《趣味振动力学》简介

本书以通俗有趣的方式讲述振动力学,包括线性振动的传统内容,从单自由度振动到多自由度和连续体振动,也涉及非线性振动,如干摩擦阻尼、自激振动、参数振动和混沌振动等内容.在叙述方式上力图避免或减少数学公式,     

线性粘性浅水波方程解的逐点估计

考虑线性粘性浅水波方程柯西问题解的衰减估计,通过对格林函数的详细分析,得到解的逐点估计.结果显示解在特征锥外衰减很快,但在锥内衰减稍慢.且解有和热核同样的衰减速度,所以本文的估计是最优的.     

Numerical simulation of motion and deformation of ring bubble along body surface

Numerical simulation for fluid flow over an attached rigid body with a deformable ring bubble is analyzed based on the velocity potential theory together with the boundary element method （BEM）. The analysis is focused on the axisymmetric case. The bubble surface is treated as a well defined air-liquid interface and is tracked by a mixed Eulerian-Lagrangian method. The points of intersection between the bubble and body are treated, specially in the numerical procedure. The auxiliary function method is adopted to calculate the pressure on the body surface and in the flow field. The convergence study is undertaken to assess the developed numerical method and the computation code. Some case studies are undertaken in which the interactions between the bubble/body and the incoming flow field are simulated. The effects of various physical parameters on the interactions are investigated.     

Comprehensive form of solution for Lamb＇s dynamic problem expressed by Green＇s functions＊

By the analysis for the vectors of a wave field in the cylindrical coordinate and Sommerfeld＇s identity as well as Green＇s functions of Stokes＇ solution pertaining the conventional elastic dynamic equation, the results of Green＇s function in an infinite space of an axisymmetric coordinate are shown in this paper. After employing a supplementary influence field and the boundary conditions in the free surface of a senti-space, the authors obtain the solutions of Green＇s function for Lamb＇s dynamic problem. Besides, the vertical displacement uzz and the radial displacement urz can match Lamb＇s previous results, and the solutions of the linear expansion source u~r and the linear torsional source uee are also given in the paper. The authors reveal that Green＇s function of Stokes＇ solution in the semi-space is a comprehensive form of solution expressing the dynamic Lamb＇s problem for various situations. It may benefit the investigation of deepening and development of Lamb＇s problems and solution for pertinent dynamic problems conveniently.     

Nonlinear dynamical systems and bistability in linearly forced isotropic turbulence

In this paper, we present an extensive study of the linearly forced isotropic turbulence. By using analytical method, we identify two parametric choices, of which they seem to be new as far as our knowledge goes. We prove that the underlying nonlinear dynamical system for linearly forced isotropic turbulence is the general case of a cubic Lienard equation with linear damping. We also discuss a FokkerPlanck approach to this new dynamical system, which is bistable and exhibits two asymmetric and asymptotically stable stationary probability densities.     

轴流压气机级内三维粘性流动的数值模拟

考虑轴流压气机中实际气流沿径向和周向都不均匀的特点,采用亚松弛方法改进传统的混合界面模型,发展了轴流式压气机级内全三维粘性流场的数值计算程序,并以某轴流式双排对转压气机的进口导叶/转子为研究对象,将本文发展的程序与商用 NUMECA 软件的结果进行对比,对本文发展的程序进行了验证。对比结果表明：由于混合界面法引入了“人工掺混”,商业软件计算得出的总压在通过交界面时存在一定的总压损失,而自编程序计算结果保证了总压在交界面处的一致性。流场分析结果表明：该转子叶片在设计工况下处于负攻角状态,在导叶出口轮毂处、压力面50%弦长处、吸力面靠近尾缘处均出现了轻微的流动分离现象。     

保持球对称的相容流体算法的构造

重点研究如何在二维柱坐标系中保持流体运动的球对称问题．该问题需要对整个流体算法做细致的分析与设计,从而获得不同的方法．基于Caramana介绍的修正压强梯度算子构造了保持球对称的相容流体算法,该算法还包括了边人工粘性方法、子网格压力的计算方法,以及预估步与校正步相结合的策略．并且,考虑了总能量的守恒性,讨论了网格节点质量保持不变的必要性,以及基于相容格式证明了边人工粘性的耗散性．数值模拟结果与已知数据的比对验证了程序的正确性、稳定性.     

具有价格粘性的供应链动态模型及其协调策略

本文针对由一个制造商和一个零售商构成的供应链系统,在市场价格具有粘性的情况下,利用动态博弈理论分析了制造商和零售商如何确定其最优的批发价格和产品订购量以实现自身长期利润的最大化。本文首先利用汉密尔顿-雅可比-贝尔曼方程分别求解了供应链系统在Stackelberg博弈下的最优批发价格和最优产品订购数量。然后,利用数值算例说明了该供应链系统协调的必要性。最后,利用数量折扣契约协调了该供应链系统,并证明了协调的有效性。     

Dissipation of a two-mode squeezed vacuum state in the single-mode amplitude damping channel

We explore how a two-mode squeezed vacuum state sechθ e^{a+b+ tanh θ} |00> evolves when it undergoes a singlemode amplitude dissipative channel with rate of decay κ. We find that in this process not only the squeezing parameter decreases, tanh θ → e^-κt tanh θ, but also the second-mode vacuum state evolves into a chaotic state exp{b⁺bln[1 - e^-2κt tanh² θ]}. The outcome state is no more a pure state, but an entangled mixed state.     

The effect of atomic spontaneous decay on the dynamics of the negativity of the Wigner function of radiation

The exact solution of the master equation for the case of a high-Q cavity with atomic decay is found. We use the negativity of the Wigner function (WF) as an indicator of nonclassicality. It is found that the negative values of the field WF are very sensitive to any change in the damping parameter. The atomic spontaneous decay leads to the simultaneous disappearance of both entanglement and nonclassicality of quantum states. Moreover, the purity of the field states is completely lost.