Tunable band gaps of axially moving belt on periodic elastic foundation

TL;DR

This paper explores how varying the stiffness of a foundation can create tunable band gaps in an axially moving belt, enabling vibration suppression through boundary stiffness design.

Contribution

It introduces a method to manipulate band gaps via foundation stiffness modulation, allowing targeted vibration control in moving belts.

Findings

Band gaps appear at eigenvalue divergence points.

Mode shape veering correlates with wave attenuation.

Tuning stiffness achieves desired vibration suppression.

Abstract

The present paper investigates the band structure of an axially moving belt resting on a foundation with periodically varying stiffness. It is concluded that the band gaps appear when the divergence of the eigenvalue occurs and the veering phenomenon of mode shape begins. The bifurcation of eigenvalues and mode shape veering lead to wave attenuation. Hence, the boundary stiffness modulation can be designed to manipulate the band gap where the vibration is suppressed. The contribution of the system parameters to the band gaps has been obtained by applying the method of varying amplitudes. By tuning the stiffness, the desired band gap can be obtained and the vibration for specific parameters can be suppressed. The current study provides a technique to avoid vibration transmission of the axially moving material by designing the foundation stiffness.