BIFURCATIONS AND CHAOS OF AN IMMERSED CANTILEVER BEAM IN A FLUID AND CARRYING AN INTERMEDIATE MASS

The concern of this work is the local stability and period-doubling bifurcations of the response to a transverse harmonic excitation of a slender cantilever beam partially immersed in a fluid and carrying an intermediate lumped mass. The unimodal form of the non-linear dynamic model describing the beam-mass in-plane large-amplitude flexural vibration, which accounts for axial inertia, non-linear curvature and inextensibility condition, developed in Al-Qaisia et al. (2000Shock and Vibration7 , 179-194), is analyzed and studied for the resonance responses of the first three modes of vibration, using two-term harmonic balance method. Then a consistent second order stability analysis of the associated linearized variational equation is carried out using approximate methods to predict the zones of symmetry breaking leading to period-doubling bifurcation and chaos on the resonance response curves. The results of the present work are verified for selected physical system parameters by numerical simulations using methods of the qualitative theory, and good agreement was obtained between the analytical and numerical results. Also, analytical prediction of the period-doubling bifurcation and chaos boundaries obtained using a period-doubling bifurcation criterion proposed in Al-Qaisia and Hamdan (2001 Journal of Sound and Vibration244, 453-479) are compared with those of computer simulations. In addition, results of the effect of fluid density, fluid depth, mass ratio, mass position and damping on the period-doubling bifurcation diagrams are studies and presented.     

STABILITY OF SECOND KIND OF DUMBBELL DOMAINS SUBJECTED TO AN IN-PLANE FIELD AT DIFFERENT BIAS FIELDS

The softening process of the second kind of dumbbell domalns(liDs) in garnet bubble films subjected to an in-plane field H_ip at different static bias field H_b was studied experimentally. It was found that when H_b is larger, the remaining percentage of IID, R_IID, drops sharply at a certain H_ip, and with the increase of H_b the drop occurs at lower H_ip and becomes more intensive. We have confirmed that this is related to the "spontaneous-shrink" 0f IIDs, which plays an important role for the breakdown oF vertical Bloeh line chains of lids subjected to joint fields H_ip and H_b .     

立方磁晶各向异性对面内磁场中条畴和磁泡稳定性的影响

在八个(111)面磁泡膜上,观察了施加面内(in-plane)磁场后在不同晶轴方向上条状畴的消失过程,测量了条畴消失场H_s^*和磁畴消失场H_k^*与面内磁场的方向的关系。本文计及立方磁晶各向异性,完善了面内磁场中条畴的稳定性理论。用该理论定性地解释了实验结果的主要特点。导出了H_s^*与立方各向异性及面内场方向的两种近似的理论关系,它们分别适用于面内场方向靠近和不十分靠近〈110〉晶轴的情形。它们和实验结果是大致符合的。在〈110〉晶轴上,理论关系具有下列简单的形式:H_k^*<110>=H_s^*<110>=H_k{1+(k₁/2K_u)-[al/h(4πM_s/H_k)²]^2/3},此式与实验结果符合得相当好。 关键词：     

DYNAMIC STABILITY OF SKEW PLATES SUBJECTED TO AERODYNAMIC AND RANDOM IN-PLANE FORCES

This paper presents an investigation into the dynamic stability of skew plates acted upon simultaneously by an aerodynamic force in the chordwise direction and a random in-plane force in the spanwise direction. Due to this random in-plane force, the plate may become unstable before the aerodynamic force reaches its critical value. In this work, the finite element formulation is applied to obtain the discretized system equations. The system equations are then partially uncoupled and reduced in size by the modal truncation method. Finally, the unsmoothed and the smoothed versions of the stochastic averaging are used to calculate the system response, and the second-moment stability criterion is utilized to determine the stability boundary of the system. Numerical results show that the stability boundary obtained by the smoothed stochastic averaging is less conservative than that obtained by the unsmoothed version, and the former is the tangent of the latter at zero spectral density of the random in-plane force.     

可压缩理想等离子体柱的稳定性

本文从描述理想等离子体运动的线性化磁流体方程出发,导出了压缩量▽·ξ的一个表示式。一般情况下,它由两部分组成:第一部分与纵向惯性运动有关,第二部分与载等离子体力管的均匀运动(膨胀与压缩)有关。对于等离子体柱,我们讨论了几种可以将含有压缩量项的运动方程作某些简化的情形。利用这些结果,导出和分析了描述具有均匀分布电流的等离子体柱运动的色散关系。     

VIBRATION AND STABILITY OF ROTATING POLAR ORTHOTROPIC ANNULAR DISKS SUBJECTED TO A STATIONARY CONCENTRATED TRANSVERSE LOAD

In the present paper, natural frequencies and stability of a spinning polar orthotropic disk subjected to a stationary concentrated transverse load are investigated. The analysis of the free vibration of a spinning disk is performed first to find natural frequencies and corresponding vibration modes. The resulting eigenfunctions obtained from the free vibration are used as deflection functions of the forced vibration of a disk where the load is modelled as a mass-spring-dashpot system fixed in space. By using the Galerkin approximation method, eigenvalues of the whole system are determined. Results show that disks with higher values of modulus ratios or the Poisson ratios have higher natural frequencies, and the stability of the whole system can be improved by raising the value of the modulus ratio or lowering that of the Poisson ratio.     

有心力场轨道稳定性的判据

根据有心力为保守这一特性，利用变分法给出有心力场轨道稳定性的判据。     

VIBRATION POWER TRANSMISSION OVER A RECTANGULAR AREA OF AN INFINITE PLATE SUBJECT TO UNIFORM CONPHASE VELOCITY EXCITATION

In the study of vibration isolation, mobility is normally used to reflect the characteristics of power transmission over the contact region between the exciting machine and its supporting structure. However, recent investigations indicated that power transmission is influenced by the dimensions and shape of the contact region and the use of classical point mobility can lead to significant errors. The surface mobility of an infinite plate over a rectangular contact region subject to a uniform conphase velocity excitation has been derived using the effective point mobility concept for various aspect ratios of the contact region. Results show that power transmission is distributed in a ring-like manner, with the transmission in the central region and along the edges of the contact area being rather small. As the width-based Helmholtz number kw/2 increases, the ring-like region expands outward but less power is transmitted. The surface mobility decreases rapidly as Helmholtz number increases. For the same Helomholtz number, the surface mobility decreases as the aspect ratio of the contact region increases and for the same contact area, it is virtually independent of the shape of the contact region for aspect ratio less than 2 or at large Helmholtz numbers (greater than 4). Experimental measurements of a simulated infinite plate confirm the theoretical calculations. Unlike uniform conphase force excitation, the surface mobility due to uniform conphase velocity distribution does not oscillate with Helmholtz number.     

A COMPARISON OF THREE TECHNIQUES USING STEADY STATE DATA TO IDENTIFY NON-LINEAR MODAL BEHAVIOR OF AN EXTERNALLY EXCITED CANTILEVER BEAM

Non-linear system identification is used to generate models of modes in physical structures. Analysis of the theoretical non-linear model of a cantilevered beam is used to predict the inputs to the physical system that will produce responses suitable for enhanced parameter estimation, thereby improving the model. Three identification techniques are described and applied to both numerical and experimental data: the first is based on the continuous-time differential equation model of the system, the second uses relationships generated by the method of harmonic balance, and the third is based on fitting steady state response data to the amplitude and phase modulation equations resulting from a multiple time scales analysis. The performance of each method improves as the non-linearities in the system become more pronounced. The benefits and limitations of the methods are discussed.     

几类有心力场轨道稳定性的判据

本文通过将比耐公式变分得到的“轨道相图”，分析有心力场轨道的稳定性，得到了如下几种情况轨道稳定性的统一判据：（１）一般有心力场中以力心为中心的圆形轨道；（２）平方反比力场中的各类轨道；（３）立方反比力场中的各类轨道；（４）平方反比和立方反比力场叠加的有心力场中的各类轨道，据此可以十分简捷地解决上述几种情况下的轨道稳定性问题。     

磁场下量子点的电子态

原子和核结构的少体理论方法改进后用以研究磁场下包含三个电子的二维量子点的电子性质。我们首先解析地证明了对应于三电子系统基态的幻数角动量的存在起源于量子力学对称性的要求。基于少体理论方法的计算确认了上述理论分析的正确性,计算同时显示出磁场强度和约束势对三电子系统基态的影响。 关键词：     

测量电源电动势的一种简易方法

补偿法是测量电源电动的一种巧妙方法，但电路复杂，操作繁琐。本介绍一种电路简单、操作方便、精确度高的测量电源电动势的新方法。     

具有精馏装置的自动复叠制冷循环分析

本文提出了一种新的具有精馏装置的自动复叠式制冷循环,并以 Ｒ１３４ａ／Ｒ２３为制冷剂。对新循环进行了热力学分析,建立了能量与质量平衡方程,分析了循环工质配比、吸气温度及精馏塔操作压力对压缩机压比及系统ＣＯＰ的影响。作者进一步将新循环与二级分凝循环在压比控制于９～１２、冷凝器出口温度保持在４０℃的前提条件下进行了性能上的比较,发现新循环既可达到更低的制冷温度,又可在相同平均蒸发温度下获得更高的ＣＯＰ。     

匀强磁场对刚性载流线圈磁力矩公式的一般推导

利用矢量代数和矢量场论的有关结果严谨地推证了匀强磁场中载流线圈所受合磁力矩表达式。     

ANNIHILATION OF VERTICAL-BLOCH-LINE CHAINS IN THE WALLS OF THE SECOND KIND OF DUMBBELL DOMAINS SUBJECTED TO AN IN-PLANE FIELD

An experiment was statistically performed on the annihilation of vertical-Bloch-line (VBL) chains in the walls of the second kind of dumbbell domains (ⅡDs) subjected to an in-plane field H_ip. It was again confirmed that there is a critical in-plane field H′_ip, above which all VBL chains of hard domains in garnet bubble films, including ⅡDa, disappear. Just like ordinary hard bubbles (OHBs), it was also found that there exists a critical range of H_ip, from (H_ip)_ID to H′_ip, for ⅡD softening. Over this range, with the increase of H_ip, more and more ⅡDs are softened, accompanied by the successive appearance of the first kind of dumbbell domains, OHBs and soft bubbles. In addition, for the five samples tested, the ratio, H′_ip/(H_ip)_ID, is obviously greater than 2^1/2.     

VIBRATION OF A T-TYPE CURVED FRAME DUE TO A MOVING FORCE

This work presents the formulation of governing equations for a curved frame. An analytic method is also presented to examine the vibration of the curved frame. The orthogonality of any two distinct sets of mode shape functions of the frame is also derived. The forced vibration of the frame owing to a moving concentrated force is examined. The strain energy characteristics of the frame induced by the moving force are investigated as well.     

TOPOLOGY DESIGN OF STRUCTURES SUBJECTED TO PERIODIC LOADING

Although a lot of attention in the topology optimization literature has focused on the optimization of eigenfrequencies in free vibration problems, relatively little work has been done on the optimization of structures subjected to periodic loading. In this paper, we propose two measures, one global and the other local, for the minimization of vibrations of structures subjected to periodic loading. The global measure which we term as the “dynamic compliance” reduces the vibrations in an overall sense, and thus has important implications from the viewpoint of reducing the noise radiated from a structure, while the local measure reduces the vibrations at a user-defined point. Both measures bring about a reduction in the vibration level by moving the natural frequencies which contribute most significantly to the measures, away from the driving frequencies, although, as expected, in different ways. Quite surprisingly, the structure of the dynamic compliance optimization problem turns out to be very similar to the structure of the static compliance optimization problem. The availability of analytical sensitivities results in an efficient algorithm for both measures. We show the effectiveness of the measures by presenting some numerical examples.     

RADIAL FORCE TRANSMISSION TO THE HUB FROM AN UNLOADED STATIONARY TYRE

The static and dynamic stiffness of a tyre sidewall are calculated as a function of geometry, load parameters and frequency. Two different expressions were used for below and above the ring frequency. The air pressure and section aspect ratio are found to be the controlling influences below the ring frequency. This sidewall stiffness was inserted into previously obtained wave equations to obtain the dispersion relationships and impedances for a tyre belt with sidewalls. The stiffness and force transmission to the hub in the region of the contact patch was also calculated and compared with measured values. The sidewall stiffness in the region of the contact patch is found to be strongly dependent on the belt wavespeed, giving a stiffer value in the region of the contact patch above the ring frequency.