On the use of hollow tube geometries for resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) can nondestructively obtain the elastic constants of compact specimens, however many materials have hollow cross-sections and frequency analysis of such geometries is required before inclusion in the RUS methodology. Resonant mode shapes of tubes with length equal to diameter and varying ratios of tube inner to outer diameter (Λ) as well as Poisson's ratio (ν) were identified by eigenvalue analysis using a commercial finite element code. Longitudinal and shear RUS experiments were conducted on tubes with Λ varying between 0 and 0.95 and compared to the numerical results. Simulations predict that the fundamental mode transitions from pure torsion to symmetric or antisymmetric ring bending at Λ = 0.3. The frequency of the first torsion mode is invariant to Λ and unequivocal identification of this mode is obscured by overlap of bending harmonics as Λ approaches 0.95. In the context of rapid calculation of isotropic elastic constants, shear moduli were calculated from the first torsional mode and Poisson's ratio was inferred from the Demarest maps of the mode structure's dependence upon Poisson's ratio. An average shear modulus of 27.5 + 1.5 ∕ -0.6 GPa, about 5% larger than literature values for 6061 aluminum, and ν of 0.33 were inferred. Errors are attributed to tube aspect ratios slightly greater than 1 and weak material anisotropy. Existing analytical solutions for ring bending modes derived from shell approximations and for infinitely long tubes under plane strain assumptions do not adequately describe the fundamental modes for short tubes. The shear modulus can be calculated for all Λ using the existing analytical solution.     

Elastic characterization of closed cell foams from impedance tube absorption tests

A method is presented to determine the bulk elastic properties of isotropic elastic closed-cell foams from impedance tube sound absorption tests. For such foams, a resonant sound absorption is generally observed, where acoustic energy is transformed into mechanical vibration, which in turn is dissipated into heat due to structural damping. This article shows how the bulk Young's modulus, Poisson's ratio, and damping loss factor can be deduced from the resonant absorption. Also, an optimal damping loss factor yielding 100% of absorption at the first resonance is defined from the developed theory. The method is introduced for a sliding edge condition which is an ideal condition. Then, the method is extended to a bonded edge condition which is more easily achievable and additionally enables the identification of the Poisson's ratio. The method is experimentally tested on expanding closed-cell foams to find their elastic properties in both cases. Using the found properties, sound absorption predictions using an equivalent solid model with and without surface absorption are compared to measurements. Good correlations are obtained when considering surface absorption.     

Free-vibration acoustic resonance of a nonlinear elastic bar

Free-vibration acoustic resonance of a one-dimensional nonlinear elastic bar was investigated by direct analysis in the calculus of variations. The Lagrangian density of the bar includes a cubic term of the deformation gradient, which is responsible for both geometric and constitutive nonlinearities. By expanding the deformation function into a complex Fourier series, we derived the action integral in an analytic form and evaluated its stationary conditions numerically with the Ritz method for the first three resonant vibration modes. This revealed that the bar shows the following prominent nonlinear features: (i) amplitude dependence of the resonance frequency; (ii) symmetry breaking in the vibration pattern; and (iii) excitation of the high-frequency mode around nodal-like points. Stability of the resonant vibrations was also addressed in terms of a convex condition on the strain energy density.     

Pulsating one-dimensional detonations in hydrogen–air mixtures

The propagation of one-dimensional detonations in hydrogen–air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit time marching algorithm. The hydrogen–air combustion is modelled with a 9-species, 19-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies for an equivalence ratio range of 0.4–2.0, initial pressure range of 0.2–0.8 bar and different degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel–air equivalence ratio and pressure. For equivalence ratios less than approximately 1.2 and for all pressures, the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures exhibit a period-doubled bifurcation that depends on the initial pressure. Parametric studies over a degree of overdrive range of 1.0–1.2 for stoichiometric mixtures at 0.42 bar initial pressure indicate that stable detonation wave propagation is obtained at the high end of this range. For degrees of overdrive close to one, the detonation wave exhibits a low-frequency mode characterized by large fluctuations in the detonation wave speed. The McVey–Toong short-period wave-interaction theory is in qualitative agreement with the numerical simulations; however, the frequencies obtained from their theory are much higher, especially for near-stoichiometric mixtures at high pressure. Modification of this theory to account for the finite heat-release time significantly improves agreement with the numerically computed frequency over the entire equivalence ratio and pressure ranges.     

Application of a very long cavity laser to atom slowing down and optical pumping

A method to slow down an atomic beam with a counter-propagating resonant laser beam is proposed. The laser radiates across the full Doppler profile of the atomic beam with a longitudinal mode separation which is slightly less than the homogeneous linewidth of the atoms. This allows the atoms to come to rest without the need for frequency tuning or laser chirping. The required mode separation can be obtained from a very long-cavity laser. The application to optical pumping will be also discussed.     

Elastic constants of a plate from impact-echo resonance and Rayleigh wave velocity

A new method is proposed for calculating the dynamic elastic constants of an isotropic plate from measurements of the impact-echo resonance and Rayleigh wave velocity. Poisson's ratio is shown to be a single-valued function of the ratio between thickness frequency and Rayleigh wave velocity. This dependence is derived theoretically from the condition of resonance at the minimum frequency of the first-order symmetric Lamb mode. A finite element model is developed to determine how this frequency varies with Poisson's ratio. The results obtained by modal analysis and the power-spectral density technique are in good agreement with those calculated as the solution of the S1 Lamb mode equation. The method is verified by impact-echo tests on concrete and methacrylate plates. A laser interferometer is used to detect the vibration. Thickness frequencies are accurately identified by applying the multicross-spectral density to the signals detected at several points close to the impact point. In a separate experiment, Rayleigh waves are generated by the mediator technique. The wave velocities are determined from the arrival times of the surface wave at several points. Finally, the main sources of uncertainty are evaluated.     

Stability and a fast calculation method of travel speed of pulse peak in convergence zone

A long-range sound propagation experiment was conducted in the West Pacific Ocean in summer 2013.The signals received by a towed array indicate that the travel speed of pulse peak(TSPP)in the convergence zones is stable.Therefore,an equivalent sound speed can be used at all ranges in the convergence zones.A fast calculation method based on the beam-displace-ment ray-mode(BDRM)theory and convergence zone theory is proposed to calculate this equivalent sound speed.The computation speed of this proposed method is over 1000 times faster than that of the conventional calculation method based on the normal mode theory,with the computation error less than 0.4%compared with the experimental result.Also,the effect of frequency and sound speed profile on the TSPP is studied with the conventional and fast calculation methods,showing that the TSPP is almost independent of the frequency and sound speed profile in the ocean surface layer.     

High precision, short range ultrasonic sensing by means of resonance mode-locking

This report describes a novel method of continuous-wave operation of ultrasonic transducers, which enables short-range measurement with a resolution much finer than the sound wavelength. The transducer is locked into a particular resonant mode of the transducer-gap-reflector system by a resonance-locking phase-locked loop. The resonant frequency depends on the relative coherence of the transmitted and reflected waves, so that a change in the position of the reflecting surface will require a corresponding change in the resonance frequency if the resonant mode is to be retained. A simple system of this type has been implemented using a cheap, commercially available transducer with far-from-optimum characteristics. The system has been found to operate successfully in a range well below the typical ring-down range of a corresponding pulse-echo system, and has displayed a resolution much finer than the sound wavelength for the transducer.     

场分析法与阻抗叠加方法在速调管输出腔间隙阻抗计算中的应用

 从分析速调管输出回路的电磁场分量入手，结合微波电路理论，提出了计算速调管输出回路间隙阻抗的场分析法。对于在谐振模式交叠频带上，群聚电子束电流同时与各模式的阻抗相作用，总阻抗是各模式阻抗的代数叠加的情况，提出了阻抗叠加方法。该方法原则上可求解任意给定间隙电阻所对应的间隙电抗值。计算表明，场分析法与等效间隙阻抗法计算结果最大相对误差为1.5％，阻抗叠加方法计算结果与冷测数据最大相对误差为10％。分析表明，多个谐振模式的引进是速调管输出腔加载滤波器展宽频带的物理实质。     

Finite element simulation of wave propagation in an axisymmetric bar

An accurate solution for high-frequency pulse propagation in an axisymmetric elastic bar is obtained using a new finite element technique that yields accurate non-oscillatory solutions for wave propagation problems in solids. The solution of the problem is very important for the understanding of dynamics experiments in the split Hopkinson pressure bar (SHPB). In contrast to known approaches, no additional assumptions are necessary for the accurate solution of the considered problem. The new solution helps to elucidate the complicated distribution of parameters during high-frequency pulse propagation down the bar as well as to estimate the applicability of the traditional dispersion correction used in the literature for the analysis of wave propagation in a finite bar. Due to the dimensionless formulation of the problem, the numerical results obtained depend on Poisson's ratio, the length of the bar and the pulse frequency, and are independent of Young's modulus, the density and the radius of the bar.     

新型小铷钟微波腔谐振特性的研究

采用模匹配法对一种陶瓷介质填充的圆柱谐振腔TE₀₁₁、TE₁₁₁模的谐振特性进行了理论分析和软件仿真. 计算了该种谐振腔的谐振频率,并与其他理论方法得到的仿真结果进行了比较,验证了理论方法的正确性. 在此基础上,分析了陶瓷介质尺寸对谐振频率的影响. 与目前铷钟广泛使用的微波腔相比,该种谐振腔腔体的体积在很大程度上得到减小,这对于铷原子钟小型化的实现具有重要的作用.     

渐变慢波结构的太赫兹过模表面波振荡器北大核心CSCD

模拟研究了一种在均匀慢波结构后增加渐变慢波结构段的太赫兹过模表面波振荡器,获得了输出功率和模式纯度的显著提高。首先根据S参数方法,研究分析了这种复合高频结构中TM_(01)模的谐振特性。然后采用2.5维PIC(Particle-in-cell)软件UNIPIC,模拟研究了振荡器输出性能随渐变慢波结构周期数的变化关系。结果表明:随着周期数的增加,输出太赫兹波中的TM_(02)和TM_(03)等高次模成分降低,TM_(01)模的功率比例增大至80%以上;选择合适长度的渐变慢波结构,能使得器件输出功率增大50%。     

Investigation of pertubation effect for plasma in TM010-mode microwave excited gas laser

Characteristic equation for the cylindrical TM₀₁₀-microwave plasma cavity is given. Analytical expression and perturbation formula for the resonant frequency of TM₀₁₀ mode dependence of plasma are derived. A comparison between exact and approximate solution shows that the perturbation theory can be used accurately to analyze the detuning of the cavity caused by microwave plasma with a tolerance less than 5%.     

结构和变形对单壁碳纳米管力学性能的影响

使用分子动力学方法模拟了单壁碳纳米管的拉伸变形行为和泊松比,并从单壁碳纳米管晶胞单元的结构特征角度,系统分析了管径、螺旋性和应变对力学性能的影响．模拟结果显示,单臂性碳纳米管(8,8)-(22,22)和锯齿性碳纳米管(9,0)-(29,0)的拉伸弹性变形可以分别达到35％-38％和20％-27％,拉伸条件下这些碳纳米管的弹性模量随管径的增大从960 GPa下降到750 GPa,并且锯齿性碳纳米管的弹性模量比单臂性碳纳米管的弹性模量要高．通过对三根具有相同直径和不同螺旋性的碳纳米管(9,9),(12,6)和(16,0)分别在拉伸和压缩条件下的模拟发现,随着变形的增大,碳纳米管的泊松比将减小;在相同的拉伸应变下,碳纳米管的泊松比随其螺旋角的减小而减小,而在相同的压缩应变下,碳纳米管的泊松比随其螺旋角的减小而增大．     

Resonant vibration control of rotating beams

Rotating structures, like e.g. wind turbine blades, may be prone to vibrations associated with particular modes of vibration. It is demonstrated, how this type of vibrations can be reduced by using a collocated sensor-actuator system, governed by a resonant controller. The theory is here demonstrated by an active strut, connecting two cross-sections of a rotating beam. The structure is modeled by beam elements in a rotating frame of reference following the beam. The geometric stiffness is derived in a compact form from an initial stress formulation in terms of section forces and moments. The stiffness, and thereby the natural frequencies, of the beam depend on the rotation speed and the controller is tuned to current rotation speed to match the resonance frequency of the selected mode. It is demonstrated that resonant control leads to introduction of the intended level of damping in the selected mode and, with good modal connectivity, only very limited modal spill-over is generated. The controller acts by resonance and therefore has only a moderate energy consumption, and successfully reduces modal vibrations at the resonance frequency.     

Light transmission through metallic slit with a bar

The transmission characteristics of a metallic slit with a bar are investigated by using the two-dimensional finite difference time-domain method. It is found that the introduction of a bar enriches the transmission spectrum. As the bar locates at the center of the electric (magnetic) field antinodes, the transmission peaks have longer (shorter) wavelengths in comparison with the corresponding resonant peaks of the single slit. It is true for both the fundamental mode and second order mode. The proposed mode in a previous paper [Y. Wang, Y. Wang, Y. Zhang, S. Liu, Opt. Express 17 (2009) 5014] can well explain the above phenomenon. The increase in ability to accumulate charge or decrease in the length of current flow dominates when the bar lies at different positions, which results in a redshift or blueshift of transmission peaks. Moreover, it is also found that the transmission spectrum of the studied structure can be tuned by adjusting the length and width of the bar. It is expected that our results may be utilized to control the electromagnetic wave in subwavelength optics.     

Resonance spectroscopy of gravitational states of antihydrogen

We study a method to induce resonant transitions between antihydrogen ( \(\bar {H}\) ) quantum states above a material surface in the gravitational field of the Earth. The method consists in applying a gradient of magnetic field which is temporally oscillating with the frequency equal to a frequency of a transition between gravitational states of antihydrogen. Corresponding resonant change in a spatial density of antihydrogen atoms can be measured as a function of the frequency of applied field. We estimate an accuracy of measuring antihydrogen gravitational states spacing and show how a value of the gravitational mass of the \(\bar {H}\) atom can be deduced from such a measurement.     

反射系数相位法计算谐振腔外观品质因数的局限性

 分析了反射系数相位法原理中所采用的完全耦合电路和实际等效电路之间的差异,指出采用反射系数相位法计算谐振腔外观品质因数失效的原因是：传输线与谐振腔只通过部分电感耦合;π模双间隙腔中存在耦合槽。定量计算表明：当谐振腔中耦合电感与非耦合电感之比小于0.1,或者缝模频率小于2π模频率时,反射系数相位法就会失效。结合实际谐振腔的参数值进行分析得出：导致反射系数相位法失效的最主要原因是传输线与谐振腔只通过部分电感耦合,并且耦合电感太小。     

弯曲圆盘换能器与镜像虚源的互辐射作用

建立了弯曲圆盘换能器镜像虚源等效模型,利用脉动球源互作用原理对弯曲圆盘与其镜像虚源的互辐射作用进行理论分析,给出了互辐射阻抗及系统谐振频率的数学表达。提出了虚源互作用的低频换能器设计思想,将刚性反射板引入弯曲圆盘换能器临近辐射面的声场中,通过理论分析、有限元模拟和样机实验研究了低频换能器谐振频率与主要结构参数之间的关系。结果表明,弯曲圆盘与镜像虚源间的互辐射作用可以有效降低换能器的谐振频率,当反射板直径与弯曲圆盘辐射面直径相当时,谐振频率可降低至其自身谐振频率的50%以下;当反射板直径为弯曲圆盘辐射面直径2倍时,谐振频率可降低至37%。      

Efficiency and stability enhancement of a virtual cathode oscillator

A virtual cathode oscillator(VCO) with a resonant cavity is presented and investigated numerically and theoretically,and its efficiency and stability are enhanced. An equivalent circuit method is introduced to analyze the resonant cavity composed of anode foil and feedback annulus, and a theoretical expression for the fundamental mode frequency of the resonant cavity is given. The VCO is investigated in detail with a particle-in-cell method. We obtain the microwave frequencies from simulation, theoretical expression, and relative references, and draw three important conclusions. First, the microwave frequency is a constant when the diode voltage is changed from 588 kV to 717 kV. Second, the fluctuation of the microwave frequency is very small when the AK gap is changed from 1.2 cm to 1.6 cm. Third, the microwave frequency agrees with the theoretical result. The relative error, which is calculated according to the theoretical and simulation frequencies, is only1.7%.