Small-amplitude Vibrations Research Articles

Experiments on Flexible Filaments in Air Flow for Aeroelasticity and Fluid-Structure Interaction Models Validation

Several problems in science and engineering are characterized by the interaction between fluid flows and deformable structures. Due to their complex and multidisciplinary nature, these problems cannot normally be solved analytically and experiments are frequently of limited scope, so that numerical simulations represent the main analysis tool. Key to the advancement of numerical methods is the availability of experimental test cases for validation. This paper presents results of an experiment specifically designed for the validation of numerical methods for aeroelasticity and fluid-structure interaction problems. Flexible filaments of rectangular cross-section and various lengths were exposed to air flow of moderate Reynolds number, corresponding to laminar and mildly turbulent flow conditions. Experiments were conducted in a wind tunnel, and the flexible filaments dynamics was recorded via fast video imaging. The structural response of the filaments included static reconfiguration, small-amplitude vibration, large-amplitude limit-cycle periodic oscillation, and large-amplitude non-periodic motion. The present experimental setup was designed to incorporate a rich fluid-structure interaction physics within a relatively simple configuration without mimicking any specific structure, so that the results presented herein can be valuable for models validation in aeroelasticity and also fluid-structure interaction applications.

Nonlinear dynamic behavior of a flexible asymmetric aero-engine rotor system in maneuvering flight

Aero-engine rotor systems installed in aircraft are considered to have a base motion. In this paper, a flexible asymmetric rotor system is modeled considering the nonlinear supports of ball bearings and Squeeze Film Dampers (SFDs), and the dynamic characteristics of the rotor system under maneuvering flight are systematically studied. Effects of the translational accelerative motions, the angular motions and the pitching flight with combined translational and angular motions on nonlinear dynamic behavior of the rotor system are investigated. The results show that, due to the nonlinear coupled effects among the rotor, ball bearings and SFDs, within the first bending resonance region, responses of the rotor show obvious nonlinear characteristics such as bistable phenomenon, amplitude jumping phenomenon and non-synchronous vibration. Translational acceleration motion of the aircraft leads to axis offset of the rotor system and thus results in the reduction and the final disappearance of the bistable rotating speed region. The pitching angular motion mainly affects rotational vibration of the rotor system, and thus further induces their transverse vibrations. For the pitching flight with combined translational and angular motions, a critical flight parameter is found to correspond to the conversion of two steady responses of the rotor system, in which one response displays small amplitude and synchronous vibration, and the other shows large amplitude and non-synchronous vibration.

Nonlinear vibrations of a 3 × 3 reduced scale PWR fuel assembly supported by spacer grids

The core of Pressurized Water Reactors (PWR) is composed by nuclear fuel assemblies, bundles of slender fuel rods containing uranium pellets, kept in position by spacer grids equipped with elastic elements for retention, and exposed to an axial flow of coolant. Fuel assemblies are subjected to fluid-induced vibrations causing fretting at the interface with spacer grids; events such as earthquakes may also constitute an external excitation resulting in large-amplitude vibrations of the fuel rods. The relationship between the excitation amplitude and the damping during large-amplitude forced vibrations of nuclear fuel assemblies in the presence of flowing fluid is not fully understood. The present experimental study investigated the vibrations of a 3 × 3 tube assembly composed by eight regularly spaced fuel rods installed around a guide tube and supported by spacer grids; tests were performed in still and flowing water. In addition to experimental modal analysis under small random excitation, stepped-sine experiments at different levels of harmonic excitation that caused large-amplitude vibrations were performed. The equivalent viscous damping ratios of the fundamental model at different excitation levels were extracted by fitting the results with a single degree-of-freedom model. The vibrations of the fuel assembly were strongly influenced by the vibrational behavior of the single rods, which constitute coupled oscillators. An increase of damping with the excitation amplitude was observed both in still and in flowing water and acted in the direction of structural safety. The water flow did not cause instabilities in the operational range; instead, the increment of flow speed increased the damping ratios in the linear (small-amplitude vibrations) and nonlinear (large-amplitude vibrations) regime.

Vibration control combining nonlinear isolation and nonlinear absorption

Quasi-zero stiffness system has been widely used to isolate structural vibrations. However, its small dynamic stiffness may result in drastic low-frequency vibration. This is a curse of employing quasi-zero stiffness systems in engineering. In this paper, a nonlinear energy sink (NES) is used to overcome this difficulty. In order to reduce the additional weight of the NES, the mass of the NES is replaced by an inerter. By superposing the quasi-zero stiffness system and the inertial NES together, a combined vibration control technique is proposed. The equations of the motion of the primary structure and the combined control system are established. The steady-state response of the system is solved by the harmonic balance method and verified numerically. The suppression performance is evaluated based on the resonance suppression efficiency and the effective vibration isolation bandwidth. In addition, the parameters of the inertial NES are optimized. The results show that the combined control system has a better vibration control effect than the quasi-zero stiffness isolator. Specifically, the combined control system provides a smaller resonance amplitude and a wider vibration isolation band. In summary, the combined control scheme has both effects of the nonlinear isolation and the nonlinear absorption. Therefore, this paper proposes a vibration control technique that can achieve a wide band of vibration isolation and small vibration amplitude with a very little additional mass.

Investigation on the Tool Wear Suppression Mechanism in Non-Resonant Vibration-Assisted Micro Milling.

Excessive tool wear during hard and brittle material processing severely influences cutting performance. As one of the advanced machining technologies, vibration-assisted micro milling adds high-frequency small amplitude vibration on a micro milling tool or workpiece to improve cutting performance, especially for hard and brittle materials. In this paper, the tool wear suppression mechanism in non-resonant vibration-assisted micro milling is studied by using both finite element simulation and experiment methods. A finite element model of vibration-assisted micro milling using ABAQUS is developed based on the Johnson cook material and damage models. The tool-workpiece separation conditions are studied by considering the tool tip trajectories. The machining experiments are carried out on Ti-6Al-4V with a coated micro milling tool (fine-grain tungsten carbide substrate with ZrO2-BaCrO4 (ZB) coating) under different vibration frequencies (high, medium, and low) and cutting states (tool-workpiece separation or non-separation). The results show that tool wear can be reduced effectively in vibration-assisted micro milling due to different wear suppression mechanisms. The relationship between tool wear and cutting performance is studied, and the results indicate that besides tool wear reduction, better surface finish, lower burrs, and smaller chips can also be obtained as vibration assistance is added.

A Combination of a Vibrational Electromagnetic Energy Harvester and a Giant Magnetoimpedance (GMI) Sensor.

An energy harvesting device combined with a giant magnetoimpedance (GMI) sensor is presented to analyze low frequency vibrating systems. An electromagnetic harvester based on magnetic levitation is proposed for the electric power generation. The device is composed of two fixed permanent magnets at both ends of a cylindrical frame, a levitating magnet acting as inertial mass and a pick-up coil to collect the induced electromotive force. At the resonance frequency (10 Hz) a maximum electrical power of 1.4 mW at 0.5 g is generated. Moreover, an amorphous wire was employed as sensor nucleus for the design of a linear accelerometer prototype. The sensor is based on the GMI effect where the impedance changes occur as a consequence of the variations of the effective magnetic field due to an oscillating magnetic element. As a result of the magnet’s periodic motion, an amplitude modulated signal (AM) was obtained, its amplitude being proportional to mechanical vibration amplitude (or acceleration). The sensor’s response was examined for a simple ferrite magnet under vibration and compared with that obtained for the vibrational energy harvester. As a result of the small amplitudes of vibration, a linear sensor response was obtained that could be employed in the design of low cost and simple accelerometers.

Sound waves move matter

A recent Letter has reported that sound waves can carry gravitational mass. I analyze this effect in a Hooke's law solid, considering a wave packet moving in the $z$ direction with an amplitude that is independent of $x$ and $y$. The analysis shows that, at second order in an expansion around small amplitude vibrations, there is a small net motion of material, and thus mass, in the direction opposite to the wave packet propagation. This is a straightforward consequence of Newton's laws.

Hybrid Passive/Active Vibration Control of a Loosely Connected Spacecraft System

In this paper, a hybrid passive/active vibration (HPAV) controller of a loosely connected spacecraft consisting of a servicing satellite, a target and an X-shape structure isolator is first proposed to suppress vibrations of the system when subjected to the impulsive external excitations during the on-orbit missions. The passive dynamic response of the combined system can be adjusted appropriately to achieve the desired vibration isolation performance by tuning the structural parameters of the bio-inspired X-shape structure. Moreover, the adaptive control design through dynamic scaling technique is selected as the active component to maintain high vibration isolation performance in the presence of parameter uncertainties such as mass of the satellite platform, the damping and rotation friction coefficients of the X-shape structure. Compared with the pure passive system and the traditional spring-mass-damper (SMD) isolator, the HPAV strategy witnesses lower transmissibility, smaller vibration amplitude and higher convergence rate when subjected to the post-capture impact. Numerical simulations demonstrate the feasibility and validity of the proposed hybrid control scheme in suppressing vibrations of the free-floating spacecraft.

Viscoelasticity of Rubber Springs Affects Vibration Characteristics of a Flip-Flow Screen With the High G Value

With the high G value of vibration, outstanding sieving behaviors of a flip-flow screen are more likely to appear, but structural damages are aggravated under the high amplitude vibration. Considering rubber springs role on the vibration energy dissipation, viscoelasticity of rubber springs (i.e., shear springs and vibration isolation springs), is noticed to deal with the above contradiction. However, when rubber springs experience large amplitude vibration, viscoelastic responses influence more on the amount of damping than in the linear (i.e., small amplitude) vibration regime, as the frequency dependence of rubber springs is noteworthy. For this purpose, the Generalized Maxwell model is used to depict the frequency dependence of rubber springs and the practical damping is converted to a series damping parameters of the system, numerical models of the flip-flow screen under startup and shutdown modes and steady working conditions are proposed and verified firstly. Secondly, in order to explore kinetics responses of the elastic screen panel under different rubber springs damping coefficients, nonlinear finite element model of which is established. Finally, effects of rubber springs nonlinear damping on screen frames vibrations and screen panels nonlinear responses are studied. Results indicate that hysteretic damping of rubber springs can effectively solve the conflict between vibration strength and structural reliability of the flip-flow screen, since the low sensitivities of maximum stresses and the high sensitivities of accelerations to rubber springs damping are found.

The origin of heavy element doping to relieve the lattice thermal vibration of layered materials for high energy density Li ion cathodes

We report an effective strategy to inhibit the phase transition of LiCoO2 from hexagonal layered to cubic spinel during delithiation. The small thermal vibration amplitude of the Sn dopant helps pin the lattice vibration, stabilizing CoO6 octahedra during charge/discharge.

Anti-Symmetric Mode Vibration of Electrostatically Actuated Clamped-Clamped Microbeams for Mass Sensing.

This paper details study of the anti-symmetric response to the symmetrical electrostatic excitation of a Micro-electro-mechanical-systems (MEMS) resonant mass sensor. Under higher order mode excitation, two nonlinear coupled flexural modes to describe MEMS mass sensors are obtained by using Hamilton’s principle and Galerkin method. Static analysis is introduced to investigate the effect of added mass on the natural frequency of the resonant sensor. Then, the perturbation method is applied to determine the response and stability of the system for small amplitude vibration. Through bifurcation analysis, the physical conditions of the anti-symmetric mode vibration are obtained. The corresponding stability analysis is carried out. Results show that the added mass can change the bifurcation behaviors of the anti-symmetric mode and affect the voltage and frequency of the bifurcation jump point. Typically, we propose a mass parameter identification method based on the dynamic jump motion of the anti-symmetric mode. Numerical studies are introduced to verify the validity of mass detection method. Finally, the influence of physical parameters on the sensitivity of mass sensor is analyzed. It is found that the DC voltage and mass adsorption position are critical to the sensitivity of the sensor. The results of this paper can be potentially useful in nonlinear mass sensors.

A study on the crack detection in beams using linear and nonlinear normal modes

Linear and nonlinear normal mode motions may provide promising information about the condition of mechanical structures under small and large amplitude vibrations, respectively. In this view, this study investigates the nonlinear dynamics of cracked beams through use of the nonlinear mode motion and extends the crack identification methods that utilize the linear characteristics to nonlinear vibrating structures. At first, the nonlinear normal modes of the intact and cracked beams are calculated by a continuation algorithm. A finite element model of a geometrically nonlinear prismatic beam was created based on crack stress intensity. Subsequently, a method based on normal mode motion and minimization of strain energy, which is valid for linear and nonlinear vibrating beams, was developed as an optimization problem. To this end, hybrid optimization was also used due to its capability in finding global minimum along with its computational efficiency. It was shown that the proposed crack detection technique is applicable to beams vibrating in linear and/or nonlinear regimes and well capable of detecting both crack location and severity.

Bifurcation behavior for mass detection in nonlinear electrostatically coupled resonators

The nonlinear coupled vibrations widely exist in coupled resonant structures, which can lead to complex dynamic bifurcation behavior and expand the research scope of fundamental physics. A new micro-mass detection method is proposed by using bifurcation jumping phenomenon in nonlinear electrostatically coupled resonators in this article. Considering the fundamental frequency excitation, the one-to-one internal resonance equations to describe electrostatically coupled resonant sensor are obtained by using Hamilton’s principle and Galerkin method. Then, the perturbation analysis method is introduced to study the response and stability of the system for small amplitude vibration. Through bifurcation analysis, it is found that the isolated response branches appear in nonlinear electrostatically coupled resonators and present the physical conditions of this phenomenon. Typically, we demonstrate the exploitation of the bifurcation jump phenomena of two electrostatically coupled microbeam resonators to realize the mass quantitative detection and threshold detection, which overcomes the detection inaccuracy caused by frequency drift in the nonlinear vibration. Finally, the numerical experiments verify the validity of the method. The results of this paper can be potentially useful in micro-mass detection.

Analysis and synthesis of creation of vibration machines with an estimation of their efficiency and reliability

The analysis of processes occurring in the medium under the influence of vibrational forces is considered. The obtained results are synthesized for the development of a new class of vibration machines that provide criteria for efficiency and reliability. The main criterion for evaluating the effectiveness is adopted function of the amplitude and frequency of vibrations, which determines the speed or acceleration of the compaction process. At the same time, the logic of the stage-by-stage examination of the compaction process is proved. The first of them – the process of reconnecting the components of the mixture – intensively proceeds only in the absence of any significant external loads. This process is realized by providing a machine with a low speed, that is, large amplitude and a low frequency of vibrations. The second is the process of approaching the particles of a mixture with a denser, more compact conclusion of the components of this mixture with each other. It proceeds in the presence of significant dynamic loads, the increase of which to a certain limit gives a positive effect. At this stage, small vibration amplitudes and a high frequency are realized. One of the most problematic places in solving this approach is the lack of not only generally accepted methods for assessing these properties, but even a single view of its nature. In a newly vibration machine, these processes are achieved through the targeted use of shock and vibration. Structurally, this is ensured by the use of vibration limiters. The object of research is vibration and vibration shock processes in machines for compaction of building mixtures in road and construction industries. Particulars of the corresponding selection of the rigidity of the vibration limiters are determined, the rational choice of the ratio of the impact time and the vibration period is made. Thanks to this, new phenomena are discovered during the implementation of staged modes of operation with the installation of several stable modes. The reliability analysis of vibration machines is carried out by methods of qualitative and quantitative analyzes. The simplicity of the machine design ensures its reliability. The mode of compaction of the concrete mix is reduced by half in comparison with the existing vibration parameters.

An ultrafast 2-D non-resonant cutting tool for texturing micro-structured surfaces

Surface texturing using two-dimensional non-resonant vibration cutting tools (2-D NRVCT) has emerged as a promising method to fabricate micro-structured surfaces. The non-resonant vibration tool is able to work in a continuous frequency range with precise control of the tool trajectories compared with their resonant counterparts. The existing designs, however, usually suffer from either small vibration amplitudes or a low bandwidth due to a set of contradictory design requirements. This study presents a tool design that features a high bandwidth of up to 6 kHz without extra cooling, a working space of 9.3 μm × 16 μm, and a small cross-axis coupling within 5%. In addition, this study attempts to generalize the design requirements for 2-D non-resonant vibration cutting tools in five key functional specifications, including the stroke, output stiffness, resonant frequency, drive current, and coupling coefficient. Analytical modeling of the working performance on structural stiffness and output strokes using the compliance matrix method is presented and verified by finite element analysis. Dimensions of the proposed design have been optimized to achieve a balance between the amplification ratio and the bandwidth. The tool performance is then experimentally evaluated along with surface texturing results using the elliptical, quadrate and modulated elliptical tool trajectories.

One-way coupled simulation of FIV in a 7-pin wire-wrapped fuel pin bundle

A common fuel geometry found in sodium cooled reactor designs is the hexagonal lattice of wire-wrapped fuel pins. The wire-wrappers, which replace the more common spacer grids, act as a spacer between the fuel pins, while simultaneously increasing the fluid mixing between subchannels. The induced transverse flow, while good for mixing, increases the force load experienced by the fuel pins, increasing the possibility of problematic flow induced vibrations. The primary source of vibrations is turbulent buffeting, so very small in amplitude, but capable of rupturing the fuel cladding by fretting. The vast majority of research on fretting has been for bare rods with spacer grids. There are several significant ways that wire-wrapped fuel pins differ from bare rods that may have significant impact on the vibrations present. The increased transverse flow and asymmetrical flow pattern may result in larger and imbalanced force loads on the pins. The helical bracing of each pin may result in unique vibration patterns, and gaps may form between pins affecting how they are braced. Simulation allows for the observation of the forces present, how the flow field affects these forces, and how the structure responds and can be repeated for multiple cases for relatively low cost. In the present study, simulation of the flow induced vibrations for a 7-pin wire-wrapped fuel pin bundle is carried out by coupling Nek5000, a spectral element LES/DNS solver with DIABLO, a finite element CSM solver. The small amplitude vibrations allow for the assumption that the structure motion has negligible effect on the fluid flow, permitting the much less computationally expensive one-direction coupling. In order to gather significant force history data for the 2.63 helical pitch structure, a scheme was developed to artificially create force history from the power spectrum density of the one-pitch CFD simulation forces. The vibrations could then be simulated in the structure multiple times varying the contact and gaps between various pins. This allows for the search of worst-case scenarios and informs about the types of fretting that might be present. The simulation geometry is based on an experiment for comparison. However, the viscosity of the simulation was increased by a factor of four to make the simulation computationally feasible. While validation is not possible, comparisons are still valuable.

Vibration control of a tunnel boring machine using adaptive magnetorheological damper

With a large number of tunnel boring machines (TBM) being used in various tunnel constructions, the vibration problem under complex geological conditions have become increasingly prominent. In order to solve the problem, this article investigates the application of an adaptive magnetorheological (MR) damper on the vibration reduction of a TBM. The MR damper could reduce the horizontal vibration of the TBM system and adjust its dragging force on the propulsive system under different geological conditions. The MR damper can also provide large enough damping force even under a small amplitude vibration, which is required by TBM. In this paper, an MR damper was designed, prototyped and its properties were tested by an MTS system, including its current-dependency, amplitude-dependency and frequency-dependency features. A scaled TBM system incorporated with the MR damper was built to evaluate the vibration reduction effectiveness of the MR damper on the TBM system. The experimental test results demonstrate that the displacement and the acceleration amplitudes of the TMB vibration could be reduced by 52.14% and 53.31%, respectively.

Development of Langevin Piezoelectric Transducer-based Two Dimensional Ultrasonic Vibration Assisted Machining (2D UVAM) on 5-axis Micro-milling Machine

The purpose of this study is to design and develop a Two-Dimensional Ultrasonic Vibration Assisted Micro-milling (2D UVAMM) system. Two-dimensional ultrasonic vibrations produced by 2D UVAMM are used to vibrate the workpiece in the micro-milling process. The system is developed using the principle of two Langevin piezoelectric transducers which have the ability to produce ultrasonic vibrations with small vibration amplitude. Process of 2D UVAMM design optimization was done by modal simulation using Finite Element Analysis method. Both Langevin piezoelectric transducers are designed to have symmetrical and asymmetrical vibration modes with the same natural frequency, so that elliptical pattern vibrations can be generated on the workpiece. The 2D UVAMM system operates at a natural frequency of 24 kHz and has an estimated total displacement on the normal and tangential axes respectively 0.766 μm and 0.382 μm. Two power sources with frequency of 24 kHz, phase difference of 90 degrees, and peak-peak voltage of 212 volt were supplied by an ultrasonic generator to excite both of the Langevin piezoelectric transducers. To confirm the developed 2D UVAMM system, experiments were conducted to compare the surface roughness of Aluminum 6061-T6 through micro-milling with conventional method and with additional of the 2D UVAMM system.

Three-dimensional vibrations of multilayered hollow spheres submerged in a complex fluid

Fluid–structure interaction is fundamental to the characteristics of the induced flows due to the motion of structures in fluids and also is crucial to the performance of submerged structures. This paper presents a three-dimensional analytical study of the intrinsic free vibration of an elastic multilayered hollow sphere interacting with an exterior non-Newtonian fluid medium. The fluid is assumed to be characterized by a compressible linear viscoelastic model accounting for both the shear and compressional relaxation processes. For small-amplitude vibrations, the equations governing the viscoelastic fluid can be linearized, which are then solved by introducing appropriate potential functions. The solid is assumed to exhibit a particular material anisotropy, i.e. spherical isotropy, which includes material isotropy as a special case. The equations governing the anisotropic solid are solved in spherical coordinates using the state-space formalism, which finally establishes two separate transfer relations correlating the state vectors at the innermost surface with those at the outermost surface of the multilayered hollow sphere. By imposing the continuity conditions at the fluid–solid interface, two separate analytical characteristic equations are derived, which characterize two independent classes of vibration. Numerical examples are finally conducted to validate the theoretical derivation as well as to investigate the effects of various factors, including fluid viscosity and compressibility, fluid viscoelasticity, solid anisotropy and surface effect, as well as solid intrinsic damping, on the vibration characteristics of the submerged hollow sphere. Particularly, our theoretically predicted vibration frequencies and quality factors of gold nanospheres with intrinsic damping immersed in water agree exceptionally well with the available experimentally measured results. The reported analytical solution is truly and fully three-dimensional, covering from the purely radial breathing mode to the torsional mode to any general spheroidal mode as well as being applicable to various simpler situations, and hence can be a broad-spectrum benchmark in the study of fluid–structure interaction.

Modeling of High-Tc Superconducting Bulk using Different Jc–T Relationships over Dynamic Permanent Magnet Guideway

The linear temperature dependence of critical current density Jc∝((Tc-T)/(Tc-T0)) and the nonlinear functions of Jc∝(1-(T/Tc)2)α with the exponent α equal to 1, 3/2, and 2 are used to calculate the dynamic levitation force, the temperature distribution, and the current density distribution of the high-temperature superconducting (HTS) YBaCuO bulk over a permanent magnetic guideway (PMG). The calculations were based on the H-formulation and E–J power law. The model of the HTS bulk and the PMG has been built as a geometric entity by finite element software. To simulate the magnetic field fluctuation caused by the PMG arrangement irregularity, a small amplitude vibration in the vertical direction is applied to the PMG during the calculations. Both the low vibration frequency of 2 Hz and the high vibration frequency of 60 Hz are analyzed as the representative converted linear speeds of 34 km/h and 1018 km/h for magnetic levitation (Maglev) application. We compared the electromagnetic-thermo-force modeling with the experiments and the previous model without considering the thermal effect. The levitation force computed by the Jc–T relationship, in which Jc is proportional to (1-(T/Tc)2)2, is found to be in best agreement with the experimental data under quasi-static conditions. This work can provide a reference for the HTS electromagnetic-thermal-force coupling reproduction method of HTS Maglev at high speed.