A simplified transfer matrix approach for the determination of the complex modulus of viscoelastic materials

Nowadays, several analytical and numerical approaches are available for analysing the performance of materials used in noise and vibration control applications. All these methodologies require knowledge of a set of input parameters which, in the case of viscoelastic materials, could exhibit strong dependence on frequency in the entire audible range. The aim of this paper is to present a simplified transfer matrix approach for the determination of the complex modulus for longitudinal waves of isotropic viscoelastic materials as a function of frequency. To that effect, the tested material is excited by an electromagnetic shaker and longitudinal waves are investigated. Using a frequency sweep as an excitation signal, the time domain response is measured downstream and upstream of the sample itself. A velocity transfer function is measured and, by using a transfer matrix model of the experimental setup, the complex wave number for longitudinal waves and, consequently, the complex modulus can be determined once the Poisson’s ratio is known in advance. The results are presented and discussed for different materials and compared with well-established quasi-static and dynamic techniques.