Session: MSNDC-04/VIB-09-05: Nonlinear Dynamics of Systems and Structures

Paper Number: 117688

117688 - Dynamics of Nonlinear Blades Equipped With Locally Resonant Meta-Structures 

In this study, we investigate dynamics of a rotor with nonlinear meta-structure blades. The main structure of the system is a symmetrical circular structure, composed of three identical cantilever beams with cubic stiffness connected through linear springs. The coupling between nonlinear blades is weak compared to the cantilever beam stiffness, and each cantilever beam is excited with uniform harmonic forcing. An array of four local resonators is embedded in each cantilever beam, to efficiently absorb vibrational energy from the host beam. Each resonator is tuned to the linear frequency of the beam.

First, we use the harmonic balance method to analyze the amplitude-frequency response of a single cantilever beam and show how the frequency response changes with the embedded linear resonators. We show that the frequency ranges where the nonlinear beam shows a bistable response reduce as the linear resonators are added to the system. As we increase the total mass of the resonators up to 20% of the system mass (i.e. 4m/(4m+M) = 20%), the bistable region shrinks even more, and the system starts showing a linear-like behavior. We show that for a system with cubic nonlinearity, high-amplitude vibrations occurring in the bistable region can be suppressed through means of embedding meta-structures into the system. The amplitude reduction is achieved through both the reduction of the peak values, and the disappearance of the bistable region.

We then extend this study to a system of three circularly arranged, weakly-coupled, nonlinear beams with circular symmetry. Using the harmonic balance method, we first find the frequency response of coupled beams without the embedded meta-structures. The system shows a multi-stable behavior. The multi-stable solutions include an energy localization, where one of the beams can have a high response amplitude compared to the others. When the cantilever beams are equipped with linear resonators, the frequency ranges where the system shows multi-stable behavior becomes narrower, similar to the reduction in bistable region of a cantilever beam. When the mass of the resonator reaches 20% of the system mass, the energy localization phenomenon completely disappears. In other words, resonators with smaller mass are effective in a small frequency range, whereas resonators with relatively larger mass (e.g., 20%) can suppress energy localization effectively in a wider frequency range and induce a linear-like behavior. The results are validated through numerical simulations at  for systems with a total mass ratio of 10% and 20%.

In summary, this study proposes a new method of controlling the dynamic behavior of a nonlinear rotor system by embedding meta-structures into the blades. We establish that high amplitude vibrations and energy localization behavior in nonlinear rotors can be effectively mitigated by designing local resonators according to the guidelines outlined using the single-blade response.

Presenting Author: Gizem Acar Stevens Institute of Technology

Presenting Author Biography: Bing joined the Acar Lab as a Ph.D student at Stevens Institute of Technology in 2022, which is a laboratory that studies nonlinear dynamics and vibrations. His current research focus on the phenomenon of energy localization in nonlinear systems.

Authors:

bing Wu Stevens Institute of Technology
Gizem Acar Stevens Institute of Technology