Noise transmission from a curved panel into a cylindrical enclosure: analysis of structural acoustic coupling

Much of the research on sound transmission through the aircraft fuselage into the interior of aircraft has considered coupling of the entire cylinder to the acoustic modes of the enclosure. Yet, much of the work on structural acoustic control of sound radiation has focused on reducing sound radiation from individual panels into an acoustic space. Research by the authors seeks to bridge this gap by considering the transmission of sound from individual panels on the fuselage to the interior of the aircraft. As part of this research, an analytical model of a curved panel, with attached piezoelectric actuators, subjected to a static pressure load was previously developed. In the present work, the analytical model is extended to consider the coupling of a curved panel to the interior acoustics of a rigid-walled cylinder. Insight gained from an accurate analytical model of the dynamics of the noise transmission from the curved panels of the fuselage into the cylindrical enclosure of an aircraft is essential to the development of feedback control systems for the control of stochastic inputs, such as turbulent boundary layer excitation. The criteria for maximal structural acoustic coupling between the modes of the curved panel and the modes of the cylindrical enclosure are studied. For panels with aspect ratios typical of those found in aircraft, results indicate that predominately axial structural modes couple most efficiently to the acoustic modes of the enclosure. The effects of the position of the curved panel on the cylinder are also studied. Structural acoustic coupling is found to not be significantly affected by varying panel position. The impact of the findings of this study on structural acoustic control design is discussed.     

CSNS-II超导椭球腔失谐研究

中国散裂中子源二期束流功率升级到500 kW，直线加速器H-的能量增益由现在的80 MeV提高到300 MeV以上，其中150 ~ 300 MeV能量段采用648 MHz β_g=0.60的5-cell超导椭球腔结构。超导椭球腔具有加速梯度高、结构简单、后处理容易等优点，缺点是结构强度弱、易失谐。本文主要研究该椭球腔的失谐特性。利用COMSOL Multiphysics软件进行了计算分析，在两端固定边界条件下，裸腔的氦压敏感性系数K_P=–45.705 Hz/mbar(1 mbar=100 Pa)，洛伦兹力失谐因子K_L=1.574 Hz/(MV/m)2。增加加强环并优化其位置来改善氦压敏感性系数和洛伦兹力失谐因子，通过计算分析最终确定选择双加强环方案来减小椭球腔的失谐。两个加强环位置分别取在75和120 mm的位置，腔体失谐的改善最大，K_P=6 Hz/mbar，K_L=0.43 Hz/(MV/m)2。为了更准确地计算椭球腔的氦压敏感性系数和洛伦兹力失谐因子，本文引入调谐刚度边界条件进行失谐分析，在椭球腔调谐器端设置30 kN/mm边界条件，另一端固定，计算得到氦压敏感性系数为4.8 Hz/mbar，洛伦兹力失谐因子1.99 Hz/(MV/m)2，满足工程要求。另外，用CST软件对椭球腔的动态洛伦兹力失谐进行了初步分析，用软件Workbench计算了椭球腔的振动本征频率，结果显示，振动本征频率离射频脉冲重复频率及环境振动频率较远，不易发生共振失谐。     

SOUND TRANSMISSION THROUGH PERIODICALLY STIFFENED CYLINDRICAL SHELLS

A relatively long circular cylindrical shell stiffened by periodically deployed stiffeners is found in many practical applications such as the aircraft fuselage. For the sound transmission analysis of such a system, not only structural interactions between the shell and stiffeners but also vibro-acoustic interactions between the structure and acoustic media have to be considered. By idealizing the system as an infinitely long cylinder subjected to a plane wave incidence, an exact solution is obtained for the first time for this type of problem. In the analysis, the solution is obtained in a series form by expanding the system responses in terms of the space harmonics of the stiffener spacing. Characteristics of the system responses and effects of important design parameters are studied using the transmission losses calculated from the analysis.     

A parametric multi-body section model for modal interactions of cable-supported bridges

A parametric section model is formulated to synthetically describe the geometrically nonlinear dynamics of cable-stayed and suspended bridges through a planar elastic multi-body system. The four-degrees-of-freedom model accounts for both the flexo-torsional motion of the bridge deck and for the transversal motion of a pair of hangers or stay cables. After linearization around the pre-stressed static equilibrium configuration, the coupled equations of motion governing the global deck dynamics and the local cable motion are obtained. A multi-parameter perturbation method is employed to solve the modal problem of internally resonant systems. The perturbation-based modal solution furnishes, first, explicit formulae for the parameter combinations which realize the internal resonance conditions and, second, asymptotic approximations of the resonant frequencies and modes. Attention is focused on the triple internal resonance among a global torsional mode of the deck and two local modes of the cables, due to the relevant geometric coupling which maximizes the modal interaction. The asymptotic approximation of the modal solution is found to finely describe the multiple veering phenomenon which involves the three frequency loci under small variation of the most significant mechanical parameters, including terms of structural coupling or disorder. Moreover, the veering amplitude between any two of the three frequency loci can be expressed as an explicit parametric function. Finally, the disorder is recognized as the only parameter governing a complex phenomenon of triple modal hybridization involving all the resonant modes. The entire hybridization process is successfully described by an energy-based localization factor, presented in a new perturbation-based form, valid for internally resonant system.     

Basilar membrane mechanics at the base of the chinchilla cochlea. II. Responses to low-frequency tones and relationship to microphonics and spike initiation in the VIII nerve

Low-frequency stimuli (40- to 1000-Hz tones) have been used to correlate the motion of the 8-to 9-kHz place of the chinchilla basilar membrane with the cochlear microphonics recorded at the round window and with the responses of auditory nerve fibers with appropriate characteristic frequency. At the lowest stimulus frequencies, maximum displacement of the basilar membrane toward scala tympani occurs in near synchrony with maximum rarefaction at the eardrum and maximum negativity at the round window; at higher frequencies, the mechanical and microphonic response phases progressively lag rarefaction, reaching - 240 deg at 1000 Hz. At most frequencies (40-1000 Hz) near-threshold neural responses, once corrected for neural travel-time and synaptic delays, somewhat lead (by some 40 deg) maximal scala tympani displacement and maximal negativity of the round window microphonics. The variation of sensitivity with frequency is similar for basilar membrane displacement and microphonic responses: Under open-bulla conditions, sensitivity is constant for frequencies between 100 and 1000 Hz; below 100 Hz, sensitivity decreases at rates close to 12 dB/oct toward lower frequencies. Neural response sensitivity matches BM displacement more closely than BM velocity.     

Experimental identification of the lateral human–structure interaction mechanism and assessment of the inverted-pendulum biomechanical model

Within the context of crowd-induced lateral bridge vibration, human–structure interaction (HSI) is a widely studied phenomenon. Central to this study is the self-excited component of the ground reaction force (GRF). This force harmonic, induced by a walking pedestrian, resonates with lateral deck motion, irrespective of the pedestrian?s pacing frequency. Its presence can lead to positive feedback between pedestrian GRFs and structural motion. Characterisation of the self-excited force as equivalent structural mass and damping has greatly improved the understanding of HSI and its role in developing lateral dynamic instability. However, despite this evolving understanding, a key question has remained unanswered; what are the features of a pedestrian?s balance response to base motion that gives rise to the self-excited force? The majority of the literature has focussed on the effects of HSI with the underlying mechanism receiving comparatively little attention. This paper presents data from experimental testing in which 10 subjects walked individually on a laterally oscillating treadmill. Lateral deck motion as well as the GRFs imposed by the subject was recorded. Three-dimensional motion capture equipment was used to track the position of visual markers mounted on the subject. Thus whole body response to base motion was captured in addition to the GRFs generated. The data presented herein supports the authors’ previous findings that the self-excited force is a frequency sideband harmonic resulting from amplitude modulation of the lateral GRF. The gait behaviour responsible for this amplitude modulation is a periodic modulation of stride width in response to a sinusoidally varying inertia force induced by deck motion. In a separate analysis the validity of the passive inverted pendulum model, stabilised by active control of support placement was confirmed. This was established through comparison of simulated and observed frontal plane CoM motion. Despite the relative simplicity of this biomechanical model, remarkable agreement was observed.     

Elastic response of an acoustic coating on a rib-stiffened plate

This paper develops a three-dimensional analytical model of a fluid-loaded acoustic coating affixed to a rib-stiffened plate. The system is loaded by a plane wave that is harmonic both spatially and temporally. The model begins with Navier-Cauchy equations of motion for an elastic solid, which produces displacement fields that have unknown wave propagation coefficients. These are inserted into stress equations at the boundaries of the plate and the acoustic coating. These stress fields are coupled to the fluid field and the rib stiffeners with force balances. Manipulation of these equations develops an infinite number of indexed equations that are truncated and incorporated into a global matrix equation. This global matrix equation can be solved to determine the wave propagation coefficients. This produces analytical solutions to the systems’ displacements, stresses, and scattered pressure field. This model, unlike previously developed analytical models, has elastic behavior and thus incorporates higher order wave motion that makes it accurate at higher wavenumbers and frequencies. An example problem is investigated for three specific model results: (1) the dynamic response, (2) a sonar array embedded in the acoustic coating, and (3) the scattered pressure field. An expression for the high frequency limitation of the model is derived. It is shown that the ribs can have a significant impact on the structural acoustic response of the system.     

Attenuation of flexural vibration for floating floor and floating box induced by ground vibration

This paper investigates the vibration isolation performance of floating floor and floating box structures to control rail vibration transmission. Simple theoretical and experimental methods are developed to analyze the effects of stiffener beam, mass and arrangement of isolator on the fundamental natural frequency of the flexural vibration of floating floor and box structure.The vibration reduction performances of floating floor and box structure are found to be degraded by flexural vibration of the floor or supporting stiffener beam. From the results of vibration measurements; stiffener beams increase the fundamental natural frequency of flexural vibration of floating floor and enhance vibration isolation. Also they can further alleviate the effect of flexural vibration using optimum isolator arrangement effectively. The proposed floating box design achieved a vibration reduction of 15-30 dB in frequency region of critical rail vibration (30-200 Hz).     

Interior near-field acoustical holography in flight

In this paper boundary element methods (BEM) are mated with near-field acoustical holography (NAH) in order to determine the normal velocity over a large area of a fuselage of a turboprop airplane from a measurement of the pressure (hologram) on a concentric surface in the interior of the aircraft. This work represents the first time NAH has been applied in situ, in-flight. The normal fuselage velocity was successfully reconstructed at the blade passage frequency (BPF) of the propeller and its first two harmonics. This reconstructed velocity reveals structure-borne and airborne sound-transmission paths from the engine to the interior space.     

Sound pressure in cylindrical shells with regular orthogonal system of stiffeners excited by a random fields of forces

To identify deterministic and random vibrations of a closed cylindrical shell with a regular orthogonal system of stiffeners (stringers and frames) the effective prediction method was worked out. This method is a generalization of the known method of space-harmonic expansion based on the theorem of Bloch-Floquet for a two-dimensional case. The method permits considering correctly the stiffener discreteness and their interaction with the shell through all the components of displacement. On the basis of the method worked out the task of determining the sound field inside the cylindrical volume bounded by the shell excited by the deterministic and random fields of external forces is solved. The high efficiency of the method permits making the prediction of the shell vibrations and of the sound pressure levels inside the volume with account for sound-insulating layers over a wide frequency range. Examples of predicting the strengthened shell vibrations at large aircraft fuselage parameters are given as well as the sound pressure levels inside it under the point force excitation and under excitation by the random field of wall pressure fluctuations of the turbulent boundary layer (within the limits of one of the representation of the space correlation spectrum).     

一种新型微机电系统扫描镜的谐振频率研究

在微光机电系统(MOEMS)技术的基础上,采用绝缘体上硅(SOI)的体硅加工工艺,设计并加工制作了一种新型的静电驱动的谐振式微机电系统(MEMS)扫描镜。介绍了其基本工作原理及结构设计特点;理论计算了圆形和方形两种结构的尺寸扫描镜的谐振频率,并利用ANSYS有限元软件进行仿真;设计并搭建了一个简单易操作的光学测试系统,对研制出的MEMS扫描镜(7.1mm×5.2mm)进行扫描角度测试。利用该器件参数激励的迟滞频率特性,对其谐振频率进行实际测量。同时,为验证其所测谐振频率的准确性,利用激光多普勒测振(LDV)系统对其进行测试。在工作电压10V,方形和圆形扫描镜的驱动频率分别为556Hz和596Hz时,机械扫描角度分别可达到约6°和5°,谐振频率分别约为300Hz和277Hz。并分析误差产生的原因及其结果。     

Modified independent modal space control of m.d.o.f. systems

The performance of the independent modal space control (IMSC) algorithm for structural vibration control is examined in this paper. Both the theoretical analysis and numerical simulation show that, for a multi-degree-of-freedom system, the modal control forces may increase the contributions of the vibration of higher modes (uncontrolled modes) to the system response if the IMSC algorithm is used to design a structural control system. Therefore, the responses of the controlled structure may be underestimated if the effects of control forces on the higher modes are not considered in the response analysis. A new control algorithm—modified independent modal space control (MIMSC) algorithm is proposed in this paper for eliminating the effect of modal control force on the uncontrolled modes. Numerical example shows that the structural responses can be effectively reduced when control system design is carried out based on the proposed algorithm. By comparing the simulated results obtained by the IMSC and MIMSC algorithms, it is found that, in order to achieve the same control objective, the proposed algorithm is more effective than IMSC since the modal control forces do not have any effect on the uncontrolled modes. In order to verify the effectiveness of the proposed algorithm, a practical example—active control design of UCLA Math-Science Building is presented and discussed.     

Vibration and sound signatures of human footsteps in buildings

The acoustic signature of a footstep is one of several signatures that can be exploited for human recognition. Early research showed the maximum value for the force of multiple footsteps to be in the frequency band of 1-4 Hz. This paper reports on the broadband frequency-dependent vibrations and sound pressure responses of human footsteps in buildings. Past studies have shown that the low-frequency band (below 500 Hz) is well known in the literature, and generated by the force normal to the ground/floor. The seismic particle velocity response to footsteps was shown to be site specific and the characteristic frequency band was 20-90 Hz. In this paper, the high-frequency band (above 500 Hz) is investigated. The high-frequency band of the vibration and sound of a human footstep is shown to be generated by the tangential force to the floor and the floor reaction, or friction force. The vibration signals, as a function of floor coverings and walking style, were studied in a broadband frequency range. Different walking styles result in different vibration signatures in the low-frequency range. However, for the walking styles tested, the magnitudes in the high-frequency range are comparable and independent of walking style.     

Wave localization on a submerged cylindrical shell with rib aperiodicity

The results of a numerical study of vibration localization due to stiffener variability in a framed shell are reported. An axisymmetric finite element (FE)-infinite element model is used to obtain predictions in good general agreement with previously reported experimental results. Over the frequency band of this study, up to three times the ring frequency, two structural resonances dominate the vibratory response of the shell for high circumferential orders (n > 10). Localization is shown to be linked to the sensitivity of the local resonance frequencies of the system to specific geometrical parameters. Specifically, rib thickness variations strongly affect the first pass band, while rib spacing variations strongly affect the second pass band.     

Finding the impedance of the organ of Corti

Measurements of the nonlinear response of the basilar membrane to a pure tone are shown to have a simple form for moderate membrane velocities: V(x,f;Vu)/Vu approximately [V(x,f)/Vu]v(x,f), f less than or equal to fc(x), where the response V is the velocity of the membrane at measurement position x, Vu is the umbo velocity, f is the frequency of the stimulus, and fc(x) is the local characteristic frequency. The frequency dependence of the functions v(x,f) and V(x,f) is determined from the data, and v(x,f) and ln V(x,f) are shown to be analytic functions in the lower half of the complex frequency plane, with Re [v(x,f)] a monotonically increasing function of f at fixed x. The linear limit of basilar membrane motion is characterized by a transfer function T(x,f) = (V/V1)v/(1-v), estimated by extrapolating V(x,f;Vu)/Vu to a small membrane velocity V1.T(x,f) and ln T(x,f) are shown to be analytic functions in the lower half of the complex frequency plane. The inverse of the amplitude of the transfer function, which has both a deep dip at f approximately fc(x) and a broad shoulder at lower frequencies, bears a striking resemblance to the neural threshold tuning curve. The functional form of T(x,f) is used to deduce the equation governing the motion of a section of the organ of Corti. Each section acts like a negatively damped harmonic oscillator stabilized at time t by a feedback force proportional to the velocity at the previous time t-tau. The time delay tau is proportional to the oscillator period [tau approximately 1.75/fc(x)]. Like a laser, the organ of Corti pumps energy into harmonic traveling waves. Unlike the laser, the direction of energy flow abruptly reverses as the traveling wave approaches the point of maximum membrane velocity [fc(x) approximately f]. All accumulated wave energy is then pumped back into a small section of the organ of Corti where transduction presumably occurs. Outer hair cells are conjectured to be active elements contributing to the negative damping and feedback of the cochlear amplifier.     

Middle-ear response in the chinchilla and its relationship to mechanics at the base of the cochlea

The responses of the malleus and the stapes to sinusoidal acoustic stimulation have been measured in the middle ears of anesthetized chinchillas using the M?ssbauer technique. With "intact" bullas (i.e., closed except for venting via capillary tubing), the vibrations of the tip of the malleus reach a maximal peak velocity of about 2 mm/s in responses to 100-dB SPL tones in the frequency range 500-6000 Hz; vibration velocity diminishes toward lower frequencies with a slope of about 6 dB/oct. Opening the bulla widely increases the responses to low-frequency stimuli by as much as 16 dB. At low frequencies, malleus response sensitivity with either open or intact bullas far exceeds all previous measurements in cats and matches or exceeds such measurements in guinea pigs. Whether measured in open or intact bullas, phase-versus-frequency curves closely approximate those predicted from the magnitude-versus-frequency curves by minimum phase theory. The stapes responses are similar to those of the malleus, except that stapes response magnitude is lower, on the average, by 7.5 dB at frequencies below 2 kHz and 10.7 dB at 2 kHz and above. Comparison of the responses of the middle ear with those of the basilar membrane at a site 3.5 mm from the stapes indicates that, at frequencies below 150 Hz, the basilar membrane displacement is proportional to stapes acceleration. At frequencies between 150 and 2000 Hz, basilar membrane displacement is proportional to stapes velocity.     

Second quantization in a waveguide with variable cross section

The motion of a system consisting of noninteracting bosons in a waveguide with variable cross section is studied. These particles have transverse as well as longitudinal degrees of freedom, but only a finite number of transverse modes can propagate in the waveguide. While for a waveguide with constant cross section, the numbers of particles in a given state of longitudinal and transverse modes remain constant, in the case of a waveguide with variable cross section there is conversion between these modes, although the total number of particles is conserved. By considering the equations of motion for the annihilation (or creation) operator, it is shown that the boundaries act as an external force, and thus generate localized transverse modes in the waveguide.     

Using optimized wall section to improve low frequency response in a room

Three different wall sections with step shape were applied in the finite element analysis models set up to investigate the effect on low frequency sound field by wall modification. The heights of the step in three cases are taken as equal, random and optimized. The optimized value is obtained by using an optimization process with an objective function of minimum fluctuation in sound field. The frequency responses of rooms with original and modified walls were calculated in a range from 60 Hz to 120 Hz. The results showed that the room with an optimized wall section had the flattest frequency response. Same thing was true as the ratio of the room was changed. The largest improvement on fluctuation reached 4.5 dB. In addition, wall section with semicircle and triangle were studied. The rooms that wall section had optimized radius and heights also gave a better performance than those that had fixed radius and heights. Therefore, it is possible to use optimized wall section to improve low frequency sound field.     

Biomechanically inspired modelling of pedestrian-induced forces on laterally oscillating structures

Despite considerable interest among engineers and scientists, bi-directional interaction between walking pedestrians and lively bridges has still not been well understood. In an attempt to bridge this gap a biomechanically inspired model of the human response to lateral bridge motion is presented and explored. The simple inverted pendulum model captures the key features of pedestrian lateral balance and the resulting forces on the structure. The forces include self-excited components that can be effectively modelled as frequency-dependent added damping and mass to the structure. The results of numerical simulations are in reasonable agreement with recent experimental measurements of humans walking on a laterally oscillating treadmill, and in very good agreement with measurements on full-scale bridges. In contrast to many other models of lateral pedestrian loading, synchronisation with the bridge motion is not involved. A parametric study of the model is conducted, revealing that as pedestrians slow down as a crowd becomes more dense, their resulting lower pacing rates generate larger self-excited forces. For typical pedestrian parameters, the potential to generate negative damping arises for any lateral bridge vibration frequency above 0.43 Hz, depending on the walking frequency. Stability boundaries of the combined pedestrian–structure system are presented in terms of the structural damping ratio and pedestrian-to-bridge mass ratio, revealing complex relations between damping demand and bridge and pedestrian frequencies, due to the added mass effect. Finally it is demonstrated that the model can produce simultaneous self-excited forces on multiple structural modes, and a realistic full simulation of a large number of pedestrians, walking randomly and interacting with a bridge, produces structural behaviour in very good agreement with site observations.     

Frequency response of sloshing in an annular cylindrical tank subjected to pitching excitation

Frequency responses of stable planar and rotary motions in a partially filled annular cylindrical tank, subjected to a pitching excitation at a frequency in the neighborhood of the lowest resonant frequency, are investigated. The nonlinearity of the liquid surface oscillation and the nonlinear coupling between the dominant modes and other modes (e.g., an axisymmetric mode) are considered in the response analysis of the sloshing motion. The basic equations of the liquid motion are derived by using the variational principle and the nonlinear equations of motion of the liquid surface displacement are formulated. The characteristics of the liquid motion in an annular cylindrical tank are discussed. The equations governing the amplitude of the stable planar and rotary liquid motions are derived and the stability of each motion is analyzed. An experiment was carried out using a model tank. It is shown that the nonlinear characteristic of the liquid motion in an annular cylindrical tank is more complicated than that in a circular cylindrical tank. Furthermore, it is shown that the nonlinear analysis is important for estimating the sloshing responses.