Elastic characterization of closed cell foams from impedance tube absorption tests

A method is presented to determine the bulk elastic properties of isotropic elastic closed-cell foams from impedance tube sound absorption tests. For such foams, a resonant sound absorption is generally observed, where acoustic energy is transformed into mechanical vibration, which in turn is dissipated into heat due to structural damping. This article shows how the bulk Young's modulus, Poisson's ratio, and damping loss factor can be deduced from the resonant absorption. Also, an optimal damping loss factor yielding 100% of absorption at the first resonance is defined from the developed theory. The method is introduced for a sliding edge condition which is an ideal condition. Then, the method is extended to a bonded edge condition which is more easily achievable and additionally enables the identification of the Poisson's ratio. The method is experimentally tested on expanding closed-cell foams to find their elastic properties in both cases. Using the found properties, sound absorption predictions using an equivalent solid model with and without surface absorption are compared to measurements. Good correlations are obtained when considering surface absorption.     

Using shock waves to improve the sound absorbing efficiency of closed-cell foams

Producing closed-cell foams is generally cheaper and simpler than open-cell foams. However, the acoustic and filtration efficiency of closed-cell foam materials is generally poor because it is very difficult for fluid or acoustic waves to penetrate into the material. A new method using shock waves to remove the membranes closing the cell pores (known as reticulation) and thus to improve the acoustic and filtration behavior of closed-cell foam material is presented. Various shock treatments have been carried out on polyurethane and polyimide foams and the following conclusions were drawn: (1) reticulation efficiency increased and thus the airflow resistivity and tortuosity decreased when increasing the amplitude of the shock treatment; (2) the rigidity of the foam is decreased; (3) the process is reliable and repeatable and (4) obtained acoustic performance is comparable to classical thermal reticulation.     

Solid-perforated panel layout optimization by topology optimization based on unified transfer matrix

This paper presents a numerical method for the optimization of the sequencing of solid panels, perforated panels and air gaps and their respective thickness for maximizing sound transmission loss and/or absorption. For the optimization, a method based on the topology optimization formulation is proposed. It is difficult to employ only the commonly-used material interpolation technique because the involved layers exhibit fundamentally different acoustic behavior. Thus, an optimization method formulation using a so-called unified transfer matrix is newly proposed. The key idea is to form elements of the transfer matrix such that interpolated elements by the layer design variables can be those of air, perforated and solid panel layers. The problem related to the interpolation is addressed and bench mark-type problems such as sound transmission or absorption maximization problems are solved to check the efficiency of the developed method.     

Improving the Morphological Parameters of Aluminum Foam for Maximum Sound Absorption Coefficient using Genetic Algorithm

Fabricating of metal foams with desired morphological parameters including pore size, porosity and pore opening is possible now using sintering technology. Thus, if it is possible to determine the morphology of metal foam to absorb sound at a given frequency, and then fabricate it through sintering, it is expected to have optimized metal foams for the best sound absorption. Theoretical sound absorption models such as Lu model describe the relationship between morphological parameters and the sound absorption coefficient. In this study, the Lu model was used to optimize the morphological parameters of Aluminum metal foam for the best sound absorption coefficient. For this purpose, the Lu model was numerically solved using written codes in MATLAB software. After validating the proposed codes with benchmark data, the genetic algorithm (GA) was applied to optimize the affecting morphological parameters on the sound absorption coefficient. The optimization was carried out for the thicknesses of 5 mm to 40 mm at the sound frequency range of 250 Hz–8000 Hz. The optimized parameters ranged from 50% to 95% for porosity, 0.1 mm to 4.5 mm for pore size, and 0.07 mm to 0.6 mm for pore opening size. The result of this study was applied to fabricate the desired Aluminum metal foams for the best sound absorption. The novel approach applied in this study, is expected to be successfully applied in for best sound absorption in desired frequencies.     

含泡沫铝防护结构的超高速撞击数值模拟研究

 泡沫铝是一种新型航天器防护材料,拥有良好的抵御空间碎片超高速撞击的特性。模仿泡沫金属的生产原理,建立了泡沫金属微结构几何模型,结合自编的光滑质点流体动力学程序进行了超高速撞击数值仿真,通过与实验结果的对比,验证了模型的有效性。提出了两种含泡沫铝的空间碎片防护结构,即填充泡沫铝结构和夹层泡沫铝结构。对这两种结构分别进行了仿真计算,获得了其撞击极限曲线。分析结果表明,在空间碎片防护领域涉及的大部分撞击速度区间内,填充泡沫铝结构的防护性能优于夹层泡沫铝结构。     

Microstructure,strength and creep of aluminium-nickel open cell foam

Al–6.4 wt% Ni open-cell foams produced by replication are tested in compression and in tension at room temperature and creep tested in tension at 450°C. The mechanical behaviour of this foam at room temperature is consistent with that observed for other open-cell metallic foams. A strong dependence on relative density as well as dependence on stress and temperature of the steady-state creep rate are captured by the model described by Mueller et al. [Scripta Mater. 57 (2007) p.33], itself a simplification of variational estimates by Ponte Castañeda and Suquet [Adv. Appl. Mech. 34 (1998) p.171]. The foam exhibits two regimes of creep, separated by a critical stress; these features can be interpreted on the basis of the microstructure of the Al–6.4 wt% Ni alloy making the foam. This microcellular eutectic Al–Ni exhibits attractive creep failure resistance compared to other open-cell aluminium alloy foams.     

Foams in contact with solid boundaries: Equilibrium conditions and conformal invariance

A liquid foam in contact with a solid surface forms a two-dimensional foam on the surface. We derive the equilibrium equations for this 2D foam when the solid surface is curved and smooth, generalising the standard case of flat Hele-Shaw cells. The equilibrium conditions at the vertices in 2D, at the edges in 3D, are invariant by conformal transformations. Regarding the films, conformal invariance only holds with restrictions, which we explicit for 3D and flat 2D foams. Considering foams confined in thin interstices between two non-parallel plates, normal incidence and Laplace’s law lead to an approximate equation relating the plate profile to the conformal map. Solutions are given for the logarithm and power laws in the case of constant pressure. The paper concludes on a comparison with available experimental data.     

Experimental Cosserat elasticity in open-cell polymer foam

Reticulated open-cell polymer foams exhibit substantial size effects in torsion and bending: slender specimens are more rigid than anticipated via classical elasticity. Such size effects are predicted by Cosserat (micropolar) elasticity, which allows points to rotate as well as translate and incorporates distributed moments (couple stresses). The Cosserat characteristic length is larger than the cell size. The Cosserat coupling coefficient is larger than in dense closed-cell foams and approaches 1 for foam with 0.4 mm cells.     

Investigations on the acoustic transmission characteristics of underwater perforated panel structures

Perforated panel structures have a wide potential in underwater applications. However, up to now there has been little related research. The acoustic impedance of an underwater perforated panel is obtained based on the theories for air perforated panel sound absorption. In this paper sound transmission characteristics of underwater perforated panel structures are theoretically analyzed by the transfer matrix method. A formula for normal incidence sound transmission coefficients is given. The main factors that have effects on the acoustic transmission coefficient are analyzed by numerical simulations. The perforated panel structures made by ourselves are tested in a standing-wave tube by the four-sensor transfer-function method. The experimental results are well in accord with the results obtained by the numerical method, which proves that the theoretical analysis is correct. This paper has provided theoretical and experimental bases for the design of underwater perforated panel structures.     

Sound insulation property of Al–Si closed-cell aluminum foam sandwich panels

Al–Si closed-cell aluminum foam sandwich panels (1240 mm × 1100 mm) of different thicknesses and different densities were prepared by molten body transitional foaming process in Northeastern University. The experiments were carried out to investigate the sound insulation property of Al–Si closed-cell aluminum foam sandwich panels of different thicknesses and different densities under different frequencies (100–4000 Hz). Results show that sound reduction index (R) is small under low frequencies, large under high frequencies; thickness affects the sound insulation property of material obviously: when the thicknesses of Al–Si closed-cell aluminum foam sandwich panels are 12, 22, and 32 mm, the corresponding weighted sound reduction indices (R_W) are 26.3, 32.2, and 34.6 dB, respectively, the rising trend tempered; the increase of density of Al–Si closed-cell aluminum foam can also increase the sound insulation property: when the densities of aluminum foam are 0.31, 0.51, and 0.67 g/cm³, the corresponding weighted sound reduction indices (R_W) are 28.9, 34.3, and 34.6 dB, the increasing value mitigating.     

Neural networks for prediction of acoustical properties of polyurethane foams

This paper presents a study of neural networks for prediction of acoustical properties of polyurethane foams. The proposed neural network model of the foam uses easily measured parameters such as frequency, airflow resistivity and density to predict multiple acoustical properties including the sound absorption coefficient and the surface impedance. Such a model is quite robust in the sense that it can be used to develop models for many different classes of materials with different sets of input and output parameters. The current neural network model of the foam is empirical and provides a useful complement to the existing analytical and numerical approaches.     

An axisymmetric poroelastic finite element formulation.

In the past, various two- and three-dimensional Cartesian, poroelastic finite element formulations have been proposed and demonstrated. Here an axisymmetric formulation of a poroelastic finite element is presented. The intention of this work was to develop a finite element formulation that could easily and efficiently model axisymmetric sound propagation in circular structures having arbitrary, axially dependent radii, and that are lined or filled with elastic porous sound absorbing materials such as foams. The formulation starts from the Biot equations for an elastic porous material expressed explicitly in axisymmetric form. By following a standard finite element development, a u-U formulation results. Procedures for coupling the axisymmetric elements to an adjacent acoustical domain are described, as are the boundary conditions appropriate for unfaced foams. Calculations described here show that the present formulation yields predictions as accurate as a Cartesian, three-dimensional model in much reduced time. Predictions made using the present model are also compared with measurements of sound transmission through cylindrical foam plugs, and the predicted results are shown to agree well with the measurements. Good agreement was also found in the case of sound transmission through a conical foam plug.     

Homogeneous sound-absorbing structures for aircraft engine ducts

As applied to the ducts of aircraft engines, a new method is studied for extending the frequency range of sound absorption by using special homogeneous materials of a rigid structure. A through- or blind-hole perforation of such a homogeneous material is for the first time suggested with a view to substantially extend its capabilities. A theory is developed for sound-absorbing structures of perforated homogeneous material that allows for computing their wave parameters and impedance on the basis of those of the starting material. Based on this theory, one can calculate the impedance of any, no matter how complex a structure built up of several layers differing in thickness and perforation percentage and diameter. The results of calculations made for the impedance and sound absorption coefficient of single and multiple layer samples show good agreement with experimental data.     

Laguerre approximation of random foams

Stochastic models for the microstructure of foams are valuable tools to study the relations between microstructure characteristics and macroscopic properties. Owing to the physical laws behind the formation of foams, Laguerre tessellations have turned out to be suitable models for foams. Laguerre tessellations are weighted generalizations of Voronoi tessellations, where polyhedral cells are formed through the interaction of weighted generator points. While both share the same topology, the cell curvature of foams allows only an approximation by Laguerre tessellations. This makes the model fitting a challenging task, especially when the preservation of the local topology is required. In this work, we propose an inversion-based approach to fit a Laguerre tessellation model to a foam. The idea is to find a set of generator points whose tessellation best fits the foam’s cell system. For this purpose, we transform the model fitting into a minimization problem that can be solved by gradient descent-based optimization. The proposed algorithm restores the generators of a tessellation if it is known to be Laguerre. If, as in the case of foams, no exact solution is possible, an approximative solution is obtained that maintains the local topology.     

Sound absorption of cellular metals with semiopen cells

A combined experimental and theoretical study is presented for the feasibility of using aluminum foams with semiopen cells for sound-absorption applications. The foams are processed via negative-pressure infiltration, using a preform consisting of water-soluble spherical particles. An analytical model is developed to quantify the dependence of pore connectivity on processing parameters, including infiltration pressure, particle size, wetting angle, and surface tension of molten alloy. Normal sound-absorption coefficient and static flow resistance are measured for samples having different porosity, pore size, and pore opening. A theory is developed for idealized semiopen metallic foams, with a regular hexagonal hollow prism having one circular aperture on each of its eight surfaces as the unit cell. The theory is built upon the acoustic impedance of the circular apertures (orifices) and cylindrical cavities due to viscous effects, and the principle of electroacoustic analogy. The predicted sound-absorption coefficients are compared with those measured. To help select processing parameters for producing semiopen metallic foams with desirable sound-absorbing properties, emphasis is placed on revealing the correlation between sound absorption and morphological parameters such as pore size, pore opening, and porosity.     

Enhancing the low frequency sound absorption of a perforated panel by parallel-arranged extended tubes

This paper is concerned with the use of a perforated panel with extended tubes (PPET) to improve the sound absorption confined to low frequencies. In comparison with a micro-perforated panel (MPP), the sound absorption can be significantly improved by using the PPET at the expense of the bandwidth of the sound absorption. A particular configuration combining four parallel-arranged PPETs with different cavities is introduced to achieve a wider bandwidth of the sound absorption at low frequencies. The analysis is extended to the combination of three parallel-arranged PPETs and a MPP to further increase the bandwidth of the sound absorption. A theoretical model is described to predict the sound absorption coefficient and the simulated annealing method is introduced to the proposed absorbers, allowing optimization of the overall performance. The theory with experimental validations demonstrates that the proposed configurations offer a potential improvement of more than one octave in the bandwidth of the sound absorption at low frequencies.     

Computational study on cell structure evolution of random liquid and metal-melt foams

A method for geometrical and topological modeling the evolution of close-cell metallic foams based on the Voronoi tessellation in three-dimensional space is presented. Numerical computations were carried out to examine the evolution of the bubble size distribution and topological and geometric properties of aluminum foams in the liquid state, which were implemented by using McPherson’s new theory on coarsening of microstructures as well as the topological transition rules (T1 and T2 processes) in 3D foams, accounting for remarkable effects of both the gas diffusion and surface tension. Computational results show that the bubble size distributions of metallic foams are strongly coupled to the evolution of the cellular structure and dependent on the gas diffusivity and surface tension. The way of foam coarsening can be expressed as RR ₃₂=−mt ²+1 approximately, and gas diffusion between bubbles dominates the evolution of bubble sizes and foam structures. It is found that the average number of faces per bubble is 〈f〉=13.8, which is in good agreement with the values reported in the literature.     

复合应力下泡沫铝屈服行为实验研究

 采用ARCAN双轴加载装置和材料实验机（INSTRON 5544）,对相对密度为8.5%的闭孔泡沫铝（Alporas）进行了不同应变率下的双轴加载实验。在宏观等效应变率为7.0×10^-3~1.0×10^-1 s^-1范围内测得实验屈服面,并与泡沫金属的3种屈服准则进行了比较。比较结果表明：在主应力空间下,实验屈服面与Miller和Deshpande-Fleck屈服准则吻合较好,Gibson屈服准则过小估计了测试泡沫铝的实验屈服面;被测泡沫铝的实验屈服面在宏观等效应变率7.0×10^-3~1.0×10^-1 s^-1范围内对应变率不敏感。     

Structure of random foam

The Surface Evolver was used to compute the equilibrium microstructure of dry soap foams with random structure and a wide range of cell-size distributions. Topological and geometric properties of foams and individual cells were evaluated. The theory for isotropic Plateau polyhedra describes the dependence of cell geometric properties on their volume and number of faces. The surface area of all cells is about 10% greater than a sphere of equal volume; this leads to a simple but accurate theory for the surface free energy density of foam. A novel parameter based on the surface-volume mean bubble radius R32 is used to characterize foam polydispersity. The foam energy, total cell edge length, and average number of faces per cell all decrease with increasing polydispersity. Pentagonal faces are the most common in monodisperse foam but quadrilaterals take over in highly polydisperse structures.     

In situ observations of compressive behaviour of aluminium foams by local tomography using high-resolution X-rays

We have investigated the compressive behaviour of closed-cell aluminium foams using a high-resolution X-ray CT. The microstructures of cell walls or Plateau borders in the foams were visualized in 3D using the local tomography technique which is a high-resolution CT method to reconstruct a region of interest within a large sample. The shapes and the 3D distribution of micropores, particles, and regions of solute segregation in the foams are evaluated, comparing the cell walls with the Plateau borders. Under compressive loads, the damage behaviour of such microstructures has been observed using an in situ test rig. It is found that the microcracks were mainly initiated from the cell walls and the micropores with large diameters were also damaged. The crack initiation sites are classified from the results. In addition, a method for non-destructive characterization of elastic and plastic deformation in the foams, which is called a 3D microstructure gauge (MG) method, is presented. Thousands of micropores as markers on each load were automatically matched by the information of those volumes and surface areas. The local strain mapping by the MG indicates that the edges of the micropores with large diameters have large strain under compression and this is consistent with the crack analyses.