A New Testing Machine for the Dynamic Characterization of High Strength Low Damping Fiber Materials

This work describes a novel method for measuring the damping, the elastic modulus and the non-linear behavior of high strength low damping fiber materials such as para-aramids, silicon carbide (SiC) and carbon. The method is based on resonant response characterization of a spring-mass system excited by a sine-wave forcing term which is applied as a vertical force to the suspended mass. The damping is obtained from the measured resonance quality factor Q, the elasticity modulus is calculated from the resonance frequency, and the non-linear coefficient is obtained with the backbone approach from resonance profile variations as a function of the forcing term amplitude. It is argued that the method is very sensitive, to the point that a maximum excitation amplitude of the order of a few percent of resistance is sufficient to obtain an estimate of the non-linear coefficient. This claim is supported by experimental results. A testing machine is also discussed, which provides the necessary sensitivity at such small excitation amplitudes and the capability of evaluating very small damping values, as expected in high strength low damping fiber materials. The sensitivity is guaranteed by an optical position sensor with sub-micron resolution. To evaluate small damping values, particular care has been taken to ensure that energy dispersions in the generator are much smaller than energy dispersions in the fibers themselves. Examples of dynamic characterization are shown for para-aramid, silicon carbide, and carbon fibers.     

Flow-acoustic coupling in coaxial side branch resonators with rectangular splitter plates

Flow past symmetrically located side branches mounted in a duct can give rise to pronounced flow oscillations due to coupling between separated shear layers and standing acoustic waves. The acoustically-coupled flows were investigated using digital particle image velocimetry (PIV) in conjunction with unsteady pressure measurements. Global instantaneous, phase- and time-averaged flow images were evaluated to provide insight into the flow physics during flow tone generation. Onset of the locked-on resonant states was characterized in terms of the acoustic pressure amplitude and frequency of the resonant pressure peak. Structure of the acoustic noise source was discussed in terms of patterns of generated acoustic power, which was evaluated by applying the vortex sound theory in conjunction with global quantitative flow imaging and numerical simulation of the acoustic field. In addition to the basic side branch configuration, the effect of bluff rectangular splitter plates located along the centerline of the main duct was investigated. The first mode of the shear layer oscillation was inhibited by the presence of the plates, which resulted in substantial reduction of the amplitude of acoustic pulsations and the strength of the acoustic source.     

Generation of locked-on flow tones: Effect of damping

The overall objective of this investigation is to determine the effect of variable damping on the pressure response of a deep cavity. The pressure fluctuations arise from coupling between the unsteady shear layer along the cavity opening and a resonant mode of the cavity. The damping of the cavity is tuned to desired values without changes of geometry or other parameters.The amplitude of the cavity pressure fluctuation as a function of flow velocity is characterized for the first, second and third acoustic modes of the cavity. For each mode, variation of the value of damping over a relatively wide range yields corresponding attenuation of the pressure amplitude. For higher acoustic modes and sufficiently large damping, abrupt decreases of the pressure amplitude occur at threshold values of flow velocity.The variable damping of the deep cavity does not significantly alter the eigenfrequencies of the system. The peak response amplitude of the pressure fluctuation, however, occurs at a value of Strouhal number that increases with increasing values of damping. Moreover, this peak response amplitude, when normalized by the free stream dynamic head, generally shows a linear variation with the value of damping, for three acoustic modes of the cavity.The strength of lock-on of the pressure oscillation, as a function of the degree of damping, is evaluated in terms of the coherent and broadband pressure amplitudes. Both amplitudes are attenuated for increased damping; the difference between them, however, remains relatively large (40 dB minimum), thereby indicating well-defined lock-on, even when the amplitude of the spectral peak of the coherent component is substantially attenuated.     

Investigation on two-phase flow-induced vibrations of a piping structure with an elbow

The dynamic behaviors of a horizontal piping structure with an elbow due to the two-phase flow excitation are experimentally investigated. The effects of flow patterns and superficial velocities on the pressure pulsations and vibration responses are evaluated in detail. A strong partition coupling algorithm is used to calculate the flow-induced vibration (FIV) responses of the pipe, and the theoretical values agree well with the experimental results. It is found that the lateral and axial vibration responses of the bend pipe are related to the momentum flux of the two-phase flow, and the vibration amplitudes of the pipe increase with an increase in the liquid mass flux. The vertical vibration responses are strongly affected by the flow pattern, and the maximum response occurs in the transition region from the slug flow to the bubbly flow. Moreover, the standard deviation (STD) amplitudes of the pipe vibration in three directions increase with an increase in the gas flux for both the slug and bubbly flows. The blockage of liquid slugs at the elbow section is found to strengthen the vibration amplitude of the bend pipe, and the water-blocking phenomenon disappears as the superficial gas velocity increases.     

Steady-state responses of a belt-drive dynamical system under dual excitations

The stable steady-state periodic responses of a belt-drive system with a one-way clutch are studied. For the first time, the dynamical system is investigated under dual excitations. The system is simultaneously excited by the firing pulsations of the engine and the harmonic motion of the foundation. Nonlinear discrete–continuous equations are derived for coupling the transverse vibration of the belt spans and the rotations of the driving and driven pulleys and the accessory pulley. The nonlinear dynamics is studied under equal and multiple relations between the frequency of the firing pulsations and the frequency of the foundation motion.Furthermore, translating belt spans are modeled as axially moving strings. A set of nonlinear piecewise ordinary differential equations is achieved by using the Galerkin truncation.Under various relations between the excitation frequencies,the time histories of the dynamical system are numerically simulated based on the time discretization method. Furthermore, the stable steady-state periodic response curves are calculated based on the frequency sweep. Moreover, the convergence of the Galerkin truncation is examined. Numerical results demonstrate that the one-way clutch reduces the resonance amplitude of the rotations of the driven pulley and the accessory pulley. On the other hand, numerical examples prove that the resonance areas of the belt spans are decreased by eliminating the torque-transmitting in the opposite direction. With the increasing amplitude of the foundation excitation, the damping effect of the one-way clutch will be reduced. Furthermore, as the amplitude of the firingpulsations of the engine increases, the jumping phenomena in steady-state response curves of the belt-drive system with or without a one-way clutch both occur.     

Influence of excitation amplitude on the characteristics of nonlinear butyl rubber isolators

The purpose of this study is to explore the advantages and characteristics of nonlinear butyl rubber (type IIR) isolators in vibratory shear by comparison with linear isolators. It is known that the mechanical properties of viscoelastic materials exhibit significant frequency and temperature dependence, and in some cases, nonlinear dynamic behavior as well. Nonlinear characteristics in shear deformation are reflected in mechanical properties such as stiffness and damping. Furthermore, even when the excitation amplitude is small the response amplitude may often be large enough that nonlinearities cannot be ignored. The treatment involves developing phenomenological models of the effective storage modulus and effective loss factor of a rubber isolator material as a function of excitation amplitude. The transmissibility of a nonlinear viscoelastic isolator is compared with that of a linear isolator using an equivalent linear damping coefficient. Forced resonance vibration and impedance tests are used to characterize nonlinear parameters and to measure the normalized transmissibility. It is found that as the excitation amplitude of the nonlinear viscoelastic isolator increases, the response amplitude decreases and the transmissibility is improved over that of the linear isolator for excitation frequency that exceeds a particular value governed by the temperature and excitation amplitude. The method of multiple scales and numerical simulations are used to predict the response characteristics of the isolator based on the phenomenological modeling under different values of system parameters.     

Dynamic analysis of a dielectric elastomer-based microbeam resonator with large vibration amplitude

A non-linear vibration equation with the consideration of large amplitude, gas damping and excitation is developed to investigate the dynamic performance of a dielectric elastomer (DE)-based microbeam resonator. Approximate analytical solution for the vibration equation is obtained by applying parameterized perturbation method (PPM) and introducing a detuning variable. The analysis exhibits that active tuning of the resonant frequency of the resonator can be achieved through changing an applied electrical voltage. It is observed that increasing amplitude will increase the natural frequency while it will decrease the quality factor of the resonator. In addition, it is found that the initial pre-stretching stress and the ambient pressure can significantly alter the resonant frequency of the resonator. The analysis is envisaged to provide qualitative predictions and guidelines for design and application of DE-based micro resonators with large vibration amplitude.     

Effect of the stiffness,inertia and oscillation kinematics on the thrust generation and efficiency of an oscillating-foil propulsion system

This paper presents an experimental study that has investigated the effects of the foil stiffness, inertia and oscillation kinematics on the thrust generation and efficiency of a flexible oscillating-foil propulsion system. A semi-empirical damped-oscillator model, which included a quadratic damping element, was developed and fitted to the experimental results. The model was used to develop explanations for the observed trends in the propulsive performance. For all of the foils constructed for the study, a consistent relationship between the efficiency and frequency ratio was observed. The maximum efficiency occurred at the same frequency ratio that resulted in both a beneficial phasing of the deformation with respect to the driven motion and also the maximum overall amplitude of the motion. For foils of equivalent resonant frequency operating at the same frequency ratio, the stiffer and heavier foils were found to develop greater thrust, likely because the lower effective damping allowed for a greater amplitude of the motion. Increasing the amplitude of the driven motion was found to cause the frequency ratio providing the maximum efficiency to shift towards lower values. The use of combined pitch and heave motions was shown to increase efficiency while reducing thrust compared to the heave-only case.     

负刚度时滞反馈控制动力吸振器的等峰优化

相比于传统动力吸振器, 负刚度动力吸振器同时具有更好的减振能力和更宽的有效减振频带宽度, 为了进一步降低共振峰幅值, 在负刚度吸振器系统耦合时滞反馈控制. 对负刚度时滞反馈控制动力吸振器系统进行等峰优化设计, 优化设计的准则是:第一和第二共振峰的峰值相等; 同时兼顾两个目标, 一个目标是在优化时的最大共振峰幅值小于被动负刚度吸振器系统的反共振峰幅值, 另一目标是在优化时共振峰幅值与反共振峰幅值差小于被动吸振器系统. 接着, 通过设计和调节负刚度系数、吸振器阻尼系数和时滞反馈控制系数对控制系统进行等峰优化设计. 最后, 在降低幅值的同时, 分析结构参数对有效减振频带宽度的影响. 经过等峰优化之后, 选择本文的一组结构参数与两个典型的模型进行对比. 为了定量比较不同模型的降幅效果, 定义了减幅百分比, 研究发现在有效减振频带区间内减幅百分比超过40%以上. 结果表明, 通过等峰优化准则对结构参数进行优化设计和调节增益系数和时滞量, 共振峰幅值的减幅百分比也近似达到40%, 也可以调节增益系数和时滞量, 使得幅频响应曲线具有较宽的有效减振频带和较低的共振峰幅值与反共振峰幅值的差值.      

On the transient response of forced nonlinear oscillators

We consider the transient response of a prototypical nonlinear oscillator modeled by the Duffing equation subjected to near resonant harmonic excitation. Of interest here is the overshoot problem that arises when the system is undergoing free motion and is suddenly subjected to harmonic excitation with a near resonant frequency, which leads to a beating type of transient response during the transition to steady state. In some design applications, it is valuable to know the peak value of this response and the manner in which it depends on system parameters, input parameters, and initial conditions. This nonlinear overshoot problem is addressed by considering the well-known averaged equations that describe the slowly varying amplitude and phase for both transient and steady state responses. For the undamped system, we show how the problem can be reduced to a single parameter χ that combines the frequency detuning, force amplitude, and strength of nonlinearity. We derive an explicit expression for the overshoot in terms of χ, describe how one can estimate corrections for light damping, and verify the results by simulations. For zero damping, the overshoot approximation is given by a root of a quartic equation that depends solely on χ, yielding a simple bound for the overshoot of lightly damped systems.     

Effects of modifying the blade trailing edge profile on unsteady pressure pulsations and flow structures in a centrifugal pump

In the present work, the effects of modifying the blade pressure side (EPS profile) on unsteady pressure pulsations and flow structures in a low specific speed centrifugal pump are carried out by experimental and numerical methods. Results are compared to the original trailing edge (OTE profile). Unsteady pressure signals are captured at twenty measuring points at flow rate of 0–1.6Q_d. It is observed that the pump head of the EPS profile is improved for all the concerned working conditions. Pressure amplitudes at the blade passing frequency are compared and discussed in detail. It is found that the EPS profile contributes to pressure pulsation reduction obviously. For all the measured flow rates, pressure amplitudes are attenuated evidently at major measuring positions, especially at high flow rates. As for the mean pressure amplitude of twenty measuring points, pressure amplitude is reduced more than 20% at the nominal flow rate using the EPS profile. From relative velocity distribution, it is found that the uniformity of flow field at the blade outlet region would be improved significantly by the EPS profile. Besides, the corresponding vorticity magnitude at the blade outlet would be reduced compared to the OTE profile. The combined effects contribute to the reduction of pressure amplitude using the EPS profile.     

The response of nonlinear systems to modulated high-frequency input

We study the response of a single-degree-of-freedom system with cubic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contain frequencies much lower than the carrier frequency of the excitation. We apply the theory to different types of amplitude modulation and find that resonant excitation of the system may occur under some conditions.     

基于等效阻尼理论的金属橡胶弹性迟滞力学模型及实验研究

针对弹性多孔金属橡胶非线性迟滞特性力学行为,将迟滞恢复力-位移曲线分解为非线性单值曲线和椭圆,并将等效阻尼理论用于动态力学性能参数识别,从而建立了一种新型的适用于黏弹性阻尼材料的宏观唯象力学模型。采用不同相对密度的环形金属橡胶进行动态实验测试,以验证理论模型的准确性,结果表明该模型可将具有非线性特性的金属橡胶系统进行降阶处理,提高金属橡胶力学模型的预测效率,并能很好地描述金属橡胶的迟滞力学行为。另外,研究了在不同激励频率条件下金属橡胶的阻尼耗能特性。实验结果表明:在高频加载的条件下,黏性阻尼系数对动态加载频率不敏感,阻尼耗能与加载幅值之间呈线性正相关。基于等效阻尼理论的弹性迟滞力学模型具有一定的普适性,可进一步推广应用于类似弹性多孔材料的力学性能表征,为其工程应用提供理论基础。     

Nonlinear dynamic analysis of a quarter vehicle system with external periodic excitation

In this paper, a nonlinear dynamic model of a quarter vehicle with nonlinear spring and damping is established. The dynamic characteristics of the vehicle system with external periodic excitation are theoretically investigated by the incremental harmonic balance method and Newmark method, and the accuracy of the incremental harmonic balance method is verified by comparing with the result of Newmark method. The influences of the damping coefficient, excitation amplitude and excitation frequency on the dynamic responses are analyzed. The results show that the vibration behaviors of the vehicle system can be control by adjusting appropriately system parameters with the damping coefficient, excitation amplitude and excitation frequency. The multi-valued properties, spur-harmonic response and hardening type nonlinear behavior are revealed in the presented amplitude-frequency curves. With the changing parameters, the transformation of chaotic motion, quasi-periodic motion and periodic motion is also observed. The conclusions can provide some available evidences for the design and improvement of the vehicle system.     

FLUID FORCES AND DYNAMICS OF A HYDROELASTIC STRUCTURE WITH VERY LOW MASS AND DAMPING

In this paper we present some central new results from a study of the dynamics and fluid forcing on an elastically mounted rigid cylinder, constrained to oscillate transversely to a free stream. With very low damping, and with a low specific mass that is around 1% of the value used in the classic study of Feng (1968), we show that the cylinder excitation regime extends over a large range of normalized velocity (around four times that found by Feng), with a large amplitude which is around twice that of Feng. Four distinct regions of response are identified, namely the initial excitation region, the “upper branch” (of very high amplitude response), the “lower branch” (of moderate amplitude response), and the desynchronization region. There are distinct differences in the character of mode transitions, as follows. As normalized velocity is increased, there is a hysteretic jump from an initial excitation regime to the upper branch, whereas the jump from the upper to the lower branch involves an intermittent switching, which is illustrated by plotting the instantaneous phase between lift force and displacement using the Hilbert transform. Contrary to classical “lock-in”, whereby the oscillation frequency matches the structural natural frequency, we find that the oscillation frequency increases markedly above the natural frequency, through the excitation regime. Finally, we present the first lift force measurements for such a freely vibrating cylinder experiment, yielding a maximum lift coefficient of around 4·5, whereas a maximum drag coefficient of 6·0 is also measured. The lift is comparable, but somewhat higher, than the forces measured (C_L∼2·0) in the equivalent free-vibration experiments of Hoveret al.(1997), involving force-feedback and on-line computer-simulation of the modelled structure. Both the lift and drag maxima exhibit at least a five-fold increase over the stationary cylinder case. Perhaps the largest effect is found for the fluctuating drag, which is found to be upto 100 times that measured for a static cylinder.     

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler–Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton's principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency–response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency–response curves. We also study the difference between the nonlinear lumped-parameter and distributedparameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested.We also illustrate that the damping and load resistance affect the initiation excitation threshold.     

Vibration and dynamic buckling of shear beam-columns on elastic foundation under moving harmonic loads

The vibration and buckling of an infinite shear beam-column, which considers the effects of shear and the axial compressive force, resting on an elastic foundation have been investigated when the system is subjected to moving loads of either constant amplitude or harmonic amplitude variation with a constant advance velocity. Damping of a linear hysteretic nature for the foundation was considered. Formulations in the transformed field domains of time and moving space were developed, and the response to moving loads of constant amplitude and the steady-state response to moving harmonic loads were obtained using a Fourier transform. Analyses were performed to examine how the shear deformation of the beam and the axial compression affect the stability and vibration of the system, and to investigate the effects of various parameters, such as the load velocity, load frequency, shear rigidity, and damping, on the deflected shape, maximum displacement, and critical values of the velocity, frequency, and axial compression. Expressions to predict the critical (resonance) velocity, critical frequency, and axial buckling force were proposed.     

Maximal Lyapunov exponent and almost-sure sample stability for second-order linear stochastic system

The principal resonance of second-order system to random parametric excitation is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The effects of damping, detuning, bandwidth, and magnitudes of random excitation are analyzed. The explicit asymptotic formulas for the maximum Lyapunov exponent is obtained. The almost-sure stability or instability of the stochastic Mathieu system depends on the sign of the maximum Lyapunov exponent.     

参数振动系统响应的频谱成分及其分布规律

采用Sylvester理论和Fourier级数展开方法分别研究了参数振动系统自由响应和强迫响应的频谱特性(频谱成分及其分布规律),讨论了系统稳定性和阻尼对于频谱幅值的影响,并给出了系统外激励共振条件. 理论研究结果表明:由于参数激励作用使得系统响应具有多频特点,这些频谱成分与系统固有频率、参数激励频率和外激励频率具有密切联系,而且其在频域分布也呈现出一定的规律. 此外,参数振动系统具有多个外激励共振点,除了外激励频率等于系统固有频率将发生共振外,当外激励频率等于系统固有频率和参数激励频率的组合值时,同样将发生外激励共振现象.      

SELF-EXCITED VIBRATION OF A CONTROL VALVE DUE TO FLUID–STRUCTURE INTERACTION

In this paper, the mechanism causing self-excited vibration of a piping system is determined using a dynamic model which couples the hydraulics of a piping system with the structural motion of an air-operated, plug-type automatic control valve. In the dynamic model developed, the structural system consists of a valve spring–mass system, while the fluid system consists of a pump, upstream piping, control valve and downstream piping. The coupling between the structural and the fluid systems at the control valve is obtained by making the fluid flow coefficient at the control valve to be a function of valve plug displacement, and by making the valve plug displacement to be a function of fluid pressure and velocity. The dynamic model presented in this paper, for the first time, considers compressibility of the fluid in both the upstream and downstream piping. The dynamic model presented was benchmarked against in situ measurements. The data used for the benchmarking are provided in the paper. A review of the numerical results obtained indicates that the self-excited vibration occurs due to the coincidence of water hammer, acoustic feedback in the downstream piping, high acoustic resistance at the control valve, and negative hydraulic stiffness at the control valve.