Inherent non-linear damping in resonators with inertia amplification

Abstract

Inertia amplification is a mechanism coupling degrees of freedom within a vibrating structure. Its goal is to achieve an apparent high dynamic mass and, accordingly, a low resonance frequency. Such structures have been described for use in locally resonant metamaterials and phononic crystals to lower the starting frequency of a bandgap without adding mass to the system. This study shows that any non-linear kinematic coupling between translational or rotational vibrations leads to the appearance of amplitude-dependent damping. The analytical derivation of the equation of motion of a resonator with inertia amplification creates insight in the damping process and shows that the vibration damping increases with its amplitude. The theoretical study is validated by experimental evidence from two types of inertia-amplification resonators. Finally, the importance of amplitude-dependent damping is illustrated when the structure is used as a tuned mass damper for a cantilever beam.

Tunable topological interface states in one-dimensional inerter-based locally resonant lattices with damping

“…The basic idea of inerter elements in mechanical systems is to make a two-terminal device whose resistive force is proportional to the relative acceleration between the terminals. Such features can be achieved in many ways including pure mechanical [48], electromechanical [49], acoustic [50] or fluid-based inerters [51]. The force-displacement relationship of the ideal inerter is given as…”

“…where F is the resistive force, b is the inertance parameter and u 1 and u 2 are the displacements of two terminals. However, behavior of real inerter devices is far from ideal and different damping, hysteric or nonlinear effects need to be considered for accurate modelling [48].…”

A Nonlinear Metamaterial Induced by Nonlinear Damping Effect With Inertia Amplifiers

“…Single linear attachment, e.g., tuned mass damper [2] and piezoelectric shunting [3]; 2. Single nonlinear attachment, e.g., nonlinear energy sink [4] and nonlinear damping [5]; 3. Multiple linear attachments, e.g., multiple tuned mass dampers [6], and linear locally resonant metamaterials [7,8]; 4.…”

“…Thus, NES is considered to be applied with large vibration amplitudes. Take the example of nonlinear damping [5], and it is particularly suitable for shock wave attenuation with large velocity impact, which results in significant nonlinear damping or drag force to further dissipate the mechanical energy compared with a linear damped system.…”

Nonlinear Anti-Vibration Compliant Mechanism with Inertia Amplification

“…Though inertia amplification mechanisms offer impressive vibration isolation benefits, they have not been widely used in real engineering applications because of their complexity in implementation, stability difficulties, and gear backlash. With the ongoing development of 3D printing, compliant mechanism, and mechanical metamaterial, the inertia amplification mechanisms may now be made more compact and dependable [32]. Instead of driven by conventional mechanical system, new inertia amplification mechanisms are driven by compliant mechanism or comes in the form of mechanical metamaterial [33,34].…”