Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
On the influence of nonlinear stiffness on the design of vibration absorber and neutralizers
Submission Author:
Atila Almeida , SP , Brazil
Co-Authors:
Atila Almeida, Paulo José Paupitz Gonçalves
Presenter: Atila Almeida
doi://10.26678/ABCM.COBEM2021.COB2021-2075
Abstract
Vibration neutralizers are devices used to reduce vibration on a primary structure and are usually tuned to the frequency of an external harmonic force. The vibration absorber consists of a similar device, but the target tuning frequency is a resonance of the primary structure. Their result is the creation of a notch filter in frequency. A single degree vibration neutralizer has stiffness and mass and damping. The objective frequency can be adjusted by changing the stiffness or mass elements. Regarding the nonlinear behaviour of such devices, there are two cases to be considered. One occurs when there is an interest to improve the performance of neutralizer exploring nonlinearity. The second case occurs when the neutralizer can exhibit nonlinear behaviour if submitted to large amplitude oscillations but not intentionally designed. This paper focuses on the analysis of such cases when they operate in a nonlinear regime. Nonlinearity in systems is possible with greater deformations of the spring, called stiffening or softening stiffness. The cases of hardening and softening stiffness can be modelled using a cubic polynomial to represent the elastic restoring force. The analysis is based on a system with at least two degrees of freedom where the neutralizer is attached. Frequency response functions are obtained considering an approximation of nonlinear forces obtained by the harmonic balance method, based on the fundamental frequency. Differently from the traditional harmonic balance method, here the equations of motion are computed assuming a complex exponential excitation force, so are the displacements variables expanded into real and imaginary components and solved using a continuation method. In some cases, the nonlinear vibration neutralizer can improve the system's performance compared to the linear defined, but only if correctly designed. The analytical results obtained by the harmonic balance method are also verified by numerical integration of the equations of motion.
Keywords
vibration isolation, Nonlinear Dynamic, Absorber
