冲击载荷下Al2O3陶瓷的动态响应

 通过平面飞片碰撞实验，研究了质量分数为90%的Al₂O₃陶瓷在0～11.0 GPa的动态响应行为，给出了该材料的Hugoniot弹性极限（σ_HEL）、动态屈服强度、高压声速和Hugoniot曲线。结果表明：当冲击应力在σ_HEL≈11.0 GPa的范围内，Al₂O₃陶瓷的塑性区压缩特性表现出较明显的弥散行为；在远低于σ_HEL的应力区，Al₂O₃陶瓷已表现出明显的压缩损伤效应，即出现所谓的破坏波效应。     

冲击波压缩PVDF膜的电响应研究

 应用冲击加载技术,研究了PVDF膜在与其极化矢量方向平行的冲击波压缩下的冲击电响应。通过实验和数值模拟得到了PVDF释放电荷q(t)与冲击波压力p(t),给出了峰值电荷q_max与峰值压力p_max的关系,建立了PVDF膜的冲击电响应的理论模型及数值模拟方法。     

材料预加热冲击压缩实验技术及高温下不锈钢的动态响应

 建立了用于轻气炮上冲击压缩实验的材料预加热系统及相关实验技术。介绍这一系统的原理、构造及操作。利用这一系统，在加载幅度8 GPa的恒定载荷下，得到了初始温度300～980 K范围内HR-2抗氢不锈钢的动态响应特性，包括层裂强度、Hugoniot弹性极限、卸载声速及它们随温度的变化规律。     

ANALYSIS OF THE MULTIPLE-SOLUTION RESPONSE OF A FLEXIBLE ROTOR SUPPORTED ON NON-LINEAR SQUEEZE FILM DAMPERS

The multiple-solution response of rotors supported on squeeze film dampers is a typical non-linear phenomenon. The behaviour of the multiple-solution response in a flexible rotor supported on two identical squeeze film dampers with centralizing springs is studied by three methods: synchronous circular centred-orbit motion solution, numerical integration method and slow acceleration method using the assumption of a short bearing and cavitated oil film; the differences of computational results obtained by the three different methods are compared in this paper. It is shown that there are three basic forms for the multiple-solution response in the flexible rotor system supported on the squeeze film dampers, which are the resonant, isolated bifurcation and swallowtail bifurcation multiple solutions. In the multiple-solution speed regions, the rotor motion may be subsynchronous, super-subsynchronous, almost-periodic and even chaotic, besides synchronous circular centred, even if the gravity effect is not considered. The assumption of synchronous circular centred-orbit motion for the journal and rotor around the static deflection line can be used only in some special cases; the steady state numerical integration method is very useful, but time consuming. Using the slow acceleration method, not only can the multiple-solution speed regions be detected, but also the non-synchronous response regions.     

冲击波中横向、纵向应力计响应初步研究

 采用低阻值锰铜压阻应力计，通过一维平板撞击实验和理论分析对横向、纵向应力计在有机玻璃和陶瓷材料中的不同响应进行了研究。实验结果表明，在陶瓷等硬质材料中进行横向应力测量时，可用康铜计补偿的方法，直接用锰铜计纵向标定的压阻系数计算，而在有机玻璃中却不能简单地得到横向应力。     

冲击波加载下PZT95/5铁电陶瓷电响应的数值模拟

 在爆炸冲击波垂直加载下,考虑了介质的松弛现象及其有限电导率,建立了PZT95/5铁电陶瓷电响应的数学模型。利用这一模型,分析了PZT95/5在短路、电阻、电容和电感等各种负载下的电响应。理论模型与实验结果较好地符合。     

耗散两态系统的动力学特性

利用Born-Oppenheimer近似研究了零温时耗散两态系统的动力学特性.在不同环境谱分布下,给出了两态之间的跃迁几率随时间的变化.数值结果表明:当环境的谱分布为Ohmic形式时,跃迁几率是一个衰减的函数;而当谱分布为随机取值时,跃迁几率具有“量子跳跃”的特性.与之相对比,我们还给出了当把环境等价成无穷多个谱振子的集合时,跃迁几率随时间的变化.     

IMPROVEMENT OF THE SEMI-ANALYTICAL METHOD, FOR DETERMINING THE GEOMETRICALLY NON-LINEAR RESPONSE OF THIN STRAIGHT STRUCTURES: PART II—FIRST AND SECOND NON-LINEAR MODE SHAPES OF FULLY CLAMPED RECTANGULAR PLATES

In a previous series of papers, a semi-analytical model based on Hamilton's principle and spectral analysis has been developed for geometrically non-linear free vibrations occurring at large displacement amplitudes of clamped-clamped beams and fully clamped rectangular homogeneous and composite plates. In Part I of this series of papers, concerned with geometrically non-linear free and forced vibrations of various beams, a practical simple “multi-mode theory”, based on the linearization of the non-linear algebraic equations, written in the modal basis, in the neighbourhood of each resonance has been developed. Simple explicit formulae, ready and easy to use for analytical or engineering purposes have been derived, which allows direct calculation of the basic function contributions to the first three non-linear mode shapes of the beams considered. Also, various possible truncations of the series expansion defining the first non-linear mode shape have been considered and compared with the complete solution, which showed that an increasing number of basic functions has to be used, corresponding to increasingly sized intervals of vibration amplitudes; starting from use of only one function, i.e., the first linear mode shape, corresponding to very small amplitudes, for which the linear theory is still valid, and ending by the complete series, involving six functions, corresponding to maximum vibration amplitudes at the beam middle point up to once the beam thickness. For higher amplitudes, a complementary second formulation has been developed, leading to reproduction of the known results via the solution of reduced linear systems of five equations and five unknowns. The purpose of this paper is to extend and adapt the approach described above to the geometrically non-linear free vibration of fully clamped rectangular plates in order to allow direct and easy calculation of the first, second and higher non-linear fully clamped rectangular plate mode shapes, with their associated non-linear frequencies and non-linear bending stress patterns. Also, numerical results corresponding to the first and second non-linear modes shapes of fully clamped rectangular plates with an aspect ratio α=0·6 are presented. Data concerning the higher non-linear modes, the aspect ratio effect, and the forced vibration case will be presented later.     

混合物冲击温度的数值模拟

 介绍温度的数值模拟方法，采用三维动力学有限元程序模拟冲击压缩状态，分析了数值模拟的准确性。模拟了铜和铝两种金属单质组成混合物的冲击压缩性能，在分析了热传导影响后，计算了混合物的冲击温度和冲击绝热线。     

耗散量子隧道系统的变分法研究

本文用变分法研究了耗散量子系统中的声子基态及其对局域-退局域相变条件的影响。发现:1.声子基态不仅存在通常的位移效应,而且还有形变效应。本文提出的位移-压缩态可同时描述这两种效应;2.声子基态的选择对相变条件有很大影响。随着声子基态能量下降,相变曲线将向强耦合方向移动。 关键词：     

TRANSIENT RESPONSE ANALYSIS OF LARGE-SCALE ROTOR-BEARING SYSTEM WITH STRONG NON-LINEAR ELEMENTS BY A TRANSFER MATRIX-NEWMARK FORMULATION ITEGRATION METHOD

This paper extends the transfer matrix technique (TMT) to the transient response analysis of a large complex non-linear rotor-bearing system by a transfer matrix-Newmark formulation itegration method. Firstly, the transfer matrix is obtained via the Newmark formulation. Secondly, the deflections and velocities at the stations, containing non-linear element, are determined by iteration. Finally, the deflections, velocities and accelerations of all stations are computed by TMT and the Newmark formulation consistent with the boundary conditions. In order to eliminate the numerical instability of TMT, the transfer vector {f^T ? ë^T}^T is used, instead of the traditional one {f^T ? ë^T}^T. Owing to the advantages of TMT and the Newmark formulation, this method can be applied to calculate the transient response of a large-scale rotor-bearing system with strong non-linear elements, and to analyze its stability. Two illustration examples are given, and the results agree well with those by Runge-Kutta method, and by modal synthetic method.     

非线性撕裂模的时间演化

本文在有理面附近的局域近似下,从MHD方程出发,求出了非线性撕裂模的时间演化的解析结果。大体可划分为三个阶段:线性增长,由非线性因素导致饱和,最终过渡到一个与初始条件无关的非线性特解,并与原有的线性及非线性撕裂模的解析结果进行了比较,在线性近似下可退化到经典的结果。由本文结论还可解释托卡马克的大破裂中的有关现象。 关键词：     

A SEMI-ANALYTICAL APPROACH TO THE NON-LINEAR DYNAMIC RESPONSE PROBLEM OF BEAMS AT LARGE VIBRATION AMPLITUDES, PART II: MULTIMODE APPROACH TO THE STEADY STATE FORCED PERIODIC RESPONSE

The semi-analytical approach to the non-linear dynamic response of beams based on multimode analysis has been presented in Part I of this series of papers (Azrar et al., 1999 Journal of Sound and Vibration224, 183-207 [1]). The mathematical formulation of the problem and single mode analysis have been studied. The objective of this paper is to take advantage of applying this semi-analytical approach to the large amplitude forced vibrations of beams. Various types of excitation forces such as harmonic distributed and concentrated loads are considered. The governing equation of motion is obtained and can be considered as a multi-dimensional form of the Duffing equation. Using the harmonic balance method, the equation of motion is converted into non-linear algebraic form. Techniques of solution based on iterative-incremental procedures are presented. The non-linear frequency and the non-linear modes are determined at large amplitudes of vibration. The basic function contribution coefficients to the displacement response for various beam boundary conditions are calculated. The percentage of participation for each mode in the response is presented in order to appraise the relation to higher modes contributing to the solution. Also, the percentage contributions of the higher modes to the bending moment near to the clamps are given, in order to determine accurately the error introduced in the non-linear bending stress estimated by different approximations. Solutions obtained in the jump phenomena region have been determined by a careful selection of the initial iteration at each frequency. The non-linear deflection shapes in various regions of the solution, the corresponding axial force ratios and the bending moments are presented in order to follow the behaviour of the beam at large vibration amplitudes. The numerical results obtained here for the non-linear forced response are compared with those from the linear theory, with available non-linear results, based on various approaches, and with the single mode analysis.     

耗散三波相互作用定态的Hopf分岔

本文讨论了耗散的三波相互作用的一个模型。用本征值分析证明了当相空间体积收缩得足够慢时,三波相互作用的定态将出现Hopf分岔。从本征值得到的定态失稳的临界值和振荡频率,与解运动方程的数字实验在线性阶段符合得很好。分析结果还表明,将不会发生pitchfork分岔。 关键词：     

GENERAL SOLUTIONS OF A CLASS OF DISSIPATIVE SYSTEMS AND THEIR APPLICATIONS

General solutions are obtained for a class of quantum dissipative systems. This is achieved by calculating the characteristic function in the Heisenberg picture. The irreversible behavior of these systems is nalyzed. The general formalism is applied to some typical examples and the influence of noise on these systems is gained.     

重水的冲击压缩性

 用二级轻气炮作为加载装置，测量了重水（D₂O）的冲击压缩线，压力范围为10~43 GPa。用轴对称式电磁感应探头测量冲击波速度，测量精度约1.2%~1.5%。用电探针测量飞片速度，其精度约0.5%。用对比法原理进行测量，标准样品材料为无氧铜。实验发现，重水的冲击波速度随粒子速度变化呈斜率不同的两段直线关系，两线连结处出现拐折。分析认为，这一现象可能由液体D₂O分子在冲击波作用下的离解过程引起。     

NORMAL MODES OF A NON-LINEAR CLAMPED-CLAMPED BEAM

Non-linear modal analysis approach based on invariant manifold method proposed earlier by Shaw and Pierre (Journal of Sound and Vibration164, 85-124) is utilized here to obtain the non-linear normal modes of a clamped-clamped beam for large amplitude displacements. The results obtained for the fundamental normal mode are compared with the corresponding reported experimental and theoretical studies. The effects of modal coupling are examined in greater detail. The limitation of the present method for analyzing non-linear behavior is highlighted.     

MUSCL格式TV性质的非线性分析

分析求解非线性双曲型守恒律的MUSCL类格式的TV性质。首先从该类格式的一般形式出发,提出和证明了该类格式实现TVD的需求。所提TVD需求直接表示为对变量变差符号和量值限制,体现了双曲型方程解的依赖域原理,为分析MUSCL格式的TV性质提供了理论工具。同时提出了基于TVD需求再构数值解分布,以降低数值耗散从而提高接触面及膨胀波头/波尾分辨率的基本思路。