A finite element model of perforated panel absorbers including viscothermal effects

Most of the analytical models devoted to determine the acoustic properties of a rigid perforated panel consider the acoustic impedance of a single hole and then use the porosity to determine the impedance for the whole panel. However, in the case of not homogeneous hole distribution or more complex configurations this approach is no longer valid. This work explores some of these limitations and proposes a finite element methodology that implements the linearized Navier Stokes equations in the frequency domain to analyse the acoustic performance under normal incidence of perforated panel absorbers. Some preliminary results for a homogenous perforated panel show that the sound absorption coefficient derived from the Maa analytical model does not match those from the simulations. These differences are mainly attributed to the finite geometry effect and to the spatial distribution of the perforations for the numerical case. In order to confirm these statements, the acoustic field in the vicinities of the perforations is analysed for a more complex configuration of perforated panel. Additionally, experimental studies are carried out in an impedance tube for the same configuration and then compared to previous methods. The proposed methodology is shown to be in better agreement with the laboratorial measurements than the analytical approach.

3D numerical modelling of acoustic horns using the method of fundamental solutions

In the present work, a three-dimensional (3D) formulation based on the method of fundamental solutions (MFS) is applied to the study of acoustic horns. The implemented model follows and extends previous works that only considered two-dimensional and axisymmetric horn configurations. The more realistic case of 3D acoustic horns with symmetry regarding two orthogonal planes is addressed. The use of the domain decomposition technique with two interconnected sub-regions along a continuity boundary is proposed, allowing for the computation of the sound pressure generated by an acoustic horn installed on a rigid screen. In order to reduce the model discretization requirements for these cases, Green’s functions derived with the image source methodology are adopted, automatically accounting for the presence of symmetry conditions. A strategy for the calculation of an optimal position of the virtual sources used by the MFS to define the solution is also used, leading to improved reliability and flexibility of the proposed method. The responses obtained by the developed model are compared to reference solutions, computed by well-established models based on the boundary element method. Additionally, numerically calculated acoustic parameters, such as directivity and beamwidth, are compared with those evaluated experimentally.

Ultrasonic and X-ray computed tomography characterization of progressive fracture damage in low-porous carbonate rocks

This paper studies the fracturing process in low-porous rocks during uniaxial compressive tests considering the original defects and the new mechanical cracks in the material. For this purpose, five different kinds of rocks have been chosen with carbonate mineralogy and low porosity (lower than 2%). The characterization of the fracture damage is carried out using three different techniques: ultrasounds, mercury porosimetry and X-ray computed tomography. The proposed methodology allows quantifying the evolution of the porous system as well as studying the location of new cracks in the rock samples. Intercrystalline porosity (the smallest pores with pore radius < 1 μm) shows a limited development during loading, disappearing rapidly from the porosimetry curves and it is directly related to the initial plastic behaviour in the stress–strain patterns. However, the biggest pores (corresponding to the cracks) suffer a continuous enlargement until the unstable propagation of fractures. The measured crack initiation stress varies between 0.25 σp and 0.50 σp for marbles and between 0.50 σp and 0.85 σp for micrite limestone. The unstable propagation of cracks is assumed to occur very close to the peak strength. Crack propagation through the sample is completely independent of pre-existing defects (porous bands, stylolites, fractures and veins). The ultrasonic response in the time-domain is less sensitive to the fracture damage than the frequency-domain. P-wave velocity increases during loading test until the beginning of the unstable crack propagation. This increase is higher for marbles (between 15% and 30% from initial vp values) and lower for micrite limestones (between 5% and 10%). When the mechanical cracks propagate unstably, the velocity stops to increase and decreases only when rock damage is very high. Frequency analysis of the ultrasonic signals shows clear changes during the loading process. The spectrum of treated waveforms shows two main frequency peaks centred at low (~ 20 kHz) and high (~ 35 kHz) values. When new fractures appear and grow the amplitude of the high-frequency peak decreases, while that of the low-frequency peak increases. Besides, a slight frequency shift is observed towards higher frequencies.

Plastisol foaming process. Decomposition of the foaming agent, polymer behavior in the corresponding temperature range and resulting foam properties

The decomposition of azodicarbonamide, used as foaming agent in PVC—plasticizer (1/1) plastisols was studied by DSC. Nineteen different plasticizers, all belonging to the ester family, two being polymeric (polyadipates), were compared. The temperature of maximum decomposition rate (in anisothermal regime at 5 K min−1 scanning rate), ranges between 434 and 452 K. The heat of decomposition ranges between 8.7 and 12.5 J g−1. Some trends of variation of these parameters appear significant and are discussed in terms of solvent (matrix) and viscosity effects on the decomposition reactions. The shear modulus at 1 Hz frequency was determined at the temperature of maximum rate of foaming agent decomposition, and differs significantly from a sample to another. The foam density was determined at ambient temperature and the volume fraction of bubbles was used as criterion to judge the efficiency of the foaming process. The results reveal the existence of an optimal shear modulus of the order of 2 kPa that corresponds roughly to plasticizer molar masses of the order of 450 ± 50 g mol−1. Heavier plasticizers, especially polymeric ones are too difficult to deform. Lighter plasticizers such as diethyl phthalate (DEP) deform too easily and presumably facilitate bubble collapse.