Lumped parameter models representing impedance functions at the end of a finite beam on a viscoelastic medium

This study presents a lumped parameter model that represents impedance functions at the end of a finite flexural beam on a viscoelastic medium. This model comprises units arranged in series, each of which consists of a spring, a dashpot, and a so-called “gyro-mass element.” A formula is presented for determining the properties of the elements in the units. The impedance function simulated by the proposed model shows good agreement with the rigorous impedance function. A significant reduction in the degrees of freedom is a major advantage of this model for solving recent vibration problems.

► A lumped parameter model for a finite beam on a viscoelastic medium is proposed.
► The model comprises of springs, dashpots, and gyro-mass elements.
► A formula is presented for determining the properties of the model.
► Obtained impedance function from the model agrees well with the rigorous solution.
► A significant reduction in the degrees of freedom is a major advantage of this model.