Resonance decomposition for the vibratory response of a viscoelastic rod

The vibratory response of a driven viscoelastic rod has been used in earlier investigations to measure the complex elastic modulus of the rod material. The transfer function T, i.e., the ratio of displacements (or accelerations) at the end of the rod divided by those at the driven end, is obtained as a function of frequency and rod length. In terms of these variables, it exhibits resonance peaks. In the present work, following the developments of Fiorito et al. [J. Acoust. Soc. Am. 79, 222 (1986)], the transfer function is represented as a meromorphic function of the frequency with complex poles, in order to isolate the individual resonances. Such a representation allows a clean determination of resonance frequencies and widths, and thus leads to a more sensitive measurement of the complex elastic modulus of the rod material. Comparison of exact theory and this resonance theory formulation of T is presented for various rod materials.