Transfer function method for investigating the complex modulus of acoustic materials: Spring-like specimen

Abstract

The complex modulus of acoustic materials has to be known as a function of frequency. Among many methods for investigating the complex modulus, it is advantageous to use the transfer function method for detailed frequency analysis. In this method, a cylindrical or prismatic specimen is excited into longitudinal vibration at one end, the other end being loaded by a mass. The complex modulus can be calculated after having measured the transfer function: i.e., the vibration amplitudes of the specimen ends and the phase angle between them. In this paper the transfer function and its measurability are investigated theoretically and experimentally in that frequency range where the specimen can essentially be modelled by lumped parameter mechanical elements. The role of the measurement errors is analyzed and it is shown that the smaller the loss factor the higher the measurement accuracy that is needed. Furthermore, it is shown that disregarding the longitudinal wave motion of the specimen at higher frequencies leads to an apparent increase of the dynamic modulus and to an apparent decreases of the loss factor. This effect may be compensated up to a certain frequency by the lateral wave motion of the specimen. Experimental results supporting the theoretical predictions are presented.