Transfer impedance of a three-layer viscoelastic rod

The present work is an attempt to apply the transfer impedance method to the investigation of systems composed of several layers of a material with known viscoelastic properties. A multilayer rod excited to longitudinal vibrations is examined theoretically. The end of the rod is stiffly connected with an optional mass. We assume that the component layers are homogeneous whereas the specific wave impedance undergoes jump-like changes at the border of the layers. In order to find the expression for the transfer impedance of the rod considered, the electromechanical analogies are used. The formulae given in the work allow to find the transfer impedance modulus which well describes the ability of a given structure to energy transmission. So, knowing the sound velocity cn and loss factor ηn for a given layer of the material, one can determine the components of propagation constant αα and βn which subsequently allow to find the modulus of the transfer impedance for an optional frequency, at the fulfilled condition that the length of the longitudinal wave in the rod is much bigger than the lateral dimension of the rod. To illustrate the usefulness of the introduced formulae, a number of numerical investigations for vibroisolating materials are made. The influence of the mutual configuration of layers and their properties as components on the transfer impedance of the composed rod-like specimen is discussed.