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

The complex Young's modulus of acoustic materials as a function of frequency is generally investigated by using a cylindrical or prismatic specimen of the material excited into longitudinal harmonic vibration at one end, the other end being loaded by a mass. The transfer function method is the most advantageous to use for the investigation, which involves the measurement of the vibration amplitudes of the specimen ends and the phase angle between them. In this paper, the transfer function method is analyzed theoretically and experimentally in that frequency range where the specimen can essentially be modelled by a longitudinally vibrating rod (rod-like specimen). The analysis includes the measurability of the transfer function, the role of the measurement errors, the frequency range of the method and the maximum dynamic strain of the specimen. A special application of the method is developed for investigating the complex modulus of low loss materials at the extremes of the absolute value of the transfer function, without measuring the phase angle. Experimental results obtained by both methods are presented.