional analytical modeling for two boundary sets: absorption of a porous layer backed by a rigid wall and radiation of a vibrating plate covered by a porous layer. Compared with other criteria, the criterion associated with FSI provides information in a wider frequency range and can be used for configurations that include vibrating plates.