参数不定的旋转圆盘在有界扰动下混沌振动的滑模变结构控制

为了消除具有不确定参数的旋转圆盘横向混沌振动,克服其对整个系统及工作状况的不利影响,假设作用在旋转圆盘上的集中力不确定且有界,并鉴于干扰的普遍存在性,对有界扰动下的旋转圆盘横向振动的四维非线性方程进行了复杂动力学特征分析,包括相轨迹图、Lyapunov指数和庞加莱映射图,这些特征加深了对其的认识,同时也证明该四维动力系统含有混沌吸引子.为了保证系统控制的鲁棒性,利用滑模变结构法,将旋转圆盘从混沌轨道先后控制到任意固定点和周期轨道,并用MATLAB模拟验证其有效性.结果证明,用滑膜变结构法能够使系统严格地跟 关键词： 旋转圆盘 混沌 滑模变结构控制 有界扰动     

On the existence of higher waves in a layer of superfluid helium

The two implicit equations that contain the dispersion laws of waves propagating in a He II layer of variable thickness are formally investigated for solutions that go beyond those associated with the layer modifications of first and second sound: A series of symmetric and antisymmetric layer modes are found to exist by calculating the distribution of roots of the dispersion equations in the complex wave number plane as a function of layer thickness and angular frequency. All these modes turn out to be strongly attenuated and can be regarded as layer modifications of the viscous wave. Phase velocities, attenuation coefficients, and velocity profiles of some of them are calculated numerically.     

Regimes of terminal motion of sliding spinning disks

Analysis of the frictional motion of a uniform circular disk of radius sliding and spinning on a horizontal table reported by Farkas et al. [Phys. Rev. Lett. 90, 248302 2003] shows that the disk always stops sliding and spinning at the same instant with a terminal speed ratio epsilon = v/Romega = 0.653. We show that different terminal behaviors can be found when one considers the motion of a two-tier disk with lower section thickness H(1) and radius R(1), and upper section thickness H(2) and radius H(3). The terminal motion may be analyzed in terms of the normalized radius of gyration k. It is found that while translation and rotation cease simultaneously, their terminal ratio epsilon(0) either vanishes when k > sq.root(2/3), is a nonzero constant when k < 1/2 < k < sq.rt (2/3), or diverges when k < 1/2. Experiments performed with plastic disks sliding on a nylon fabric stretched over a horizontal plate qualitatively corroborate the three different types of terminal motion.     

On the existence of longitudinal or flexural waves in rods at nonlinear higher harmonics

This article theoretically studies the conditions for existence of longitudinal or flexural waves in nonlinear, isotropic rods and presents numerical simulations corroborating the theoretical results. It has been known that the existence of guided waves at nonlinearity induced double harmonics is subject to constraints which arise from the potential of power flux transfer from the primary generating mode to the generated higher order modes. The knowledge about the behavior of waves in rods at harmonics higher than double is still limited. This gap was addressed here by the method of perturbation coupled with wavemode orthogonality and forced response. This reduces the nonlinear problem to a forced linear problem which was subsequently investigated to formulate an angular order-based constraint as the condition of existence/nonexistence of nonlinearity-driven higher harmonics of longitudinal and flexural waves in rods.     

On the existence of ion-acoustic solitary waves in a gravitating dusty plasma having charge fluctuation

Theoretical investigation on the propagation of ion-acoustic waves in an unmagnetized self-gravitating plasma has been made for the existence of solitary waves using the reductive perturbation method. It is observed that nonlinear excitations follow a coupled third-order partial differential equation which is slightly different from the usual case of coupled Korteweg-de Vries (K-dV) system. It appears that the system so deduced is a two-component generalization of the previous one derived by Paul et al. (1999) in which it was shown that ion-acoustic solitary waves can not exist in such system.     

圆管结构中的非线性周向导波*

采用将二阶微扰近似与模式展开分析相结合的方法,可从理论上有效求解圆管结构中的非线性周向导波问题。通过数值计算和有限元仿真发现,基频与二倍频周向导波模式的相速度匹配程度,可显著影响二倍频周向导波模式随传播周向角的积累增长程度。针对基频与二倍频周向导波模式的相速度和群速度均相匹配的情形,通过实验研究发现,周向导波确可存在强烈的非线性效应,且周向导波的二次谐波发生效应可对圆管早期损伤状态做出敏感的响应。文中给出的有关结果,可为进一步开展非线性周向导波的研究工作奠定理论和实验基础。     

激光在管道中激发周向导波的有限元模拟

以超声的热弹激发机理为基础，建立了模拟激光在管道中激发周向导波的有限元模型.为了验证模型的正确性，根据Gao等人报道的实验条件［J. Appl. Phys. 91, 6114 (2002)］进行了模拟，理论模拟结果与Gao等人的实验结果符合很好，说明本数值模型的正确性.在此基础上，模拟激光在不同厚度、不同曲率半径的管道内激发的周向导波波形，同时分析了激光在管道中激发的周向导波波形与平板中激发Lamb波的差异，以及管道厚度和曲率半径对激光激发周向导波的影响.     

On the existence of long-wavelength shear-horizontal surface waves on the bcc (001) surface

Long-wavelength, low-frequency shear-horizontal surface waves are found to exist along 〈100〉, but not 〈110〉, directions of propagation on the (001) face for a simple but fairly realistic model of monatomic body-centered cubic crystals. This domain of existence contrasts with that found previously on the (001) face of monatomic simple cubic and both monatomic and rocksalt face-centered cubic structures, where such waves exist along 〈110〉, but not 〈100〉.     

充水圆柱壳声散射的环绕波分析

研究了内部充水圆柱壳散射声场的构成。采用弹性薄壳理论和Sommerfeld-Watson变换(SWT)方法导出散射声场的解析解。数值搜索环绕波的复波数极点,比较圆柱壳体内部真空和内部充水两种情况下表面环绕波的相速度、衰减等性质。用镜反射波和环绕波的叠加合成反向散射形态函数,与简正级数解符合良好。计算流体附加环绕波的回波时序并与实验数据对照。结果表明,流体附加环绕波的再辐射是内部充水圆柱壳的形态函数出现更加丰富的共振峰和回波结构形成的重要原因。     

On the dynamics,existence of chaos,control and synchronization of a novel complex chaotic system

In this paper, the authors have studied the dynamics of a novel complex chaotic system with fractional order derivative and found the existence of chaos. The novel complex system is simulated for integer as well as fractional orders which shows some unusual phenomena. The main contribution of this effort is an implementation of the Largest Lyapunov Exponent (LLE) criteria based on Wolf’s algorithm. The conditions for chaos control based on the fractional Routh–Hurwitz stability conditions and feedback control are given. Also synchronization between a fractional order novel chaotic system and a controlled fractional order novel system using the modified adaptive projective synchronization method for different scaling matrices has been obtained. Numerical simulation results are carried out using the Adams–Bashforth–Moulton method.     

Analysis of circumferential waves on a water-filled cylindrical shell

The formation of scattering field from a water-filled cylindrical shell was studied. The analytic solutions of scattering field are derived using elastic thin shell theory and Sommerfeld-Watson Transformation(SWT) method.Complex wave-number poles of circumferential waves are found numerically,the phase speed and attenuation of circumferential waves between the situation of a hollow cylindrical shell and a water-filled cylindrical shell are compared. The synthesis of backscattering form functions which are sum of specular reflection component and circumferential waves is consistent with normal mode result.The calculated echo sequences of additional fluid circumferential waves are compared with experimental results. The results show that richer resonance peaks appeared in the backscattering form functions of a water-filled cylindrical shell and the formation of echo’s structure are due to re-radiation effects of additional fluid circumferential waves.     

Characterization of circumferential guided waves in a cylindrical cortical bone-mimicking phantom

The femoral neck cortical shell was recently demonstrated to act like a waveguide for circumferential waves. Femoral neck assessment with ultrasound could be enhanced by guided waves measurement. In this study, the decomposition of the time reversal operator (DORT) method is used to measure the phase velocities of circumferential guided modes in a circular tube with dimensions characteristic of femoral neck. The tube is made of a bone-mimicking material. Five guided modes are obtained and compared to theoretical predictions. The work substantiates the feasibility of measuring guided waves in a relatively thick tube of attenuating material with the DORT method.     

旋转致密双星的引力波特征

研究了轨道和旋转效果到2.5阶后牛顿旋转致密双星拉格朗日动力学与引力波的关系, 分析了有序和混沌轨道的引力波特征.发现当加速度不考虑辐射项时, 有序双星系统辐射的引力波具有周期或拟周期的特征, 而混沌双星系统辐射的引力波却具有明显的混沌特征.当加速度含有辐射项贡献时, 双星必会出现并合现象.此时, 原保守有序双星系统需较长时间才能完成并合过程, 引力波形在双星并合前仍保留拟周期的基本特点;然而, 原保守混沌双星系统仅在较短时间内就会并合, 但因并合时间太短, 无法获取足够的动力学信息导致引力波形的特征不易分辨.     

Revolving superposed standing waves in a spinning Timoshenko Beam

The aim of the present paper is to study the revolving superposed standing waves in a spinning Timoshenko beam based on the results obtained by the first author with others in two recently published papers. The concept of superposed standing wave as normal mode and the knowledge about the helical feature of propagating wave will be used to depict a physical picture about the vibration of the spinning beam, from describing the basic constituent waves to showing the orthogonality property of the revolving normal modes. The wave-mechanics approach will be invoked throughout the study with an algebraic procedure used to reveal the two eigenvalues of the gyroscopic-coupling phase factor. A table for tabulating the phases of the centroidal positions of the beam in time and space due to the passing of a wave is invented, through which one could show the helical structure of the wave without ambiguity. From the present result, two types of revolving standing waves are identified, each manifesting as a gyroscopic precession in association with a frequency-splitting phenomenon, in either the clockwise or the anticlockwise direction. It is shown that the revolving waves should be represented by wavefunctions in a form of four-component column matrix vectors.     

Traveling waves and chaotic properties in cellular automata

Traveling wave solutions of cellular automata (CA) with two states and nearest neighbors interaction on one-dimensional (1-D) infinite lattice are computed. Space and time periods and the number of distinct waves have been computed for all representative rules, and each velocity ranging from 2 to 22. This computation shows a difference between spatially extended systems, generating only temporal chaos and those producing as well spatial complexity. In the first case wavelengths are simply related to the velocity of propagation and the dispersivity is an affine function, while in the second case (which coincides with Wolfram class 3), the dispersivity is multiform and its dependence on the velocities is highly random and discontinuous. This property is typical of space-time chaos in CA. (c) 1999 American Institute of Physics.     

脉冲激光在镀层圆柱表面激发的表面波

分别从理论和实验上研究了脉冲激光在快、慢镀层圆柱表面激发的表面波声场。脉冲激光线源在镀层圆柱周向上激发超声波信号并利用激光干涉仪检测。对钢基底锌镀层圆柱和锡基底铜镀层圆柱试样表面波的理论频散和实验信号估计频散进行了比较,瞬态位移场则利用留数定理与FFT技术数值仿真得到并与实验波形进行对比。结果显示:理论频散和仿真波形与实验信号都具有极好的一致性,而快、慢镀层圆柱之间的表面波性质有显著差异。文中所用理论分析和数值方法为使用激光超声技术反演和定量表征镀层材料参数等无损检测技术奠定了理论基础。