具有弹性支座杆件的动力稳定性研究

研究了杆件具有弹性支座时直杆的动力稳定性问题，推导出了杆件的临界频率和动力不稳定边界，分析了弹簧刚度和阻尼对杆件动力稳定性的影响，研究表明杆件的侧向刚度愈大其结构的动力稳定性愈好，阻尼对杆的振动起有利作用，并提出了在实际工程中减小杆件振动的一些措施．     

Motion of a system of seismic sources over ice on a body of water under the action of a pulse

The vertical motion of a system of two identical seismic sources and a spring truck tractor on ice under the action of a shock pulse from the seismic sources is studied to estimate the strength of ice. It is shown that during the pulse time, the interaction of the masses of the seismic sources and the tractor is small and the compressibility effect of the liquid can be ignored. Calculations show that for the seismic sources, the dynamic load far exceeds the static load and for the tractor, the static load is maximal. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 147–155, March–April, 2007.     

DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.     

Rheology of poly(methyl methacrylate-<Emphasis Type="Italic">co</Emphasis>-styrene) particles suspended in water: effects of electrostatic surface layer

 Linear and nonlinear viscoelastic properties were examined for aqueous suspensions of monodisperse poly(methyl methacrylate-co-styrene) (MS) particles having the radius a ₀ =45 nm and the volume fractions φ=0.428−0.448. These particles had surface charges and the resulting electrostatic surface layer (electric double layer) had a thickness of t_s=5.7 nm. At low frequencies in the linear viscoelastic regime, the MS particles behaved approximately as the Brownian hard particles having an effective radius a _eff=a ₀ + t_s, and the dependence of their zero-shear viscosity η₀ on an effective volume fraction φ_eff (={a _eff/a ₀}³φ) agreed with the φ dependence of η₀ of ideal hard-core silica suspensions. In a range of φ_eff < 0.63, this φ_eff dependence was well described by the Brady theory. However, the φ_eff dependence of the high-frequency plateau modulus was weaker and the terminal relaxation mode distribution was narrower for the MS suspensions than for the hard-core suspensions. This result suggested that the electrostatic surface layer of the MS particles was soft and penetrable (at high frequencies). In fact, this “softness” was more clearly observed in the nonlinear regime: the nonlinear damping against step strain was weaker and the thinning under steady shear was less significant for the MS suspension than for the hard-core silica suspensions having the same φ_eff. These weaker nonlinearities of the concentrated MS particles with φ_eff∼ 0.63 (maximum volume fraction for random packing) suggested that the surface layers of those particles were mutually penetrating to provide the particles with a rather large mobility. Received: 10 July 2001 Accepted: 2 November 2001     

连接阻尼对弹性杆纵向碰撞响应的影响

分析了刚度和阻尼并存的一般边界条件下线弹性杆与刚体的纵向碰撞过程,得到了碰撞后第一个波动周期杆振动的位移、速度和应力的解析表达式,讨论了碰撞持续时间为2倍杆长与波速比的条件.将导出的解析表达式通过具体的算例代入计算,讨论了不同质量比、不同连接刚度条件下连接阻尼对于碰撞过程中杆中质点速度及应力响应的影响.研究表明,连接阻尼改变了受碰撞弹性杆的振动模式,连接阻尼影响着碰撞反射波速度和应力的突变幅度;连接阻尼增大,杆中速度和应力响应分布变平缓:在连接刚度较大的情况下,连接阻尼变化对于杆中质点速度和应力影响较大;碰撞持续时间与质量比、连接刚度、连接阻尼及杆长有关,与碰撞的初速度无关;在质量比较大的情况下,连接阻尼使得反射波到达杆碰撞端时,杆端的应力有显著的变化.     

多孔金属薄膜阻尼减振微观机理研究

研究了多孔金属薄膜的阻尼性能和微观机理. 采用分子动力学方法及扫描电镜(SEM) 原位观察实验手段对多孔金属薄膜阻尼进行研究, 得出金属薄膜应变滞后于应力周期性变化以及弹性势能周期性衰减的规律, 并通过应变滞后应力的时间差求得损耗因子; 从微观结构上可看出, 在薄膜孔缺陷附近\langle110angle晶向上经历了位错产生、 并且位错呈阶梯状向前发射的变化; 在SEM原位拉伸、卸载实验中观察到有微裂纹的萌生、斜向阶梯扩展、收缩及消失的周期过程. 结果表明: 在周期载荷作用下, 多孔金属薄膜的孔缺陷附近产生的位错可以挣脱开弱钉扎点并限制在强钉扎点上, 由于位错的变化及附近晶界间的相对滑动产生内摩擦, 消耗了系统的部分弹性势能, 引起金属薄膜的阻尼减振效应, 从而揭示了多孔金属涂层阻尼产生的微观机理.     

振幅阻尼信道量子隐形传态保真度恢复机理

在振幅阻尼信道上进行量子隐形传态的过程中, 量子Bell纠缠态将发生退相干, 导致隐形传态质量下降甚至通信失败. 为克服该影响, 本文提出了一种Bell纠缠态补偿方法. 在估计振幅阻尼信道参数的基础上, 将对纠缠态的补偿分为纠缠退相干发生之前的预补偿以及 经历量子振幅阻尼信道之后的匹配补偿两部分. 前者在纠缠源处进行, 后者在两个量子通信 用户处进行, 预补偿及匹配补偿参数与信道特性参数相关. 纠缠补偿完成后, 再进行隐形传态. 理论推导与性能分析结果表明, 相比于不进行纠缠补偿及仅在发生退相干之后进行的纠缠补偿, 本方法能够获得更高的隐形传态保真度, 适当调整补偿参数, 可使保真度接近于1, 对克服纠缠 退相干带来的隐形传态质量下降问题具有一定的意义.     

On a wave equation with supercritical interior and boundary sources and damping terms

This article addresses nonlinear wave equations with supercritical interior and boundary sources, and subject to interior and boundary damping. The presence of a nonlinear boundary source alone is known to pose a significant difficulty since the linear Neumann problem for the wave equation is not, in general, well‐posed in the finite‐energy space H¹(Ω) × L₂(?Ω) with boundary data in L₂ due to the failure of the uniform Lopatinskii condition. Further challenges stem from the fact that both sources are non‐dissipative and are not locally Lipschitz operators from H¹(Ω) into L₂(Ω), or L₂(?Ω). With some restrictions on the parameters in the model and with careful analysis involving the Nehari Manifold, we obtain global existence of a unique weak solution, and establish exponential and algebraic uniform decay rates of the finite energy (depending on the behavior of the dissipation terms). Moreover, we prove a blow up result for weak solutions with nonnegative initial energy.     

Oscillation theorem for superlinear second order damped differential equations

In this paper, we are concerned with the oscillation of second order superlinear differential equations of the form

(a(t)y^′(t))^′+p(t)y^′(t)+q(t)f(y(t))=0.