Tuning of topological interface modes in an elastic beam array system with inerters

Abstract

Topological phononic crystals in the mechanical setup became a topic of great interest owing to their applicability in various engineering systems such as waveguides or vibration isolation devices. If such systems are composed of elastic structures, they are usually characterized by a bulk-edge correspondence where the geometrical and material properties can play important role in the existence of stable surface and boundary modes. This work investigates the band transition and topological interface modes in a beam array system, where two sub-lattices of vertically aligned, parallel, and elastically coupled beams are connected at the chain center. To illustrate the existence of interface modes and understand their behavior, the corresponding eigenvalue problem is solved and frequency response function is sought for the system with a finite number of unit cells. Localization of the interface modes is demonstrated based on the steady-state responses of the beam array system to harmonic excitation. The effects of introduced defect masses and inerters on interface states are studied separately. It is revealed that the introduction of a small defect mass in the form of concentrated mass attached to some beam in the system does not affect the interface modes within the observed frequency range. On the other side, inerters produce frequency shifts towards lower values, which even in the case of small values of the inerter parameter causes the interface modes to vanish or even to appear inside another frequency band gap. The obtained results give an insight into the influence of inerter devices and their mass amplification effect on the interface states in complex periodic elastic systems. It also investigates the possibility to tune interface modes without significantly affecting the main band structure properties of the system.