声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

Numerical analysis of shock wave and supersonic turbulent boundary interaction between adiabatic and cold walls

Direct numerical simulations of shock wave and supersonic turbulent boundary layer interaction in a 24° compression ramp with adiabatic and cold-wall temperatures are conducted. The wall temperature effects on turbulence structures and shock motions are investigated. The results are validated against previous experimental and numerical data. The effects of wall cooling on boundary layer characteristics are analysed. Statistical data show that wall cooling has a significant effect on the logarithmic region of mean velocity profile downstream the interaction region. Moreover, the influence of wall temperature on Reynolds stress anisotropy is mainly limited in the near-wall region and has little change on the outer layer. As the wall temperature decreases, the streamwise coherency of streaks increases. Based on the analysis of instantaneous Lamb vector divergence, the momentum transport between small-scale vortices on cold-wall condition is significantly enhanced. In addition, spectral analysis of wall pressure signals indicates that the location of peak of low-frequency energy shifts toward higher frequencies in cold case. Furthermore, the dynamic mode decomposition results reveal two characteristic modes, namely a low-frequency mode exhibiting the breathing motion of separation bubble and a high-frequency mode associated with the propagation of instability waves above separation bubble. The shape of dynamic modes is not sensitive to wall temperature.     

Single-beam analysis of damaged beams: Comparison using Euler–Bernoulli and Timoshenko beam theory

A new general formulation that is applicable to the damaged, linear elastic structures ‘unified framework’ is used to obtain analytical expressions for natural frequencies and mode shapes. The term mode shapes is used to mean the displacement modes, the section rotation modes, the sectional bending strain modes and sectional shear strain modes. The formulation is applicable to damaged elastic self-adjoint systems. The formulation has two unique aspects: First, the theory is mathematically rigorous since no assumptions are made regarding the physical behavior at a damage location, therefore there is no need to substitute the damage with a hypothetical elastic element such as a spring. Since the beam is not divided at the damage location, rather than an 8 by 8, only a 4 by 4 matrix is solved to obtain the natural frequencies and mode shapes. Second, the inertia effects due to damage which have till now been neglected by researchers are accounted for. The formulation uses a geometric damage model, perturbation of mode shapes and natural frequencies, and a modal superposition technique to obtain and solve the governing differential equation. Timoshenko beam theory is then taken as an example, and its results are compared with results using Euler–Bernoulli beam theory and finite element models. The range of applicability of the two theories is ascertained for damage characteristics such as depth and extent of damage and beam characteristics such as slenderness ratio and Poisson?s ratio. The paper considers rectangular notch like non-propagating damage as an example of the damage.     

Vibration analysis of annular-like plates

The existence of eccentricity of the central hole for an annular plate results in a significant change in the natural frequencies and mode shapes of the structure. In this paper, the vibration analysis of annular-like plates is presented based on numerical and experimental approaches. Using the finite element analysis code Nastran, the effects of the eccentricity, hole size and boundary condition on vibration modes are investigated systematically through both global and local analyses. The results show that analyses for perfect symmetric conditions can still roughly predict the mode shapes of “recessive” modes of the plate with a slightly eccentric hole. They will, however, lead to erroneous results for “dominant” modes. In addition, the residual displacement mode shape is verified as an effective parameter for identifying damage occurring in plate-like structures. Experimental modal analysis on a clamped-free annular-like plate is performed, and the results obtained reveal good agreement with those obtained by numerical analysis. This study provides guidance on modal analysis, vibration measurement and damage detection of plate-like structures.     

A STUDY ON MODE LOCALIZATION PHENOMENA: INFLUENCES OF THE STIFFNESS AND THE MASS OF THE COUPLER ON MODE LOCALIZATION

The influences of the stiffness and the mass that constitutes a coupler between two substructures of the periodic structures on mode localization are studied theoretically, and the results are confirmed by numerical examples. The results of this study show that the mass as well as the stiffness of the coupler has significant influences on the mode localization and weak coupling conditions. The mass of the coupler makes a periodic structure sensitive to mode localization especially in higher modes while the stiffness does in all modes. By introducing the large mass and the large stiffness into the coupler, an interesting phenomenon of delocalization can be observed in some modes for which mode localization does not occur or is very weak although structural disturbances are severe. A simple structure consisting of two substructures, each with a lumped mass and two stiffnesses, and a coupler is analysed theoretically. For example, structures for numerical analysis, simply supported continuous two-and three-span beams with couplers having a rotational stiffness and a rotational mass are considered.     

Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry

An optical low-coherence interferometry technique has been used to simultaneously resolve the mode profile and to measure the intermodal dispersion of guided modes of a few-mode fiber. Measurements are performed using short samples of fiber (about 50 cm). There is no need for a complex mode-conversion technique to reach a high interference visibility. Four LP mode groups of the few-mode fiber are resolved. Experimental results and numerical simulations show that the ellipticity of the fiber core leads to a distinct splitting of the degenerate high-order modes in group index. For the first time, to the best of our knowledge, it has been demonstrated that degenerate LP11 modes are much more sensitive to core shape variations than the fundamental modes and that intermodal dispersion of high-order degenerate modes can be used for characterizing the anisotropy of an optical waveguide.     

磷化铟单晶生长中的传热和流动分析

用有限元法对轴向磁场存在下3英寸磷化铟单晶液封提拉法生长中的传热和流动进行了求解．结果表明:液封改变了晶体表面被封部分的换热,进而影响生长界面的形状．增加磁场强度能有效减弱熔体和封层内的流动,并使生长界面形状发生变化。增加提拉速度,生长界面形状由凸变凹．随晶体转速的增加,多涡胞流动出现．     

The behavior of higher order mode shape derivatives in damaged,beam-like structures

This work considers the effect that damage has upon the higher order derivatives of mode shapes of structures having primarily beam-like vibration. Via numerical investigations, the sensitivity of various damage related parameters in inducing changes in these higher order modal derivatives is determined, leading to a more complete understanding of what factors make the most contribution to significant changes in these derivatives. It is concluded that higher order mode shape derivatives (e.g., modal curvature, third derivative, and fourth derivative) are better indicators of damage than the mode shapes. Three distinct types of response for the damage-induced higher order derivative discontinuities are identified as three key parameters (the mass loss, stiffness loss, and damage radius scale) vary. From this, formal approximations are obtained for the expected forms of the higher order derivative discontinuities based upon the underlying behavior predicted by a simple relation among these three parameters. These approximations are checked with numerical simulations, and an excellent level of agreement is observed under appropriate conditions. Finally, the potential of these higher order derivative changes for indicating the presence and location of damage in a global setting is examined.     

Analytical research on structural-acoustic coupling of a cavity surrounded by flexible panel

The structural-acoustic coupling characteristics, mechanisms, effect of structural-acoustic coupling on natural mode and natural frequencies of the system are analyzed theoretically and numerically. Formulae for the natural frequencies of the coupled system are derived. Some new conclusions are obtained. Analytical results demonstrate that the strongly coupled system indicates obvious closed-loop feedback characteristics, whereas the weakly coupled system indicates obvious feedforward characteristics, and it is because of the presence of the feedback loop that the natural characteristics and natural frequencies are changed. Cluster coupling characteristic between the structural and acoustic modes for the regular cavity and panel system is found, which determines the coupling interaction between the flexible panel and cavity. Any mode in one mode cluster only interferes the modes and the modal natural frequencies in the same cluster independently. The modal cluster coupling changes not only the natural frequencies of the system but also the modal order and structural mode shape.     

Design of shaped piezoelectric modal sensor for beam with arbitrary boundary conditions by using Adomian decomposition method

The theory for designing distributed piezoelectric modal sensors is well established for beam structures. However, the current modal sensor theory is limited in scope in that it can only be applied in the case of classical boundary conditions (i.e., either clamped, free, simply supported or sliding). In this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a beam with arbitrary boundary conditions is proposed, using the Adomian decomposition method (ADM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a function of the second spatial derivative of the structural mode shape function. Based on the ADM and employing some simple mathematical operations, the closed-form series solution of the second spatial derivative of the mode shapes can be determined. Then the shapes of the designed modal sensors are obtained. Finally, some numerical examples are given to demonstrate the feasibility of the proposed modal sensors. It is shown that, for classical boundary conditions, the shapes of the modal sensors based on the ADM agree well with analytical and numerical results given in the literature. For general boundary conditions it is found that the shape of the modal sensors is influenced by the number of modes of interest because the second spatial derivatives of the mode shapes are not orthogonal to one another. The modal sensors for general boundary conditions can be considered as modal filters within a limited frequency band.     

A new formulation for the existence and calculation of nonlinear normal modes

A new formulation is presented here for the existence and calculation of nonlinear normal modes in undamped nonlinear autonomous mechanical systems. As in the linear case an expression is developed for the mode in terms of the amplitude, mode shape and frequency, with the distinctive feature that the last two quantities are amplitude and total phase dependent. The dynamic of the periodic response is defined by a one-dimensional nonlinear differential equation governing the total phase motion. The period of the oscillations, depending only on the amplitude, is easily deduced. It is established that the frequency and the mode shape provide the solution to a 2π-periodic nonlinear eigenvalue problem, from which a numerical Galerkin procedure is developed for approximating the nonlinear modes. The procedure is applied to various mechanical systems with two degrees of freedom.     

VIBRATION ANALYSIS OF TWISTED CANTILEVERED CONICAL COMPOSITE SHELLS

The finite element method based on the Hellinger-Reissner principle with independent strain is applied to the vibration problem of cantilevered twisted plates and cylindrical, conical laminated shells. With a small number of elements, the present assumed strain finite element method is validated by convergence tests and numerical tests, comparing with the previous published vibration results for cantilevered conical shell. Computational effort and virtual storage reduce significantly due to good convergence. This study presents the twisting angle effect on vibration characteristics of conical laminated shells. Parameter studies with varying shallowness of cylindrical and conical shells are carried out. As the curvature increases, the fundamental mode shape changes from twisting mode to bending mode. For shells with a large curvature, the fundamental frequency, which is always characterized to bending mode, is almost constant independent of twisting angle. The twisting angle affects greatly twisting frequency and mode shape.     

流动等离子体对托卡马克中撕裂模的影响

本文分析了托卡马克中的等离子体具有一个整体流动速度时,撕裂模的活动情况。分析与数值计算指出,等离子体的整体流动(等价于具有一个旋转频率)不影响撕裂模的活动,只是使撕裂模具有一个和等离子体相同的旋转频率。外加螺旋场在撕裂层能有效地抑制住等离子体的旋转。螺旋场对撕裂模的稳定作用不受等离子体旋转的影响。 关键词：     

ON THE RELATION BETWEEN COMPLEX MODES AND WAVE PROPAGATION PHENOMENA

This paper discusses the well-known, but often misunderstood, concept of complex modes of dynamic structures. It shows how complex modes can be interpreted in terms of wave propagation phenomena caused by either localized damping or propagation to the surrounding media. Numerical simulation results are presented for different kinds of structures exhibiting modal and wave propagation characteristics: straight beams, an L-shaped beam, and a three-dimensional frame structure. The input/output transfer relations of these structures are obtained using a spectral formulation known as the spectral element method (SEM). With this method, it is straightforward to use infinite elements, usually known as throw-off elements, to represent the propagation to infinity, which is a possible cause of modal complexity. With the SEM model, the exact dynamic behavior of structures can be investigated. The mode complexity of these structures is investigated. It is shown that mode complexity characterizes a behavior that is half-way between purely modal and purely propagative. A coefficient for quantifying mode complexity is introduced. The mode complexity coefficient consists of the correlation coefficient between the real and imaginary parts of the eigenvector, or of the operational deflection shape (ODS). It is shown that, far from discontinuities, this coefficient is zero in the case of pure wave propagation in which case the plot of the ODS in the complex plane is a perfect circle. In the other extreme situation, a finite structure without damping (or with proportional damping), where the mode shape (or the ODS) is a straight line on the complex plane, has a unitary complexity coefficient. For simple beam structures, it is shown that the mode complexity factor can also be calculated by curve-fitting the mode to an ellipse and computing the ratio of its radii.     

Tactile Response Characterization of a Dynamic System Using Craig-Bampton Method

Vibrational characteristics in small horizontal axis wind turbine system are presented in this study with a system concept called tactile response and substructuring. The main focus is on managing the dynamic properties like vibration, noise, and harshness that occur during the operational mode. Tactile response is defined as the response of subsystem which is induced when a human body touches a vibrating system. Sub structuring is a computational method used to reduce the dynamic behavior of a large complex system with a smaller number of degrees of freedom without disturbing the mesh size of the model. Sub structuring has the ability to combine numerical results along with the experimental results. Combination of substructuring and tactile response is applied in this study. Mode shapes of the system are analyzed and results obtained are correlated within this study to provide better optimization of the results. Wind turbine excited with wind energy depends on wind speed. Torsional vibration has a significant role in determining dynamic properties. Torsional vibration is caused as a result of the rotation of the turbine blade and depends on wind speed. The study gives importance to investigating the ability to simulate the numerical method and tactile response to predict and improve dynamic properties.     

基于声辐射模态的有源结构声传入及其辐射控制

从辐射模态的概念和角度研究利用结构误差传感方法对弹性封闭空间结构声辐射进行传感和有源控制。首先分析了辐射模态的数学和物理意义并揭示了辐射模态与声腔模态之间的内在耦合关系。通过声辐射模态建立了弹性封闭空间结构声辐射传感和有源控制模型,并提出了通过传感器阵列测量结构表面有限点的振速分布和设计特定的辐射模态空间滤波器来获得控制所需的误差信号。在此基础上对封闭空间结构声辐射有源控制和误差传感策略进行了深入的理论和数值仿真分析,重点讨论了传感器的数量和布放对辐射模态传感及其有源控制效果的影响。结果表明:辐射模态与声腔模态的耦合具有严格的选择性,各阶辐射模态的形状和与相耦合的主导声模态在耦合面上的形状非常相似;利用结构传感技术传感封闭空间的辐射模态时测点不足或空间采样不足将可能产生较严重的模态泄漏问题,使得不希望的结构模态泄露进所测的辐射模态当中来。在低频范围内,一般只需传感并最小化前三阶有效辐射模态声势能,在更低频和空间声模态频率附近,只需最小化前一阶最有效辐射模态声势能,便能和总声势能最小化策略控制效果基本一样。      

二维抛物线离散映射的动力学研究

由两个一维抛物线离散映射作推广并非线性耦合,实现了一个新的二维抛物线离散映射.利用不动点稳定性分析和映射分岔分析,研究了所提出的二维离散映射的复杂动力学行为及其吸引子的演变过程,阐述了它所特有的共存分岔模式和快慢周期振荡效应等动力学特性.研究结果表明:二维抛物线离散映射具有动力学特性调节和动态幅度调节的两个功能不同的控制参数,存在Hopf分岔、分岔模式共存、锁频和周期振荡快慢效应等非线性物理现象.并基于微控制器实现的数字电路验证了相应的理论分析和数值仿真结果. 关键词： 二维离散映射 分岔 吸引子 参数     

Mode shapes analysis of a cracked beam and its application for crack detection

In this paper, mode shapes of a cracked beam with a rectangular cross section beam are analysed using finite element method. The 3D beam element is applied for this finite element analysis. The influence of the coupling mechanism between horizontal bending and vertical bending vibrations due to the crack on the mode shapes is investigated. Due to the coupling mechanism the mode shapes of a beam change from plane curves to space curves. Thus, the existence of the crack can be detected based on the mode shapes: when the mode shapes are space curves there is a crack in the beam. Also, when there is a crack, the mode shapes have distortions or sharp changes at the crack position. Thus, the position of the crack can be determined as a position at which the mode shapes exhibit such distortions or sharp changes. While in previous studies using 2D beam element, distortions in the mode shapes caused by a small crack could not be detected, these distortions in the case using the 3D beam element can be amplified and inspected clearly by using the projections of the mode shapes on appropriate planes. The quantitative analysis is also implemented to relate the size and position of the crack with the observed coupled modes. These results can be applied for crack detection of a beam. In this paper, the stiffness matrix of a cracked element obtained from fracture mechanics is presented and numerical simulations of three case studies are provided.     

Natural frequencies and vibration modes of laminated composite plates reinforced with arbitrary curvilinear fiber shape paths

The development of tow-placement technology has made it possible to control fiber tows individually and place fibers in curvilinear distinct paths in each layer of a laminated plate. This paper presents an analytical method for determining natural frequencies and vibration modes of laminated plates having such curvilinear reinforcing fibers. Spline functions are employed to represent arbitrarily shaped fibers, and Ritz solutions are used to derive frequency equations using series type shape functions. The strain energy is evaluated by numerical integration involving the fiber orientation angle, and is calculated using the derivative of the spline function in minute intervals. The results show that the natural frequencies obtained by the present method agree well with results from finite element analyses. The vibration mode shape contour plots of the plates are seen to reflect clear influences of the fiber shapes.     

激光诱导间质肿瘤热疗的数值模拟和实验研究

本文在考虑生物组织物性动态变化的情况下建立了激光诱导间质肿瘤热疗(LITT)的物理数学模型,采用MonteCarlo方法数值模拟了LITT中激光能量在生物组织内的传输过程,基于Pennes生物传热方程和Arrhenius方程数值求解了组织内的温度分布和热损伤体积的变化,分析了热物性及血液灌注率的动态变化对LITT过程的影响,并与相应的离体实验结果进行了对比。数值模拟结果表明,组织的热物性及血液灌注率的动态变化对于热损伤体积的变化具有重要的影响。因此在激光诱导间质肿瘤热疗的数值模拟中应该考虑热物性及血液灌注率的动态变化以期为临床治疗方案的制定提供更为准确的依据。