Lumped parameter models representing impedance functions at the interface of a rod on a viscoelastic medium

In this study, a lumped parameter model that properly simulates the impedance characteristics at the extremity of a uniform, isotropic, homogeneous rod on a viscoelastic medium is proposed. The lumped parameter model consists of springs, dashpots, and so-called “gyro-mass elements”. The gyro-mass elements generate a reaction force proportional to the relative acceleration of the nodes between which they are placed. This model consists of units arranged in series, each unit consisting of a spring, a damper, and a gyro-mass element arranged in parallel. A formula is proposed for determining the properties of the elements in the units calculated from a closed-form solution based on a modal expansion. The impedance function simulated by the proposed model shows good agreement with the rigorous impedance function derived from the differential equation of motion of the rod. The results obtained by employing this model in some example applications show that the accuracy of the model is appreciably high when compared with conventional finite element models. A great advantage of this model is that a significant reduction of the number of degrees of freedom can be achieved for solving recent vibration problems with high-frequency excitations, such as ultrasonic vibrations.