Aeroelastic stability of complete rotors with application to a teetering rotor in forward flight

The derivation of a set of non-linear coupled flap-lag-torsion equations of motion for moderately large deflections of an elastic, two-bladed teetering helicopter rotor in forward flight is concisely outlined. The following degrees of freedom are included in the mathematical model: rigid body flapping, rigid body lead-lag, elastic bending in flap and lead-lag, blade root torsion, and shaft torsion. Quasi-steady aerodynamic loads are considered and the effects of reversed flow are included. The aeroelastic stability of the complete rotor is investigated by using a linearized system of equations of motion. The equilibrium position about which the equations are linearized is obtained by considering the trim state of the helicopter, in true or simulated forward flight conditions. The sensitivity of the aeroelastic stability boundaries to interblade structural and mechanical coupling is illustrated by comparing the complete rotor stability boundaries with those obtained from a single blade analysis for a number of hover and forward flight cases.     

Bifurcation and chaos response of a cracked rotor with random disturbance

The Monte-Carlo method is used to investigate the bifurcation and chaos characteristics of a cracked rotor with a white noise process as its random disturbance. Special attention is paid to the influence of the stiffness change ratio and the rotating speed ratio on the bifurcation and chaos response of the system. Numerical simulations show that the affect of the random disturbance is significant as the undisturbed response of the cracked rotor system is a quasi-periodic or chaos one, and such affect is smaller as the undisturbed response is a periodic one.     

旋翼桨尖几何形状对旋翼气动噪声影响的定量计算分析

采用CFD与计算声学相结合的Euler Kirchhoff方法对UH-1H直升机旋翼跨声速悬停流动的远场噪声进行定量计算,并将计算结果与实验值进行比较,验证了Euler Kirchhoff方法的正确性.然后以UH-1H直升机旋翼为基准旋翼,定量计算了对桨尖旋翼翼型厚度、旋翼尖削度、后掠角进行变化后的旋翼悬停流场的远场噪声,分析了旋翼桨尖几何形状对噪声的影响.得出结论:降低桨尖翼型厚度、浆尖尖削、浆尖后掠均可以降低噪声峰值.     

亚音主旋翼的噪声预测和声隐身分析

本文介绍了基于FW-H方程的亚音主旋翼噪声预测方法,并在螺桨噪声预测程序基础上发展了主旋翼噪声预测程序。本文采用商用CFD软件FINE／TURBO模拟直升机旋翼流场,为噪声预测程序提供所需要的桨叶表面载荷,并用算例验证了载荷数据的准确性和噪声预测程序的有效性。本文计算和讨论了亚音悬停条件下的辐射噪声,并重点分析了不同形状桨叶对辐射噪声的影响,结果表明采用合理的薄翼型叶尖、尖削叶尖及线性扭转桨叶都可以降低辐射噪声,为通过改变桨叶形状降低旋翼辐射噪声提供了合理途径。     

共轴双旋翼悬停状态气动噪声特性分析

结合CFD(Computational fluid dynamics)方法和FW-H(Ffowcs Williams-Hawkings)方程,建立了一套适合于悬停状态下共轴刚性双旋翼气动噪声特性计算方法。为了准确模拟共轴旋翼流场的涡干扰现象和非定常特性,基于运动嵌套网格技术与双时间推进方法,采用积分形式的可压雷诺平均Navier-Stokes(RANS)方程作为双旋翼非定常流场求解控制方程,湍流模型选用Baldwin-Lomax模型。通过Farassat 1A公式计算双旋翼气动噪声特性,每个声源微面的位置和载荷信息直接从桨叶表面网格中获取。然后,对水平面内和竖直面内观测点处共轴双旋翼厚度噪声、载荷噪声和总噪声的声压时间历程和频谱特性做了细致对比。模拟结果表明:上旋翼和下旋翼反向旋转的特点对声压时间历程影响显著,不同方向观察点的声压波形峰值对应的相位不同;共轴旋翼流场中存在的文丘里效应、桨-涡干扰现象以及下洗流的作用使得桨叶气动载荷呈现明显的非定常特征,导致共轴双旋翼的载荷噪声辐射强度较大;在低频段,总噪声受厚度噪声主导,而在高频段则受载荷噪声主导。      

Estimation of damping from response spectra

In this paper procedures for estimating damping ratio from response spectra are examined. The study is restricted to an evaluation of bias and random errors introduced by signal processing requirements. A second order system is used in the study, and a Gaussian white noise input is assumed. It is shown that, due to bias errors in estimating the response spectra, calculations of damping ratio by the peak response and half-power bandwidth methods give overestimates. The bias errors of the damping ratio estimates are a function of the true damping of the system and the ratio of analysis bandwidth to resonant frequency. The bias error for the half-power bandwidth method is three times that for the peak response method. It is also shown for large ranges of damping ratio and bandwidth ratio that zero bias response occurs at a point where the response is approximately 80% of the peak response. Numerical results obtained by simulation studies are used to verify the expressions for normalized bias error. Expressions for random error associated with damping ratio estimates are also developed. Random error can be minimized by maintaining a high coherence between the system input and response.     

Moment equations for a spatially extended system of two competing species

The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulations of the time discrete version of LV equations, that is coupled map lattice (CML) model, we conclude that the anticorrelated oscillations of the species densities are strictly related to non-overlapping spatial patterns.     

Helicopter noise in hover: Computational modelling and experimental validation

The aeroacoustic characteristics of a helicopter rotor are calculated by a new method, to assess its applicability in assessing rotor performance in hovering. Direct solution of the Euler equations in a noninertial coordinate system is used to calculate the near-field flow around the spinning rotor. The far-field noise field is calculated by the Ffowcs Williams–Hawkings (FW–H) method using permeable control surfaces that include the blade. For a multiblade rotor, the signal obtained is duplicated and shifted in phase for each successive blade. By that means, the spectral characteristics of the far-field noise may be obtained. To determine the integral aerodynamic characteristics of the rotor, software is written to calculate the thrust and torque characteristics from the near-field flow solution. The results of numerical simulation are compared with experimental acoustic and aerodynamic data for a large-scale model of a helicopter main rotor in an open test facility. Two- and four-blade configurations of the rotor are considered, in different hover conditions. The proposed method satisfactorily predicts the aerodynamic characteristics of the blades in such conditions and gives good estimates for the first harmonics of the noise. That permits the practical use of the proposed method, not only for hovering but also for forward flight.     

Doubly stochastic resonance

We report the effect of doubly stochastic resonance which appears in nonlinear extended systems if the influence of noise is twofold: A multiplicative noise induces bimodality of the mean field of the coupled network and an independent additive noise governs the dynamic behavior in response to small periodic driving. For optimally selected values of the additive noise intensity stochastic resonance is observed, which is manifested by a maximal coherence between the dynamics of the mean field and the periodic input. Numerical simulations of the signal-to-noise ratio and theoretical results from an effective two state model are in good quantitative agreement.     

Phase noise generation in an amplitude limiter using saturation of a fiber-optic parametric amplifier

Generation of phase noise in an amplitude limiter using saturation of a fiber-optic parametric amplifier is analyzed. The analysis is based on the coupled differential equations for the amplitudes and phases of pump, signal, and idler involved in the four-wave mixing interaction. The equations are linearized about small fluctuations at operation points and are solved, which results in relations between the input and output phase and amplitude noise. These relations are used in deriving expressions of amplitude signal-to-noise ratio (SNR) and variance of phase noise of the output signal in terms of SNRs of input signal and pump. It is shown that optimum pump power exists for minimum output phase noise in the output signal.     

New perspective in the use of soft rotor formula for K = 2 γ-band

The use of soft rotor formula (SRF) for the level energies of K?=?2 γ-band for the shape transitional even Z even N nuclei in the medium mass region is illustrated. With proper treatment, we obtained positive values of the moment of inertia and softness parameter, as opposed to negative values reported in literature. The moments of inertia of the γ-band are almost equal to the ground state band values. The systematic dependence of the softness parameter on energy ratio R _4/2 is studied. The effect of the odd–even spin staggering on these parameters is studied in detail. In deformed nuclei, the same parameters for odd and even spin members yield fair energy values.     

The use of moment equations for calculating the mean square response of a linear system to non-stationary random excitation

The moment equations approach is used to calculate the mean square response of a linear system to non-stationary random excitation which is expressed as a product of a deterministic envelope function and a Gaussian stationary non-white noise. The moment equations are derived by performing single integrations in the time domain and are solved numerically by digital computer. Numerical examples are given for the response of single and two degree-of-freedom systems which are excited by noise with an exponentially decaying harmonic correlation function. It is shown that an overshoot, in the sense that the transient response exceeds its stationary value, may occur even in the case of an exponential envelope function, but that the response does not exhibit overshoot when the natural frequency of the system is almost coincident with the dominant frequency of the input.     

Effect of unbalanced rotor whirl on blade vibrations

In this paper, vibration of a bladed unbalanced flexible rotor is studied. The blade that is attached to the disk is considered as a fixed-free Euler-Bernoulli beam. Position of the blade with respect to the eccentric mass is taken into consideration. Coupled equations of the motion of unbalanced rotor and the blades are obtained through Lagrange equations. The dynamic equations have time variant periodic coefficients. Transient vibration analysis showed that rotor acceleration excites the blade vibration with its own natural frequency. While the rotor passes through its own natural frequency (critical speed) the blade vibration is again excited but this time with the rotor natural frequency. Modal behavior of the blades are different for subcritical, supercritical and for critical speed of the rotor. In the subcritical run of the rotor, blades located from 0° to 180° with respect to the eccentric mass are deflected in the negative direction while the rest are deflected in the positive direction. For supercritical run of the rotor, modal behavior of the blades is just the opposite. For critical speed of the rotor, blades located 90° to 270° from the eccentric mass are deflected in the positive direction while the rest of the blades are deflected in the negative direction. Blades have also different deflections. When the deflections of the blades are plotted with respect to their position angle, distribution of the blade deflections has a sinusoidal shape.     

1/f noise outperforms white noise in sensitizing baroreflex function in the human brain

We show that externally added 1/f noise more effectively sensitizes the baroreflex centers in the human brain than white noise. We examined the compensatory heart rate response to a weak periodic signal introduced via venous blood pressure receptors while adding 1/f or white noise with the same variance to the brain stem through bilateral cutaneous stimulation of the vestibular afferents. In both cases, this noisy galvanic vestibular stimulation optimized covariance between the weak input signals and the heart rate responses. However, the optimal level with 1/f noise was significantly lower than with white noise, suggesting a functional benefit of 1/f noise for neuronal information transfer in the brain.     

Noise simulation of aircraft engine fans by the boundary element method

Numerical simulation results of the civil aircraft engine fan stage noise in the far field are presented. Non-steady-state rotor–stator interaction is calculated the commercial software that solves the Navier–Stokes equations using differentturbulence models. Noise propagation to the far acoustic field is calculated by the boundary element method using acoustic Lighthill analogies without taking into account the mean current in the air inlet duct. The calculated sound pressure levels at points 50 m from the engine are presented, and the directional patterns of the acoustic radiation are shown. The use of the eddy resolving turbulence model to calculate rotor–stator interaction increases the accuracy in predicting fan stage noise.     

Signal transmission in noisy environments: auditory masking in the tympanic nerve of the bushcricket Metaballus litus (Orthoptera: Tettigoniinae)

Physiological responses of the auditory leg nerve were recorded in the tettigoniid Metaballus litus to suprathreshold tone pulses of 12.45 kHz, which is close to the carrier frequency of the male's call. This stimulus tone frequency was determined by characterizing the polar response of the foreleg. Physiological threshold of the receptors was calculated from intensity input/output curves, and the experimental stimulus was set at 40 dB above this threshold value. There was low variance in threshold values between preparations. Continuous octave filtered white noise centered on the stimulus frequency was presented at the same time as the tone pulse at increasing intensities. The summed action potentials (SAPs) of the whole leg nerve were averaged over 256 stimulus presentations and the magnitude of the response was calibrated to dB values. The range of noise levels was set between that inducing no decrease in the SAP response to the tone pulse stimulus, up to a masking intensity where the response to the tone pulse was only just observable. Decrement in SAP magnitude was linear, and complete masking occurred when the noise level was 20-25 dB above the initial level of zero masking. This final level was comparable in magnitude to the sound-pressure level of the tone pulse and within the natural range of the insect's auditory behavior. Following the cessation of the noise signal, the SAPs were monitored over intervals of 2 min until the SAP asymptoted to the preexperimental condition. The reduction in SAP magnitude during noise presentation was attributed to a loss in synchrony from the individual tympanic receptors.     

多普勒频移和干涉谱联合的水声目标运动参数估计

常见水中运动目标会辐射连续谱噪声和线谱噪声,连续谱噪声在浅海波导环境中形成明暗相间的干涉条纹。根据干涉条纹可以得到目标最近距离与速度的比值,无法直接解出两个参数值。针对利用干涉条纹无法分别估计最近距离与速度问题,提出一种多普勒频移、干涉条纹结合的运动参数估计方法。根据单条线谱多普勒频移得到最近距离与速度参数耦合曲线,再将该曲线与干涉条纹得到参数比值线相交,交点即为两参数估计结果。数值仿真估计声源运动速度、最近距离,在信噪比6 dB条件下,平均估计误差分别为0.71%与0.87%。将该方法应用在2021年6月大公岛海域海试数据,5组实验数据估计目标运动速度、最近距离平均误差分别为2.5%,4.4%,证明了方法的有效性。     

A prediction method of the response probability distribution for arbitrary sound insulation systems

This paper describes a practical evaluation method of the response probability distribution for an arbitrary sound insulation system with a random input noise of arbitrary distribution. Here, the response probability distribution is derived in a fairly simple form using the statistical Hermite expansion-type series expression. The effect of the sound insulation system and the input fluctuation on the resultant probability distribution form is hierarchically reflected in various types of statistics such as the mean, variance and each expansion coefficient. Finally, the proposed evaluation method is experimentally confirmed by applying it to the observed data for typical examples of single- and double-wall insulation system, with white noise and music excitations.     

A nonlinear system under combined periodic and random excitation

The anharmonic oscillator under combined sinusoidal and white noise excitation is studied using the Gaussian closure approximation. The mean response and the steady-state variance of the system is obtained by the WKBJ approximation and also by the Fokker-Planck equation. The multiple steadystate solutions are obtained and their stability analysis is presented. Numerical results are obtained for a particular set of system parameters. The theoretical results are compared with a digital simulation study to bring out the usefulness of the present approximate theory.     

Two-dimensional transmission type volume holograms for incident plane waves of arbitrary amplitude distribution

Based on the differential equations of [1] a general solution in closed form is obtained for the amplitudes of the transmitted and diffracted beams for Bragg angle incidence in a lossless, transmission type volume hologram. Numerical solutions are plotted for Gaussian input beams. For the range of parameter values investigated it is shown that complete power transfer into the diffracted beam is not possible.