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Scientific news from Division 1 | ||
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Characterisation of visco-elastic materials with the aid of N-parameter-models |
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When investigating building acoustical problems on downscaled models, detailed data on the mechanical properties of the used materials were needed for experimental and numerical purposes. To determine the properties such as Young's modulus and material damping a number of established measurement methods exist, partially as normative references. Unfortunately, these measurement methods usually deliver only single-number-values for a fixed frequency. Quite a number of materials can be regarded as behaving linear visco-elastically. Combining experimental measurement and numerical analysis, the visco-elastic parameters of such a material can be determined. Hence, the complex mechanical properties can be described in a wide frequency range by just a few real numbers. Parameter identification was carried out for silicone, aluminium and acrylic glass. |
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The determination of material properties, such as Young's modulus or the shear modulus, the Poisson ratio and material damping, is an ever-recurring task. Most of the classic methods stated in the standards DIN 53513, DIN 29052-1 or DIN EN ISO 6721, for example, only allow the determination of material properties at discrete frequencies, i.e. at the respective resonance- or excitation-frequency. To obtain a sufficiently closed spectrum, many individual measurements on various test pieces are, however, necessary. And also if complex material properties are needed (as, for example, for numerical calculations), classical methods often prove to be inadequate. Alternatively, to describe materials, a method can be used which comes from the field of mechanical engineering. Thereby it is assumed that the material behaves visco-elastically, which applies to most materials. Knowing this, a material can be described with a finite number of parameters - from which the designation as "N-parameter-model of a material" derives. For the building-acoustic frequency range, often only a few parameters are needed for an adequate description. From these parameters it is possible to calculate - with just a few simple formulas, and for any frequency in the validity range of the model - complex moduli, the Poisson ratio and material damping. The basic approach thereby is that a test piece (i.e. a piece of material) is mounted into a measurement set-up in such a way that the equations of motion and the marginal conditions are known as accurately as possible. On this test piece, a system answer is measured over the entire frequency range of interest. At the same time, an analytical model or an FEM model of the set-up is installed on a computer for simulation purposes. The material is thereby described by the parameters to be determined. By feeding the simulation with starter values for the parameters, the system answer having been measured before can now be simulated. After a comparison with the measured values, the parameters are corrected and the system answer can be simulated anew. In an optimization loop, the parameters are adjusted until the simulated and the measured answer agree sufficiently. For building-acoustic model measurements, several materials have been examined by means of this method. To determine the Young's modulus of silicone, a test piece, cast in a cylinder form, was hung vertically on a shaker (Figure 1). Thereby, the shaker excites the test piece to perform extension oscillations. With a mass glued to the foot of the test piece, the set-up behaves like a mass-spring-system. The system answer is first determined by measurement, i.e. the test piece is measured from the head to the mass affixed at the bottom. Then the system answer which has been derived from the analytical model is adapted optimally to this measured function. In this way, six parameters were identified which describe - between 10 Hz and 550 Hz - the tensile behavior of silicone quite well. In a similar way, aluminium and acrylic glass were characterized. In this case, however, we used test bars which were excited to perform bending vibrations. As far as the aluminium was concerned, the bar we used was very thin, so that shearing motions could be ruled out and the simulation could be carried out with a simple Euler Bernoulli bar. In contrast to this, the acrylic bar used by us was relatively thick. In that case, shear deformations exert an influence on the oscillation behavior. An adequate description as Timoshenko bar thus requires much more effort than in the case of the aluminium. However, here we have the opportunity to determine, in addition to Young's modulus, also the shear modulus. The identification furnishes 26 parameters of the material for frequencies between 3 Hz and 11 kHz. Hence, in this frequency range, the mechanical properties of the isotropic material acrylic glass are determined completely by one single experiment: Young's modulus, the shear modulus, the compression modulus, material damping and also the Poisson ratio can be calculated frequency-dependent from the 26 parameters with the aid of just a few simple formulas. Typically, the uncertainty of this method lies in the same order of magnitude as the classical method. Due to the complex identification process, accurate data on the uncertainty are, however, difficult to calculate. At first sight, characterizing materials with the aid of the N-parameter-method seems to require much more effort than with conventional methods. Particularly for the numerical part of the parameter identification, much time and experience are needed. If only simple characteristic values are sought after, the established methods are simpler and faster. If, however, frequency-dependent and complex material values are required, the N-parameter-method is superior. |
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| Figure 1: Cylindrical test piece made of silicone, mounted in the experimental set-up. The test piece is affixed to the shaker in a hanging-down position. The shaker excites it to perform longitudinal oscillations. |
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| Contact person: | |||
Christoph Kling, FB 1.7, AG 1.71, Christoph.Kling@PTB.de
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