Acoustical Characterization of Porous Materials for Automotive Application - Research Paper Example

? Acoustical Characterization of Porous Materials for Automotive Application: A Review By of Learning: Date: Acoustical Characterization of Porous Materials for Automotive Application: A Review Abstract This review mainly concerns itself with the acoustic characteristics of porous materials in various automotive applications. The porous materials in question include; artificial and natural fiber, porous material and polymer foams. There exists diversity when it comes to porous materials either artificial or natural. Sintered, steel wool, perforated materials and fiber metal are among the porous materials that have been increasingly used in automotive noise control. Following the diversity and variety of porous material characteristics, the study of porous media has proved to be wide and interesting. The review begins with outlining and comparing the models that are intended to be used in predicting the fundamental acoustical characteristics that are applicable in automotive. The paper introduces both the theoretical, empirical and numerical modeling and demonstrates how the models are used to determine the acoustic characteristics of porous materials. The analytical models indicate that the solid constituents of porous material are rigid and the fluid constituents are similar to that of a homogenous isotropic fluid that has been modified. The review also considers the acoustical characterization of porous materials and goes further to look at the porous materials modeling while having particular interests on porous materials that are elastic. The fundamental characteristics of porous materials are then illustrated using computational and experimental examples . Introduction In automotive, absorptive materials have various applications in different locations. Absorber pads can serve effectively in several locations such as in the door panel, pillar trim, headliner and bellow the carpet. Porous materials like fibers and foams are normally used in such applications. There acoustic characteristics enable them to serve as absorbers. It is the viscous losses that results in the conversion of energy to heat while sound waves navigate through the fibers or pores that are interconnected in the material. A porous material that is bonded with a barrier that is non-porous conducts the sound energy in waves that are in form of structure-borne. The characteristics which have the desirable influence on this wave form are the structural loss and bulk stiffness (Allard, 1993,p. 56). With reference to automotive applications, absorption is preferred at frequencies that are lower while the weight and thickness are to be limited. Porous materials with air flows resistance that are specific yet different have been identified as to achieve the results that are desired. However, the action of decreasing or increasing the given air flow resistance in order to achieve low frequency results affect high frequency performances. The review thus gives a presentation of a number of different material’s studies which illustrate such behavior. Several models such as the penalization approach demonstrate this behavior by simulating fluids inside and porous regions surrounding the obstacle. Such models are easy to implement and do not need a body fitting or a specific interface treatment. The models are successfully used in the introduction of new passive control methods that entail the implementation of a porous layer in between the fluid and the blue-body so as to change the characteristics of the boundary layer. Such a passive control model results in regularization that is drastic especially when it comes to high Reynolds numbers (Allard, 1992, p. 3349). Porous materials come in two phases, namely; the fibrous solid component termed as the frame and the interstitial fluid located in the pores resulting from the frame. Following their low density, porous materials cannot be generally used to make barriers but are commonly applied in the making of materials that absorb sound efficiently. The sound absorption is achieved through the conversion of acoustical organized motion to heat. Materials used to absorb sound release acoustical energy mostly due to the interaction between their fluid and solid phases. To be more particular, such material change acoustical energy to become heat through thermal means. This is witnessed in the irreversible flow of heat from the fluid to the frame fibers as a result of viscous means and also structural means (Attenborough and Walker, 1971, p. 1333). The models in this paper make use of acoustic absorption spectrum that have already been predicted then go ahead to compare them with the results from different experiments so as to verify the modeling approaches proposed by the paper. The paper goes further to conduct a parametric study in an effort to investigate the impact of the designed factors on the properties of acoustic absorption and transmission In some locations such as the rear window of the Ahmed body, the acoustic characteristics are not that significant and this calls for the mix up of strategies making use of both passive and active models so as to result in the desirable benefits. The outstanding advantage of passive control models is witnessed in its energy that is free making it convenient to implement (Beranek, 1949, p 45). Some of the applications that make use of this technology include bumps and ribelets as well as splitter plates. Passive control efficiency is closely associated with choices of the porous material permeability, its location and the porous layer thickness. The numerical models and simulations make use of passive control and regularization to control vibrations that have been induced by vortex in several sections of the vehicle. Following the mentioned consideration, this paper is going to look at the how porous materials have been acoustically characterized in automotive applications (Allard, Castagnede, Henry and Lauriks, 1994. P. 750). 2.3.2 Numerical modeling Introduction It has been generally accepted that the dynamics description made by Biot on poro-elastic materials fits as the most appropriate model. The model allows for the prediction of both the structural and acoustic response of porous material systems which can be easily achieved by models that are wave based making use of numerical and simple geometrics but end up producing exact solutions. Such numerical models give room for geometry that is more complex but still remain computationally intensive. Numerical modeling make use of parameters such as volume, pressure and area to determine the acoustic characteristics of porous materials. For example, the Barenek method takes into consideration the total volume of the acoustical material placed in a chamber that is rigid and has a specific volume. The air pressure changes in such a rigid chamber are then measured. At this point, the porous material prosperity is then calculated by applying Boyle’s law (Bies and Hansen, 1980, p. 360) Additional parameters have to be taken into consideration while using numerical model in order to achieve the best numerical findings. Such parameters include the boundary conditions, the existing statistics and concepts and the finite elements associated with the materials under test. Most of the existing methods are derived to determine sound absorption and transmission by poro-elastic material layers to an extent that is infinite. However, most of the automotive application problems need the analysis of geometrics that are more complex compared to those of flat layers. This situation called for better methods to be applied thus the need for techniques such as the finite element models and boundary element modeling (Biot, 1956, p. 172) 2.3.2.1 Finite element models The finite element models were presented by Kang to formulate poro-elastic materials that allowed easy coupling with the acoustic elements in existence. This model utilizes the node’s six degrees of freedom for the elements which include the frame and fluid displacements. The approach results in large matrices that depend on frequency which end up being inefficient to get solutions to in most cases. The above situation called for a simplified approach that made use of fluid pressure and frame displacement as their degrees of freedom. This approach simplified the frame and fluid coupling but still did not take into consideration the existing elastic coupling between the frame and fluid inside the material (Bolton and Kang, 1997, p. 237) An efficient method that took into consideration all the parameters degrees of freedom was introduced by Atalla and Panneton. In this approach, the stiffness and damping matrices that are dependent on frequency are approximated using linear functions that are very simple. Symmetric finite elements were later presented by Goransson that consisted of a formulation which required the node’s degrees of freedom of the lowest numbers. This gave room for the coupling integrals to be rigorously analyzed. The desired symmetry was reached at by making use of a fluid and a pressure displacement potential serving as parameters in the place of fluid displacement (Brown and Bolt, 1942, p. 340) The finite element model implementation has played a major role in the prediction of boundary conditions effects on sound and absorption transmission of porous material layers. The approaches have led to the conclusion that by having the linear bounded to the two surfaces inside a panel system, the transmission loss will increase at frequencies that are low due to the additional stiffness. Despite this realization, a configuration that is bounded will provide an overall performance that is best now that the transmission loss at high frequencies is maintained following the decoupling coming from the panel (Champoux, Stinson and Daigle, 1991, p. 912) 2.3.2.2 Boundary element models Tenneau formulated the boundary element modeling and it has since then been appreciated for its outstanding advantage of cutting down on mesh required size. This leads to great computational savings more specifically when it comes to mid-frequency range. This happens to be very significant to poro-elastic materials modeling following the matrices that are dependent on frequency and the degrees of freedom that are large per every node (Delany and Bazley , 1970, p. 112) The idea behind the boundary element model is to use an iterative solver to find solutions to BEM equation systems and later make use of the FMM to have the matrix-vector accelerated in every iteration step without resulting in the initial matrix explicitly. Thus the boundary element modeling has proved to be efficient and accurate is solving many problems in automotive applications. The approach is applicable in general properties predictions as it delivers predictions that are very efficient following its average schemes that are spatial of the internal structures of porous materials which only need the microstructure boundary information. Following this, the discretization boundary nature of this model results in desirable advantages. This has led to several boundary methods being developed with an aim of predicting the composite microstructures behaviors (Fahy, 2001, p. 123) 2.3.2.3 Statistical energy analysis models The initial step in statistical energy analysis modeling is elements identification. The other working option can be to identify elements with physical substructures. The above choices may however not be optimal in the event that inside a substructure or following the two or more substructure’s interactions, there exists several wave-types. Following the above developments, the most preferable option is to have statistical analysis elements assigned to the types of waves. Once the identification of elements has taken place, the energy equation balances in between the evaluated and the elements. The unknown variables in these equations happen to be the modal energies of every statistical energy analysis element (Dunn and Davern, 1986, p. 133) The modal energy in this context is the summation of all the energy in the system divided by the density of the modal or modes number per unit frequency. The losses in this modeling are of two different types, those responsible for internal loses that have been quantified using modal factors which are overlapping and those responsible for coupling losses that are measured using the conductivity. The Herein approach can be used to come up with statistical energy analysis that is applicable on multilayered structures that exist in double walls (Leonard, 1946, p. 240). The important idea is to replace the existing statistical energy analysis elements that are used to describe the cavity making the double walls with new elements that refer to specific types of walls. An assumption is made that bellow the resonance frequency double wall, the walls shift in phase and the loss in transmission is approximated by the mass law of the field-incidence (Henry, Lemarinier and Allard, 1995, p 19) Conclusion The mentioned models used in predicting porous materials characteristics have proved that this is a complex area of research. Following the nature of porous materials, there is no single model that can be in a position to examine the dynamics associated with the characteristics of such materials. Some works have been identified as being empirical in the checking of models that seem to be more complex especially those making use of rigid frames. Such works include those of Baz-leys and Delany. It is now apparent that porous material dynamics are not as complicated as it has always been believed once effective stiffness, inertial and damping terms have been acquired. To achieve this, the theoretical derivations of the above mentioned terms have been included in the several different models. Large parameter numbers have also been introduced to aid in the description of the physical characteristics of porous materials and in most cases the parameters needed in the models differ from one to the other (Jaesuk, 1999, p. 34) Following the results from a number of acoustic absorption modeling and by putting into consideration factors like aggregate shapes, void ratio and gradation, it has been seen that in order to model the porous concrete void texture, the rigid panel model that is micro-perforated and has been included with multiple layers to put into consideration air gaps has to be adopted. The parameters that are to be used in this type of modeling have to be determined by experimental and geometrical approaches following the shape and gradation of target void and aggregates ratio (Jaesuk, 1999, p. 215) The results indicate that porous materials that are sound absorbing have undergone remarkable changes to become advanced materials. In comparison to the traditional absorbing materials, the new materials have proved to be lighter, safer and optimized technologically. They are also environmental friendly in that they are recyclable, sustainable, and used in sound-absorbing green building materials (Kino, 2007, p. 1430). With the increased intensity of researches carried out in this field, it is anticipated that new porous-materials with the most desired characteristics will be expand in the years to come. Further research however needs to be conducted on the introduction of porous concrete in other fields a part from automotive applications such as civil infrastructures as such fields require acoustic absorption materials that are of excellent characteristics (Morse and Ingard , 1968, p. 23) Reference List Allard J., 1992. “New empirical equations for sound propagation in rigid frame fibrous materials.” J. Acoust Soc Am, 91:3346–3353 Allard J., 1993. Propagation Of Sound In Porous Media: Modeling Sound Absorbing Materials. Elsevier: Ireland Allard J., Castagnede B., Henry M., Lauriks W., 1994. “Evaluation of tortuosity in acoustic porous materials saturated by air”. Review of Scientific Instruments, v 65, n 3, 754-755 Attenborough K., & Walker A., 1971. “Scattering theory for sound absorption in fibrous media.”J Acoust Soc Am; 49:1331–8 Beranek, J., 1949. Acoustic Measurements. Wiley: New York. Bies D & Hansen C, 1980. “Flow resistance information for acoustical design.” Appl Acoust, 13:357–91. Bies D., 1971. Acoustic properties of porous materials. McGraw-Hill: New York Biot M., 1956. “Theory of propagation of elastic waves in a fluid saturated porous solid. I. Low-frequency range.” J Acoust Soc Am 28(2):168–178 Bolton J & Kang J., 1997. “Elastic porous materials for sound absorption and transmission control”. SAE Paper 971878 Brown R & Bolt R., 1942. “The measurement of flow resistance of porous acoustic materials.” J. Acoust. Soc. Am. 13 (4), 337-344 Champoux, Y., Stinson R., & Daigle G. A., 1991. “Air based system for the measurement of porosity”. J. Acoust. Soc. Am. 89 (2), 910-916 Delany E, & Bazley E., 1970. “Acoustical properties of fibrous absorbent materials.”Appl Acoust (3), 105–116 Dunn I & Davern W, 1986. “Calculation of acoustic impedance of multi-layer absorbers” Appl Acoust; 19:321–34. Fahy F, 2001. Foundations of Engineering Acoustics. Academic: London Henry M., Lemarinier P., Allard J., 1995. Evaluation of the characteristic dimensions for porous sound absorbing materials, Journal of Applied Physics, 77 (1), 17-20 Jaesuk L., 1999. Low-Velocity Impact and Sound Absorption Of Composite Sandwiches. Pro Quest Dissertation and Theses. Wayne State University: Michigan Kawasima Y., 1960. “Sound propagation in a fiber block as a composite medium.” Acta Acust, 10:208–17. Kino N., 2007. “Ultrasonic measurements of the two characteristic lengths in fibrous materials.” Applied acoustics, 68, 1427-1438 Leonard, R., 1946. “Simplified flow resistance measurements”. J. Acoust. Soc. Am. 17 (3), 240-241 Morse P. & Ingard U., 1968. Theoretical Acoustics. McGraw-Hill: New York: Read More