Suppression mechanism of vortex-induced vibrations using non-linear energy sink with inerter based mechanical networks

The shimmy phenomenon is a significant concern in aircraft landing gear dynamics. The prediction of the shimmy instability is an essential issue in landing gear design to develop a passive or active suppression method. This work investigates the application of the nonlinear energy sink (NES) concept to mitigate the effects of shimmy in landing gears. The NES concept has been used in recent research on mechanical vibrations. It comprises a passive target energy transfer method that refers to a one-way energy transfer from a primary to a nonlinear subsystem. The landing gear model is based on torsional displacement coupled with the tyre classical elastic string analogy model. The NES device connects to the wheel shaft, and it comprises a mass, a linear damper, and a pure cubic spring. The numerical integration in time was used to assess the shimmy onset speed and the post-shimmy limit cycle oscillations. A parametric analysis of the landing gear nonlinear dynamics without the NES is presented. The design space of possible NES parameters is given, obeying design constraints, and inspected to assess adequate NES designs. The best NES samples are included in the landing gear dynamics to study their influence. Results have shown that the NES can adequately expand the operational speed range for no shimmy and lead to lower LCO amplitudes in the post-shimmy for a reasonable range of speeds. The NES concept’s successful employment for the landing gear dynamics suggests an enormous potential form of passive shimmy control.

Shaking table test study on seismic performance of RC frame structure with NES

Improving product quality of machining components has always met with problems due to the vibration of the milling machine’s spindle, which can be reduced by adding a vibration absorber. The tuned vibration absorber (TVA) has been studied extensively and found to have a narrow bandwidth, but the cutting force possesses wide bandwidth in the process of machining parts. Introducing nonlinearity into the dynamic vibration absorber can effectively increase the bandwidth of vibration suppression and can significantly improve the robustness of the vibration absorber. In addition, a semiactive TVA has proved to be more effective than a passive TVA for many applications, so the main purpose of this study is to find some appropriate semiactive control methods for a nonlinear energy sink (NES), a nonlinear vibration absorber, in structural vibration applications. Two semiactive control methods are considered in this study: continuous groundhook damping control based on velocity and on-off groundhook damping control based on velocity. To fairly compare these vibration absorbers, the optimal parameters of a passive TVA, a passive NES, and two semiactive NESs are designed using numerical optimization techniques to minimize the root-mean-square acceleration. Two cutting forces are introduced in this study, a periodic force and an aperiodic force, and the four vibration absorbers are compared. When the primary structure is excited with aperiodic cutting force, the amplitude of the primary structure decreased by 17.73% with the passive TVA, by 72.29% with the passive NES, by 73.54% with the on-off NES, and by 87.54% with the continuous NES. When the primary structure is excited with periodic cutting force, the amplitude of the primary structure decreased by 49.01% with a passive TVA, by 86.93% with a passive NES, by 96.38% with an on-off NES, and by 99.23% with a continuous NES. The results show that the passive NES is better than the passive TVA; the semiactive NES provides more effective vibration attenuation than the passive NES, and the continuous control is more effective than the on-off control.

Design, construction and experimental performance of a nonlinear energy sink in mitigating multi-modal vibrations

A nonlinear energy sink (NES) is used to suppress panel flutter. A nonlinear aeroelastic model for a two-dimensional flat panel with an NES in supersonic flow is established using the Galerkin method. First-order piston aerodynamic theory is adopted to build the aerodynamic load. The effects of NES parameters on flutter boundaries of the panel are investigated using Lyapunov’s indirect method. The mechanism of the NES suppression of panel flutter is studied through energy analysis. Effects of NES parameters on aeroelastic responses of the panel are obtained, and a design technique is adopted to find a suitable combination of parameter values of the NES that suppresses the panel flutter effectively. Results show that the NES can increase or reduce the onset dynamic pressure of the panel flutter and it can reduce the aeroelastic response amplitude effectively within a certain range of dynamic pressure behind the onset dynamic pressure. The installation position of the NES depends on the direction of the airflow. The robust characteristics should be considered to find the suitable combination of parameter values of the NES.

Rotary-oscillatory nonlinear energy sink of robust performance

In this last of a three paper sequence, we use simultaneous multimodal broadband targeted energy transfers to multi-degree-of-freedom nonlinear energy sinks to improve the robustness of aeroelastic instability suppression of a rigid wing with structural nonlinearities. A numerical bifurcation analysis of limit cycle oscillations of the wing with the multi-degree-of-freedom nonlinear energy sinks attached shows that controlling the lower parameter value for limit point cycle bifurcation to occur above Hopf bifurcation is crucial to enhancing the robustness of limit cycle oscillation suppression. We demonstrate that multi-degree-of-freedom nonlinear energy sinks can greatly enhance the robustness of limit cycle oscillation suppression, compared with single-degree-of-freedom nonlinear energy sinks (which were studied in our previous papers), with a much smaller total mass. We also investigate the nonlinear modal interactions that occur between the aeroelastic modes and the multi-degree-of-freedom nonlinear energy sinks, in an effort to gain a physical understanding of the mechanisms governing instability suppression. We demonstrate that a properly designed multi-degree-of-freedom nonlinear energy sink provides robustness of aeroelastic instability suppression by efficiently, passively, and rapidly transferring a significant portion of unwanted vibration energy to the furthest mass of the nonlinear energy sink. Consideration of other types of multi-degree-of-freedom nonlinear energy sinks suggests that the robustness enhancement is achieved by the concentrated mass effect of the attached nonlinear energy sinks.

The targeted energy transfer (TET) phenomenon has been observed in the field of acoustics, which provides a new approach to passive sound control in low frequency domain. The TET phenomenon has been investigated firstly inside one tube (1D acoustic system) with a membrane nonlinear energy sink (NES) or a loudspeaker nonlinear absorber, then inside an acoustic cavity (3D acoustic system) with a membrane NES. 3D acoustic cavities have been considered as more general geometry for the acoustic medium in view of applications in the acoustic field and the membrane NES is mounted directly on the wall of the acoustic cavity. The placement of a membrane NES on the wall involves a weak coupling between the membrane NES and a considered acoustic mode, which constitute the two degrees-of-freedom (DOF) system. The beginning of TET phenomenon of the two DOFs system has been analyzed and the desired working zone for the membrane NES has also been defined. The two thresholds of the zone have been determined by an analytical formula and semi-analytically, respectively. The parametric analysis of the membrane NES by using the two DOFs system has been investigated to design the membrane NES. In order to enhance the robustness and the effective TET range in acoustic cavities, a three DOFs system with two membranes and one acoustic mode is studied in this paper. We consider two different membranes and two almost identical membranes to analyze the TET phenomenon, respectively. The desired working zone for the membrane NES and the value of the plateau which are obtained by the two DOFs system are applied to analyze the three DOFs system. We observe that two membranes can enlarge the desired working zone of the NES.

An enhanced rotating nonlinear energy sink (NES) is numerically investigated in this study. The rotating NES in the literature is coupled with the associated linear structure by its nonlinear inertial coupling through a rigid arm that couples the rotating NES mass with the structure. Here, the coupling arm is assumed to be elastic. Consequently, the NES mass rotates about a fixed vertical axis and allowed to oscillate along the coupling arm in a radial direction. According to this modification, the rotating NES dissipates the transferred energy from the associated structure through its angular and radial viscous damping. Therefore, the modified rotating NES by elastic arm is found to absorb and dissipate more energy than the old one for a wide range of initial input energies induced into the associated linear structure. The arm length and the angular damping coefficient of the old rotating NES are optimized first by assuming a rigid coupling arm and later the stiffness and the damping coefficients in the radial direction are optimized accordingly. The obtained numerical results have shown a significant improvement in the rotating NES performance when the NES is allowed to oscillate through the coupling arm by a linear coupling restoring spring rather than locking the NES to a rigid arm.

Vortex-induced vibrations mitigation through a nonlinear energy sink

The NES (nonlinear energy sink) is a new type of nonlinear tuned mass damper that is connected to the shock-absorbing main structure through strong nonlinear stiffness and viscous damping. The vibrational energy in the main structure is transferred to the NES oscillator by means of target energy transfer. A shaking table test of a 1:4 scaled RC (Reinforced Concrete) frame structure model with a new type of NES shock absorber was conducted to study the damping effect of the NES shock absorber, especially for the influence of joint strength and deformation. The NES used in this experiment has a relatively large nonlinear stiffness and a wide vibration absorption frequency band. The variation of reinforcement strains, node failure mode, and structural natural frequency of 1 story and two-layer joints of the model frame structure with NES were studied. The test results showed that NES could effectively reduce the strains of longitudinal reinforcement and stirrup in beams and columns and delay the plastic hinge development at the bottom and the top of the column. The frame model with NES installed has failures at the beam ends and shear failures at the nodes, realizing the seismic mechanism of solid columns and weak beams. Compared with ordinary seismic structures, the NES can effectively reduce the shear stress of concrete at the joints and alleviate the shear failure of joints. The final failure of the NES shock absorbing structure was the yielding of the steel bars at the bottom of the column and the crushing of the concrete at the foot of the column, and the connection between the column foot and the backplane became loose simultaneously. The decreasing rate of the vibration frequency declined due to the NES with varied broadband absorbing capability. It can be seen that the NES shock absorber not only has a good effect on reducing the seismic response of the structure, but more importantly, the damage of the structural nodes is greatly reduced, and therefore, the seismic capacity of the structure improved.

A state-of-the-art review on the dynamic design of nonlinear energy sinks

Numerical simulations were conducted to study flow-induced vibration of a two-dimensional airfoil with two nonlinear energy sinks (NES). The relationship between targeted energy transfer (TET) and vibration suppression is analyzed in detail. The main system has two degrees of freedom – the pitch and heave. The two NES are treated as subsystems, in which the first NES is place at the leading edge and the second NES is placed at the trailing edge. The limit cycle oscillation (LCO), which is to be suppressed by the NES, is studied from the viewpoint of the TET. The resonance capture (RC) in the coupled nonlinear system is also discussed by the means of the energy and spectrum analysis. This is followed by a detailed target energy transfer discussion of the heave and pitch modes and the NES. In addition, the empirical mode decomposition (EMD) is utilized to obtain an intrinsic mode function (IMF) to analyze resonance capture in the system. The results show that the NES can absorb vigorous amount of energy from one of the specified vibration modes. As the RC occurs, the TET between the vibration modes in the coupled system becomes more significant. In particular, the TET between the NES and the wing becomes more efficient. This results in an increase in the critical freestream velocity as the NES suppresses the nonlinear vibration of the main system in a very effective way. As the total energy exceeds the suppression range of the subsystem, the NES loses its effectiveness on vibration suppression effect on the main system. The IMF of the EMD exhibits special super-harmonic resonance and frequency competition characteristics.

This work proposes a clearance-type electromechanical nonlinear energy sink (NES) to increase the electrical energy harvested from non-stationary mechanical waves, such as those encountered during impact and intermittent events. The key idea is to trap energy in the NES such that it can be harvested over a time period longer than that afforded by the passing disturbance itself. This leads to an asymmetrical, piece-wise nonlinear device whose functionality and analysis lie at the intersection of several current research topics, including wave-based energy harvesting, non-reciprocal wave propagation, nonlinear energy sinks (NES’s), and hybrid dynamical systems. The nonlinear energy sink concept explored uses a clearance-type nonlinearity, and resulting impact, to pass the energy of the propagating wave from a primary subdomain to a secondary subdomain where a significant portion of it is subsequently trapped and harvested. Moreover, unlike traditionally-studied single-DOF NESs, both subdomains of the NES (i.e., on either side of the clearance) contain displaceable degrees of freedom, significantly increasing the complexity of analytical solution approaches as compared to systems where one side is constrained by a known (or zero) displacement. Computational and analytical techniques are employed to optimize the energy sink and explore qualitative behavior (to include bifurcations). The analysis includes insight from Poincaré sections and bifurcation diagrams, with and without harvesters. Bifurcation diagrams and trends therein provide insight into the number and state of impact events at the NES as excitation amplitude increases. However, analytic formulations are found which quantify the relationship between the impact amplitude and the energy produced, parameterized by system properties such as the harvester effective resistance, the clearance gap, and the domain mass and stiffness. Importantly, a linear relationship between the input energy amplitude and the number of NES impacts has been observed and captured by an approximate, closed-form Poincaré map. In addition to this linear relationship, a closed-form Poincaré map is derived which maps one NES impact location to the next, greatly simplifying the analysis while providing an important tool for follow-on bifurcation studies. The results may justify further exploration in which complex structures (e.g., plates and/or three-dimensional structures) incorporate one or more of the clearance-type NESs to enhance non-stationary electroacoustic wave energy harvesting.

Vibration control in fluid conveying pipes using NES with nonlinear damping