模式转换环形耦合振动超声辐射器

提出了一种新型耦合振动环形超声辐射器,辐射器由纵振换能器及变幅杆激励特定尺寸的金属圆环,使其能有效地将纵向振动转化为圆环的径向轴向耦合振动从而向环的径向、轴向辐射超声波,并且在环的中心形成聚焦声场。推导了该辐射器的等效电路,给出了等效电路法和有限元法优化设计环形超声辐射器的详细过程。研究了耦合振动环形超声辐射器的谐振特性及其辐射声场特性,根据理论计算结果加工了相应的环形超声辐射器,实验测试结果与理论计算结果符合得较好。本文提出的模式转换环形耦合超声辐射器可望在声化学等液体处理领域获得应用。     

In-plane vibrations of circular rings

Except in a few cases rings have been treated one-dimensionally as curved beams in analyses to determine their frequencies of vibration. Consequently, for thick rings there are large discrepancies between theoretical and experimental results. In this paper an analysis is carried out in which account is taken of the warping of the cross section. The displacement v in the circumferential direction is assumed to be of the form v₀ + v₁y + v₃y³ + v₅y⁵, where the v_i are functions of the angular co-ordinate θ. The frequencies of free vibration are determined by using the principle of minimum total potential energy. Numerical calculations are made for a ring of rectangular cross section. Results are in good agreement with experimental ones.     

Accurate free vibration analysis of thick laminated circular plates with attached rigid core

This paper deals with the free vibration behavior of laminated transversely isotropic circular plates with axisymmetric rigid core attached at the center. The governing equations of motion are obtained based on Mindlin's first-order shear deformation plate theory. Two possible categories of vibration modes related to up-down translation of the core and wobbly rotation of the core about a diameter are studied. Accurate natural frequencies hitherto not reported in the literature are presented for a wide range of thickness-to-radius ratio, inner-to-outer radius ratio, mass and moment of inertia ratios of the core and various boundary conditions at the outer edge of the plate. Numerical results are compared with those of a three-dimensional finite element method (3-D FEM) to demonstrate the high accuracy and reliability of the current analysis.     

Study on the step-type circular ring ultrasonic concentrator in radial vibration

In this paper, the plane radial vibration of an isotropic metal thin circular rings is studied and its equivalent circuit model is obtained. Based on the equivalent circuit model, the step-type circular ring concentrator consisting of two metal thin circular rings in radial vibration is analyzed. Its compound equivalent circuit is derived and the resonance frequency equation is obtained. The relationship between the resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions is analyzed. The resonance frequency of the step-type radial concentrator is calculated based on the resonance frequency equation. For comparison, the resonance frequency of the step-type radial concentrator is also obtained by using numerical method. It is illustrated that the resonance frequencies from these two methods are in a good agreement with each other.     

Optimization design of high power ultrasonic circular ring radiator in coupled vibration

This paper presents a new high power ultrasonic (HPU) radiator, which consists of a transducer, an ultrasonic horn, and a metal circular ring. Both the transducer and horn in longitudinal vibrations are used to drive a metal circular ring in a radial-axial coupled vibration. This coupled vibration cannot only generate ultrasound in both the radial and axial directions, but also focus the ultrasound inside the circular ring. Except for the radial-axial coupled vibration mode, the third longitudinal harmonic vibration mode with relative large vibration amplitude is also detected, which can be used as another operation mode. Overall, the HPU with these two vibration modes should have good potential to be applied in liquid processing, such as sonochemistry, ultrasonic cleaning, and Chinese herbal medicine extraction.     

In-plane free vibration analysis of cable-arch structure

Cable-stayed arch bridge is a new type of composite bridge, which utilizes the mechanical characters of cable and arch. Based on the supporting members of cable-stayed arch bridge and of erection of arch bridge using of the cantilever construction method with tiebacks, we propose a novel mechanical model of cable-arch structure. In this model, the equations governing vibrations of the cable-arch are derived according to Hamilton's principle for dynamic problems in elastic body under equilibrium state. Then, the program of solving the dynamic governing equations is ultimately established by the transfer matrix method for free vibration of uniform and variable cross-section, and the internal characteristics of the cable-arch are investigated. After analyzing step by step, the research results approve that the program is accurate; meanwhile, the mechanical model and method are both valuable and significant not only in theoretical research and calculation but also in design of engineering.     

Study on the radial vibration and acoustic field of an isotropic circular ring radiator

Based on the exact analytical theory, the radial vibration of an isotropic circular ring is studied and its electro-mechanical equivalent circuit is obtained. By means of the equivalent circuit model, the resonance frequency equation is derived; the relationship between the radial resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions, the material property is analyzed. For comparison, numerical method is used to simulate the radial vibration of isotropic circular rings. The resonance frequency and the radial vibrational displacement distribution are obtained, and the radial radiation acoustic field of the circular ring in radial vibration is simulated. It is illustrated that the radial resonance frequencies from the analytical method and the numerical method are in good agreement when the height is much less than the radius. When the height becomes large relative to the radius, the frequency deviation from the two methods becomes large. The reason is that the exact analytical theory is limited to thin circular ring whose height must be much less than its radius.     

In-plane vibrations of an elastically cantilevered circular arc with a tip mass

Upper and lower bounds are determined for the fundamental frequency of in-plane, transverse vibration of the structural system described in the title in the case of constant cross-section and moment of inertia. The upper bound is determined by approximating the fundamental mode shape with a polynomial co-ordinate function in the angular co-ordinate which includes an exponential optimization parameter. The fundamental frequency equation is generated by means of the Rayleigh-Ritz method and the resulting upper bound is minimized with respect to the previously mentioned exponential parameter. The lower bound for the frequency coefficient is obtained by means of an extension of Dunkerley's method. It is felt that the methodologies developed in the present study are especially useful in the case of variable cross-section of the arch structure, presence of internal supports, etc.     

厚圆盘弯曲振动研究

当厚跨比大于五分之一时,研究板弯曲振动中的剪切应力及由此引起的剪切、扭转变形等就不能忽略,经典的薄板理论将失效.从声学应用的角度,基于Mindlin板理论,本文推导了厚圆盘弯曲振动径向位移和横向位移的解析表达式,并得到了自由、简支、固定边界条件下的频率方程.解析方法计算得到的前几阶振型对应的频率与有限元方法计算的结果基本相符,与实验测试结果基本一致.本文的结果对厚圆盘弯曲振动辐射器的设计提供了理论参考. 关键词： 厚圆盘 弯曲振动 频率方程     

Open loop control of vortex-induced vibration of a circular cylinder

In this paper both numerical and experimental investigations have been carried out to suppress the vortex-induced vibration (VIV) of a circular cylinder in an electrically low-conducting fluid. The electromagnetic forces (Lorentz forces) in the azimuthal direction were generated through the mounted electrodes and magnets locally on the surface of the cylinder, which have been proved having an accelerating effect to the fluid on the surface of the cylinder. Results of computations are presented for synchronous vibration phenomenon of a cylinder at Re=200, which are in good agreement with previous computational results. With the Lorentz forces loaded, the VIV of the cylinder has been suppressed successfully. Experimental results have also shown the same tendency and are in reasonable agreement with the numerical results.     

均匀带电圆环的电场强度

求出了均匀带电圆环的电场强度,给出了它在3种坐标系里的表达式.     

Three-dimensional vibration analysis of a torus with circular cross section

The free vibration characteristics of a torus with a circular cross section are studied by using the three-dimensional, small-strain, elasticity theory. A set of three-dimensional orthogonal coordinates system, comprising the polar coordinate (r, theta) at each circular cross section and the circumferential coordinate phi around the ring, is developed. Each of the displacement components u(r), v(theta), and w(phi) in the r, theta, and phi directions, respectively, is taken as a product of the Chebyshev polynomials in the r direction and the trigonometric functions in the theta and phi directions. Eigenfrequencies and vibration mode shapes have been obtained via a three-dimensional displacement-based extremum energy principle. Upper bound convergence of the first seven eigenfrequencies accurate to at least six significant figures is obtained by using only a few terms of the admissible functions. The eigenfrequency responses due to variation of the ratio of the radius of the ring centroidal axis to the cross-sectional radius are investigated in detail. Very accurate eigenfrequencies and deformed mode shapes of the three-dimensional vibration are presented. All major modes such as flexural thickness-shear modes, in-plane stretching modes, and torsional modes are included in the analysis. The results may serve as a benchmark reference for validating other computational techniques for the problem.     

Radiation efficiency of a baffled circular plate in flexural vibration

The radiation efficiency of an edge-clamped circular plate, which is vibrating flexurally in one of its natural modes and is mounted in an infinite baffle, is theoretically determined from the total power radiated to the far field. The vibrations of the plate are investigated both by the classical plate theory and by the improved plate theory (Mindlin plate theory). Approximation formulae for the low frequency region are derived, and curves covering the entire frequency range for the first fifteen modes are obtained through numerical calculation. Except for frequencies much higher than the critical frequency, there exist some differences in the radiation efficiencies between the results obtainedby the two theories. The difference increases with the thickness of the plate and with the mode numbers, especially for modes having many nodal diameters.     

Distributed fiber-optic vibration sensor using a ring Mach-Zehnder interferometer

A novel distributed fiber-optic vibration sensing system is proposed and demonstrated. By employing a ring Mach-Zehnder interferometer (MZI) structure as the sensing section, both position and frequency can be determined by combining two phase signals from the ring configuration. A spatial resolution better than 38 m is successfully verified in a 1.01 km prototype system of single vibration. Moreover, the feasibility of separately locating multiple vibrations is also theoretically simulated and experimentally investigated.     

软x射线磁性圆二色吸收谱研究铁单晶薄膜的面内磁各向异性

利用软x射线磁性圆二色(XMCD)吸收谱测得Fe/MgO膜不同磁化方向的轨道磁矩和自旋磁矩.实 验表明，沿铁单晶薄膜的不同方向，铁原子轨道磁矩的改变量达到600%以上，而自旋磁矩的 变化约50%，但原子的总磁矩没有如此大的改变.结合常规方法分析了铁薄膜的宏观磁各向异 性性质，半定量地获得磁矩与宏观各向异性能的关系，并对样品的磁矩和磁各向异性能进行 了比较. 关键词： x射线磁性圆二色 磁各向异性 磁性薄膜     

In-plane free vibration analysis of combined ring-beam structural systems by wave propagation

This paper presents a systematic, wave propagation approach for the free vibration analysis of networks consisting of slender, straight and curved beam elements and complete rings. The analysis is based on a ray tracing method and a procedure to predict the natural frequencies and mode shapes of complex ring/beam networks is demonstrated. In the wave approach, the elements are coupled using reflection and transmission coefficients, and these are derived for discontinuities encountered in a MEMS rate sensor consisting of a ring supported on an array of folded beams. These are combined, taking into account wave propagation and decay, to provide a concise and efficient method for studying the free vibration problem. A simplification of the analysis that exploits cyclic symmetry in the structure is also presented. The effects of decaying near-field wave components are included in the formulation, ensuring that the solutions are exact. To illustrate the effectiveness of the approach, several numerical examples are presented. The predictions made using the proposed approach are shown to be in excellent agreement with a conventional FE analysis.