Increasing Excitation Frequency Research Articles

Boundary Layer Flashback in Premixed Hydrogen–Air Flames With Acoustic Excitation

Lean premixed combustion is prevailing in gas turbines to minimize nitrogen oxide emissions. However, this technology bears the risk of flame flashback and thermoacoustic instabilities. Thermoacoustic instabilities induce velocity oscillations at the burner exit which, in turn, can trigger flame flashback. This article presents an experimental study at ambient conditions on the effect of longitudinal acoustic excitation on flashback in the boundary layer of a channel burner. The acoustic excitation simulates the effect of thermoacoustic instabilities. Flashback limits are determined for different excitation frequencies characterizing intermediate frequency dynamics in typical gas turbine combustors (100–350 Hz). The excitation amplitude is varied from 0% to 36% of the burner bulk flow velocity. For increasing excitation amplitude, the risk of flame flashback increases. This effect is strongest at low frequencies. For increasing excitation frequency, the influence of the velocity oscillations decreases as the flame has less time to follow the changes in bulk flow velocity. Two different flashback regimes can be distinguished based on excitation amplitude. For low excitation amplitudes, flashback conditions are reached if the minimum flow velocity in the excitation cycle falls below the flashback limit of unexcited unconfined flames. For higher excitation amplitudes, where the flame starts to periodically enter the burner duct, flashback is initiated if the maximum flow velocity in the excitation cycle is lower than the flashback limit of confined flames. Consequently, flashback limits of confined flames should also be considered in the design of gas turbine burners as a worst case scenario.

Dynamics of liquid sheet breakup in the presence of acoustic excitation

We present the results of experimental investigations on the effect of acoustic excitation on the breakup of the liquid sheet formed by oblique impingement of two liquid jets for varying Weber number over a wide range of excitation frequencies (100–2000 Hz) and sound pressure levels (50–120 dB). Visualization studies reveal violent sheet flapping, reduction in the sheet breakup length and width, impact wave amplification and rise in droplet density shed from the sheet. Overall, increase in excitation frequency increases the threshold sound pressure level at which the sheet responds. Reduction in the sheet breakup length and width with frequency is observed at some selected frequencies, which rules out the possibility of resonance. For smooth sheet regime, visual observations show that the dominant sheet breakup mechanism shifts from Rayleigh–Plateau (R–P) to Kelvin–Helmholtz (K–H) instability. It is shown using temporal analysis that the reduction in the sheet breakup length may be attributed to periodic sheet collapse and reformation. Drop shedding frequencies in flapping liquid sheet are seen to synchronize with those excitation frequencies which are lower than or nearly equal to the fundamental frequency without excitation. Acoustic excitation reduces the mean droplet size significantly without altering the drop size distribution pattern that follows a universal Gamma distribution.

Quantitative analysis for acoustic characteristics of porous metal materials by improved Kolmogorov’s turbulence theory

This paper investigates the sound absorbing property of porous metal materials quantitatively using turbulence analogy model. Firstly, the improved Kolmogorov’s turbulence theory is obtained by catastrophe theory for the first time, to our knowledge. Secondly, a quantitative turbulence analogy model is proposed though the improved Kolmogorov’s turbulence theory. Finally, this model is adopted to analyze the wave propagation inside the porous metal materials. The quantitative relationship of energy spectrum density is fully obtained, which is also related to the average pore diameter and porosity. With the increase of excitation frequency, the energy spectrum density decreases with certain power law. And the energy increases with the increase of the average pore diameter. Our theoretical results are consistent with the experimental results. Our study can provide a feasible theoretical guidance for controlling the vibration and noise of porous metal materials.

On optimization of energy harvesting from base-excited vibration

This paper re-examines and clarifies the long-believed optimization conditions of electromagnetic and piezoelectric energy harvesting from base-excited vibration. In terms of electromagnetic energy harvesting, it is typically believed that the maximum power is achieved when the excitation frequency and electrical damping equal the natural frequency and mechanical damping of the mechanical system respectively. We will show that this optimization condition is only valid when the acceleration amplitude of base excitation is constant and an approximation for small mechanical damping when the excitation displacement amplitude is constant. To this end, a two-variable optimization analysis, involving the normalized excitation frequency and electrical damping ratio, is performed to derive the exact optimization condition of each case. When the excitation displacement amplitude is constant, we analytically show that, in contrast to the long-believed optimization condition, the optimal excitation frequency and electrical damping are always larger than the natural frequency and mechanical damping ratio respectively. In particular, when the mechanical damping ratio exceeds a critical value, the optimization condition is no longer valid. Instead, the average power generally increases as the excitation frequency and electrical damping ratio increase. Furthermore, the optimization analysis is extended to consider parasitic electrical losses, which also shows different results when compared with existing literature. When the excitation acceleration amplitude is constant, on the other hand, the exact optimization condition is identical to the long-believed one. In terms of piezoelectric energy harvesting, it is commonly believed that the optimal power efficiency is achieved when the excitation and the short or open circuit frequency of the harvester are equal. Via a similar two-variable optimization analysis, we analytically show that the optimal excitation frequency depends on the mechanical damping ratio and does not equal the short or open circuit frequency. Finally, the optimal excitation frequencies and resistive loads are derived in closed-form.

Nonlinear vibration analysis of a rotor supported by magnetic bearings using homotopy perturbation method

In this paper, the effects of nonlinear forces due to the electromagnetic field of bearing and the unbalancing force on nonlinear vibration behavior of a rotor is investigated. The rotor is modeled as a rigid body that is supported by two magnetic bearings with eight-polar structures. The governing dynamics equations of the system that are coupled nonlinear second order ordinary differential equations (ODEs) are derived, and for solving these equations, the homotopy perturbation method (HPM) is used. By applying HPM, the possibility of presenting a harmonic semi-analytical solution, is provided. In fact, with equality the coefficient of auxiliary parameter (p), the system of coupled nonlinear second order and non-homogenous differential equations are obtained so that consists of unbalancing effects. By considering some initial condition for displacement and velocity in the horizontal and vertical directions, free vibration analysis is done and next, the forced vibration analysis under the effect of harmonic forces also is investigated. Likewise, various parameters on the vibration behavior of rotor are studied. Changes in amplitude and response phase per excitation frequency are investigated. Results show that by increasing excitation frequency, the motion amplitude is also increases and by passing the critical speed, it decreases. Also it shows that the magnetic bearing system performance is in stable maintenance of rotor. The parameters affecting on vibration behavior, has been studied and by comparison the results with the other references, which have a good precision up to 2nd order of embedding parameter, it implies the accuracy of this method in current research.

Experimental Investigation of the Time Delay Between a Varying Applied Normal Force and the Resulting Friction Force

Recently, one of the present authors proposed a new model to explain the generation mechanism of brake squeal based on the time delay between a varying applied normal force and the resulting friction force. The present work conducts a series of experimental tests examining the behavior of this time delay using a special test apparatus. The test apparatus suppresses the effect of interference in the time delay owing to the excitation normal force to the greatest extent possible. Several calibration tests of the test apparatus are conducted to ensure the validity of the normal force and friction force measurements. The varying friction force is extracted from the overall friction force signal without phase distortion using a zero-phase filter. The test results demonstrate a time delay between the varying normal force and the resulting friction force under various testing parameters. The time delay is found to increase with increasing excitation frequency. The generation mechanism of the time delay is also discussed.

Research on Simulation for Dynamic Characteristics of Giant Magnetostrictive Actuator

The mathematical model of Giant Magnetostrictive Actuator is established. The simulation of the model for its dynamic performance with Simulink shows the curve of its characteristics under continuous current and frequency. It is shown that under continuous AC excitation amplitude, the greater the excitation frequency is, the smaller the output displacement is, and the greater the output force is; under continuous AC frequency excitation, as the excitation amplitude increases, the output displacement and output force are increased, and under fixed excitation, as the AC excitation frequency increases, the output displacement decreases. The conclusion establishes the theoretical basis to the following experiment on dynamic characteristic of the actuator and the active control of vibration of submarine mechanical equipment.

Wake vortex evolution of square cylinder with a slot synthetic jet positioned at the rear surface

Wake vortex evolution of a square cylinder with a slot synthetic jet issuing from the cylinder’s rear surface has been experimentally investigated using the time-resolved particle image velocimetry technique. The Reynolds number based on the side length of the square cylinder is $Re=836$. The excitation frequency normalized by the natural shedding frequency $f_{e}/f_{0}$ varies from 0 to 6 at the dimensionless stroke length $L_{0}/w=72.6$. The distributions of the time-averaged Reynolds stresses present significant differences as the excitation frequency increases. With control, the mean streamwise velocity deficit of the wake recovers more quickly in comparison with the natural case, and the vertical velocity fluctuation intensity becomes weaker. Moreover, a drag reduction can be achieved for the control cases, especially, for $f_{e}/f_{0}=4$ and $f_{e}/f_{0}=6$, a thrust instead of drag reduction can be obtained. The profiles of the mean streamwise velocity tend to have jet-like distributions. The wake vortex dynamics and its evolution with the excitation frequency are revealed. (i) For the low excitation frequency cases ($f_{e}/f_{0}=0.5$, 1, 2), no significant changes in the dominant frequency and the spanwise vortex structures are observed in comparison with the natural case. (ii) For the moderate excitation frequency case ($f_{e}/f_{0}=3$), the wake vortex shedding frequency is locked on half of the control frequency. In this case, the shear layer is divided into two parts by the synthetic jet vortex, and the wake vortices with smaller scales still shed asymmetrically and appear closer to the square cylinder. (iii) For the high excitation frequency case ($f_{e}/f_{0}=6$), the flow is governed by the synthetic jet. As a result of strong perturbations of the synthetic jet, the wake vortex shedding becomes symmetric with the shedding frequency consistent with the control frequency. And the separation is suppressed effectively. The different control effects of the slot synthetic jet on a square cylinder and a circular cylinder are also compared in detail. Generally speaking, the circular cylinder is easier to be controlled due to its non-fixed separation points.

The performance analysis of a new type DEAP vibration isolator

Dielectric electro-active polymer (DEAP) is a new kind of smart materials and has many advantages such as large deformation, fast response and so on. These features make dielectric elastomeric is a suitable material for actuators. In the article, a new type of DEAP vibration isolator is proposed, w hich utilizes the fiber stiffening DEAP membranes. The dynamic model of the DEAP isolator is developed by employing a nonequilibrium thermodynamic model. A set of harmonic vibration tests are conducted to identify the model parameters of DEAP isolator. The results show that the area of hysteresis loop increases with the increase of displacement amplitude, and the dynamic stiffness of DEAP isolator increases with the increase of excitation frequency. An additional stiffness component is introduced thereafter in the model in order to correct the stiffness coefficients based on the measured data. Based on the identified isolator model, a simulated study on semi-active vibration isolation is also carried out. The simulated results show that the effective frequency range of vibration isolation can be expanded in some extent under DC input voltage. It indicates the feasibility of semi-active vibration isolation with the present DEAP isolator.

A dipole model for estimating frequency versus elevation-angle trajectory of the first spectral notch of head-related transfer functions in the median plane

The first (lowest) spectral notch (N1) of head-related transfer functions is known as a cue for sound localization in the median plane. This may be due to the fact that N1 frequency gradually increases as the sound source approaches the direction above the head. The mechanism of this phenomenon, however, is still unclear. To clarify the mechanism, using finite-difference time-domain simulation, the normalized pressure amplitude patterns were visualized around the head for 12 subjects when the analysis field was excited at various frequencies from a point just outside the blocked meatus. As a result, strong radiations with different phases occurred in the upper and lower directions, while in the intermediate narrow zone, the pressure amplitude became minimum. This zone corresponded to N1 and bent upward with increasing excitation frequency. These facts implied that the two radiated sound waves canceled each other in the zone, where the path difference amounted to a phase difference of half a wavelength. Thus, the shape of the intermediate zone could be modeled by a hyperboloid whose foci were two hypothetical points on the pinna. The model could roughly estimate, for each individual, the frequency versus elevation-angle trajectory of N1 in the median plane.

Analytical assessment of elevated tank natural period considering soil effects

The main purpose of current study is to find the soil effects on natural period of elevated tank. The coupled analytical method is used to assess in this study. The current study presented models which are capable to consider the soil dynamic stiffness changes and fluid- structure interaction effects on natural period of elevated tanks. The basic of mentioned models is extracted from elastic beam and lumped mass theory. The finite element is used to verify the results. It is observed that, external excitation can change the natural period of elevated tanks. Considering the increase of excitation frequency, the natural period will be decreased. The concluded values of natural period in case of soft and very soft soil are more affected from excitation frequency values. The high range of excitation frequency may reduce the natural period values. In addition it is observed that the excitation frequency has no significant effect on convective period compare with impulsive period.

Effects of Discrete Damping on the Dynamic Behaviour of Rotating Shaft through Extended Lagrangian Formulation

Abstract The main focus of the paper is touted as effects of discrete damping on the dynamic analysis of rotating shaft. The whole analysis is being carried out through extended Lagrangian formulation for a discrete – continuous system. The variation formulation for this system is possible, considering the continuous system as one-dimensional. The generalized formulation for one dimensional continuous rotary shaft with discrete external damper has been obtained through principle of variation. Using this extended formulation, the invariance of umbra-Lagrangian density through extended Noether’s theorem is achieved. Rayleigh beam model is used to model the shaft. Amplitude equation of rotor is obtained theoretically and validated through simulation results. The simulation results reveal the important phenomena of limiting dynamics of the rotor shaft, which is due to an imbalance of material damping and stiffness of the rotor shaft. The regenerative energy in the rotor shaft, induced due to elasticity/stiffness of the rotor shaft, is dissipated partially through the in-span discrete damper and also through the dissipative coupling between drive and the rotor shaft. In such cases, the shaft speed will not increase with increase in excitation frequency of the rotor but the slip between the drive and the shaft increases due to loading of drive.

Force transmissibility and vibration power flow behaviour of inerter-based vibration isolators

This paper investigates the dynamics and performance of inerter-based vibration isolators. Force / displacement transmissibility and vibration power flow are obtained to evaluate the isolation performance. Both force and motion excitations are considered. It is demonstrated that the use of inerters can enhance vibration isolation performance by enlarging the frequency band of effective vibration isolation. It is found that adding inerters can introduce anti-resonances in the frequency-response curves and in the curves of the force and displacement transmissibility such that vibration transmission can be suppressed at interested excitation frequencies. It is found that the introduction of inerters enhances inertial coupling and thus have a large influence on the dynamic behaviour at high frequencies. It is shown that force and displacement transmissibility increases with the excitation frequency and tends to an asymptotic value as the excitation frequency increases. In the high-frequency range, it was shown that adding inerters can result in a lower level of input power. These findings provide a better understanding of the effects of introducing inerters to vibration isolation and demonstrate the performance benefits of inerter-based vibration isolators.

Bifurcation and chaos analysis for multi-freedom gear-bearing system with time-varying stiffness

This study performs a systematic dynamic analysis of a gear-bearing system with time varying stiffness, gear backlash and surface friction. At first the period expansion method is proposed to build a six-degree-of freedom nonlinear dynamic model of a spur gear pair. Then the dynamic orbits of the system are observed using the bifurcation diagrams with the mesh stiffness and the rotational speed ratio as control parameters. And the onset of chaotic motion is identified from the phase diagrams, FFT spectra, Poincaré maps and the largest Lyapunov exponents of the gear-bearing system. The numerical results reveal that the system enters into chaotic motion under several frequency jumps with the increase of excitation frequency. When the support stiffness is raised, the number of frequency jumps increases, and the system exhibits a diverse range of periodic, sub-harmonic, and chaotic behaviors. In this study the results provide a useful source of reference for engineers and technicians in designing and controlling such systems.

A quantitative investigation on vibration durability of viscoelastic relaxation in bolted composite joints

Time-dependent behavior and factors affecting preload relaxation in a carbon/epoxy composite bolted joint under resonance were studied. The effect of viscoelasticity of composite material on bolt relaxation was studied quantitatively through modal analysis from the perspective of energy dissipation and stiffness degradation. Damping ratio and resonance frequency were utilized to characterize the effects of preload relaxation on structural dynamic response. The loss of preload was found to decrease with increasing initial preloads over a 10 h vibration fatigue. However, an increase in preload loss occurred as exciting frequency increases. Vibration fatigue damage was found to result in decaying stiffness and amplitude responses of the bolted joints, along with an increase in damping ratio. As a proof-of-concept study, a beam-like specimens with and without bolted joints were comparatively excited to ascertain their respective dynamic responses; results revealed that relaxation in bolted joints could be attributed to the conjunct mechanisms between viscoelastic behavior of polymer matrix composites and interface friction for different contact surfaces, where such relaxation behavior was mainly due to viscoelasticity of the joint materials.

Experimental study on frequency and amplitude dependent behavior of dynamic parameters of steel-spring vibration isolator used in floating slab track

Dynamic stiffness and damping of vibration isolator are important parameters influencing the dynamic characteristics of the floating slab track. Based on the laboratory experiment of the steel spring vibration isolator, the paper analyzed frequency and amplitude dependent behavior of steel-spring vibration isolator. The results show that broadly the dynamic stiffness of the vibration isolator increases with the increase of excitation frequency, however, the dynamic stiffness decreases slightly near the resonant frequency; an increase of excitation frequency results in a decrease of the equivalent viscous damping coefficient with a small change near the resonant frequency; the energy dissipation ratio increases with the increase of excitation frequency; the dynamic stiffness, equivalent viscous damping coefficient and the energy dissipation ratio all have negligible variations as the excitation amplitude increases. The research results can provide references for the design of vibration isolators.

On the stability of colonnade structural systems under static and dynamic loading conditions

The structural behavior of colonnade structural systems subjected to static and dynamic loading is investigated to identify the main factors affecting the stability and to improve our understanding of their behaviour. In particular, the discrete element method of analysis is utilised to study the static and dynamic behaviour of a typical section of the two storey colonnade of the Forum in Pompeii. Static analysis indicated that the failure of colonnade structures occur at higher friction angles as the weight above the structure decreases and so a sudden collapse can occur when parts of the monument are disassembled. For the dynamic analysis, the mechanical behavior of the colonnade was investigated for both harmonic and real seismic excitations. For excitations with relatively low dominant frequencies, the primary response is rocking; as the excitation frequency increases, the response becomes more complicated demonstrating both sliding and rocking movements. It was also shown that the construction methods used in ancient times, such as multi-block segmented trabeations and solid block beam, have quite significant impact on the mechanical response of the structures under static and dynamic loading.

Steady-state vibration of a viscoelastic cylinder cover subjected to moving loads

Abstract The dynamic steady-state response of a viscoelastic cylinder cover subjected to circumferentially moving constant point and distributed loads is studied using a 1D Pasternak-type foundation model. The cover material is modeled according to the generalized Maxwell model as an incompressible frequency-dependent viscoelastic material spanning a wide relaxation spectrum. The vibration response of the cover for a moving twin point load is obtained using a modal expansion approach. On the basis of the solution, additional moving load cases are derived. In the case of a single moving point load, representing a load resultant due to rolling contact, numerical calculations show that regardless of the viscoelastic damping in the model, the critical load speed for the system can be well estimated by a resonance condition. In the vicinity of the critical speed, an incipient traveling wave arises behind the moving load. The viscoelastic cover stiffens for increasing excitation frequencies, thus, the cover response divides into two separate mode branches, of which the low-mode branch is dominant. A method to suppress the traveling wave vibrations in the cover at supercritical speeds using a moving twin point load, adjusted according to a dominant resonating mode, is presented. Using a distributed moving load, it is shown that depending on the wavelength, a traveling wave generated at the leading edge of the load may be reinforced at the trailing edge, the lift-off point, of the load. The developed model offers a fast and reliable way for practitioners to estimate the critical speeds of rolling contact machines with viscoelastic covers.

Unbalance Response of HSK Hydraulic Chuck Tooling System for High-Speed Machining

High-speed chuck is an important component of high speed machining tooling system. Its properties directly affect the performance and processing quality of advanced numerical control machine. Using the finite element method, the research analyzed influence of inertial centrifugal force caused by unbalance on the dynamic characteristics of HSK hydraulic clamping chuck tooling system and systematically revealed variation of shank, chuck and blade point displacement. It is found that blade point, as well as chuck and shank displacement response amplitude of tooling system rises as a whole with the increase of excitation frequency; the dynamic displacement response increment shows linear growth with unbalance amount, which provides a theoretical basis for optimum design and balancing control of HSK hydraulic chunk tooling system.

Experimental study of mixing enhancement of viscous liquids in confined impinging jets reactor at low jet Reynolds numbers

Mixing performance of water and glycerol–water solution in a confined impinging jets reactor (CIJR) with and without excitation was experimentally studied using planar laser induced fluorescence (PLIF) at 100≤Re≤500. The effects of the jet Reynolds number (Re), fluid viscosity and excitation on the oscillation behaviors and mixing performance in CIJR have been qualitatively and quantitatively investigated. Results show that for Re≤100 the flow is segregated with poor mixing; for Re≥150 the flow evolves to an oscillation regime with strong mixing. Compared with the Reynolds number, the fluid viscosity has an insignificant effect on the mixing in CIJR. The mixing in CIJR at low jet Reynolds number can be effectively enhanced by excitation with low frequency, as a periodic oscillation is induced by the pulsed inflow, which further causes the continuous folding and stretching of the impingement plane. The enhancement of mixing is strengthened with the increase of excitation amplitude and is weakened with the increase of excitation frequency.