A Circular Eccentric Vibration Absorber with Circumferentially Graded Acoustic Black Hole Features

A previously proposed planar axisymmetric dynamic vibration absorber (DVA), with embedded acoustic black hole (ABH) features, has been shown to suffer from the very selective coupling with the host structure, thus compromising its vibration reduction performance. To tackle the problem, an eccentric ABH-based circular DVA whose thickness profile is tailored according to a circumferential gradient variation is proposed in this paper. This new configuration preserves the ABH profile in the radial direction alongside a continuous variation along the circumferential direction and breaks the axisymmetry of the original DVA design at the same time. While the former permits the ABH features to fully play out in a continuous manner, the later entails a more effective coupling with the host structure. These salient properties have been demonstrated and confirmed both numerically and experimentally by examining a benchmark plate structure. For analyses, a coupling model embracing the host structure and the add-on DVAs is established which allows the calculation of the coupling coefficient, a vital quantity to guide the DVA design. Studies demonstrate the advantages of the proposed DVA over existing designs for the same given mass. The enriched structural coupling and the enhanced modal damping, arising from the eccentric and circumferentially graded ABH design, are shown to be the origin of such improvement. All in all, the physical process underpinning the dynamic absorber principle and waveguide absorber from the host structures is simultaneously consolidated, thus leading to superior broadband structural vibration suppression.

Analysis on Influences of Squeeze Film Damper on Vibrations of Rotor System in Aeroengine

Squeeze film damper (SFD) is widely used in the vibration suppression of aeroengine rotor systems, but will cause complex motions of the rotor system under specific operating conditions. In this paper, a lumped-mass dynamic model of the high-pressure rotor system in an aeroengine is established, and the nonlinear stiffness and damping formula of SFD are introduced into the above model. The vibration responses of the rotor system under different rotating speeds and with different unbalances are investigated numerically, and the influence of SFD on the rotor system vibration and the change of suppression ability are compared and analyzed. The results show that in the case of high speed, together with a small unbalance, the rotor system will perform a complex vibration or a bistable vibration due to SFD. If the unbalance is properly increased under the same case of high speed, the vibration of the rotor becomes single-harmonic and the bistable vibration disappears. The research results can provide a helpful reference for analyzing complex vibration mechanisms of the rotor system with SFD and achieving an effective vibration suppression through unbalance regulation.

Optimization of profile and damping layer of plates embedded with acoustic black hole indentations for broadband energy dissipation

Acoustic Black Hole (ABH) plate structure has shown promising potentials of vibration suppression above a cut on frequency. For energy dissipation below the cut on frequency, however, the ABH is less effective due to the absence of wave focusing effect. This work reports a simultaneous optimization of ABH plates for broadband energy dissipation. Two sets of design variables of ABH plates, that is, geometry of the profile and topology of the damping layer, are optimized in an alternatively nested procedure. A novel objective function, namely the upper limit of kinetic energy, is proposed. Modeling of ABH structures is implemented and dynamic characteristic is solved using finite element method. A rectangular plate embedded with two ABH indentations is presented as a numerical example. Influence of frequency ranges in the calculation and mass ratios of the damping layer on results are discussed. The achieved optimal arrangement of the damping layer is found to cover equally, if not more, above the non-ABH (uniform) part of the plate than the ABH area. This is inconsistent with the conventional believe that damping layers should cover as much of the ABH area as possible. Mechanism of the broadband energy dissipation by the optimal solution is demonstrated.

Collision enhanced hyper-damping in nonlinear elastic metamaterial

Nonlinear elastic metamaterial, a topic which has attracted extensive attention in recent years, can enable broadband vibration reduction under relatively large amplitude. The combination of damping and strong nonlinearity in metamaterials may entail auxetic effects and offer the capability for low-frequency and broadband vibration reduction. However, there exists a clear lack of proper design methods as well as a deficiency in understanding properties arising from this concept. To tackle this problem, this paper numerically demonstrates that the nonlinear elastic metamaterials, consisting of sandwich damping layers and collision resonators, can generate very robust hyper-damping effect, conducive to efficient and broadband vibration suppression. The collision-enhanced hyper damping is persistently present in a large parameter space, ranging from small to large amplitudes, and for small and large damping coefficient. The achieved robust effects greatly enlarge the application scope of nonlinear metamaterials. We report the design concept, properties and mechanisms of the hyper-damping and its effect on vibration transmission. This paper reveals new properties offered by nonlinear elastic metamaterials, and offers a robust method for achieving efficient low-frequency and broadband vibration suppression.

Vibration control through the robust nonlinear absorber with negative stiffness and internal resonance creation

In this study, a nonlinear absorber that works with a negative stiffness mechanism is suggested to mitigate vibration, and its effect on the reduction of vibration is investigated. The negative stiffness, which is inherently nonlinear, creates internal resonance; therefore, the vibration energy can be transmitted from low-frequency to high-frequency vibrating modes, causing vibration suppression. The nonlinear absorber is added to the primary nonlinear system, and when the main system is subjected to external resonance due to harmonic excitation, the negative stiffness parameter of absorber is so adjusted that autoparametric resonance occurs and vibration is reduced. First, the mathematical model of the system is presented and the governing differential equations of the motion are derived, and then, using the multiple scale method, the equations are solved for the case without, and with the 1:3 internal resonance. The responses and their stability are inspected, discussed, and compared. After that, the effect of negative stiffness and damping parameters on vibration amplitude reduction is investigated and the adequacy of the proposed absorber will be demonstrated by numerical analysis. Finally, the energy exchange between the primary system and the absorber will be demonstrated by plotting the responses in the state space and the displacement response Fourier spectrum.

Energy flow and performance evaluation of inerter-based vibration isolators mounted on finite and infinite flexible foundation structures

This study investigates the vibration power flow behavior and performance of inerter-based vibration isolators mounted on finite and infinite flexible beam structures. Two configurations of vibration isolators with spring, damper, and inerter as well as different rigidities of finite and infinite foundation structures are considered. Both the time-averaged power flow transmission and the force transmissibility are studied and used as indices to evaluate the isolation performance. Comparisons are made between the two proposed configurations of inerter-based isolators and the conventional spring-damper isolators to show potential performance benefits of including inerter for effective vibration isolation. It is shown that by configuring the inerter, spring, and damper in parallel in the isolator, anti-peaks are introduced in the time-averaged transmitted power and force transmissibility at specific frequencies such that the vibration transmission to the foundation can be greatly suppressed. When the inerter is connected in series with a spring-damper unit and then in-parallel with a spring, considerable improvement in vibration isolation can be achieved near the original peak frequency while maintaining good high-frequency isolation performance. The study provides better understanding of the effects of adding inerters to vibration isolators mounted on a flexible foundation, and benefits enhanced designs of inerter-based vibration suppression systems.