Dynamics of a Spherical Body in a Liquid with Rotational Vibration of the Cavity

The average dynamics of a single solid sphere in a liquid-filled cylindrical cavity in the presence of high-frequency rotational oscillation about the axis of symmetry is studied experimentally. In the cavity there is an impermeable membrane which forces the liquid as a whole to vibrates together with the cavity. Various orientations of the vessel in the gravity force field are considered. The action of an average force of vibrational nature on the sphere and the dependence of this force on the vibration parameters and the body dimensions and density are studied. The force is measured with respect to the floating threshold for the heavy body, when the average vibrational force balances or exceeds the action of the gravity force.     

组合荷载作用下拦污栅栅条稳定性计算通式

根据栏污栅的控制工况，指出栅条倾覆稳定的计算简图为集中力与均布荷载同时作用的双悬臂简支梁，应用瑞利商求解其倾覆稳定微分方程，给出了组合荷载作用时栅条稳定临界荷载计算方法，通过对比分析表明了本文方法的合理性，最后还介绍了该方法的工程应用，可供生产设计及修订规范参考。     

旋转流场下模型大幅俯仰运动实验研究

在中航气动院FL-8低速风洞中,采用单自由度振荡机构进行了旋转流场下大幅俯仰运动的气动特性实验研究。模型在绕风速轴连续旋转的同时,进行给定频率和振幅绕体轴的俯仰振荡运动。测量了模型的动态气动特性,着重分析了不同运动参数对模型气动特性的影响。实验结果表明,旋转速度的存在使大振幅俯仰振荡实验中的滚转力矩和偏航力矩产生了明显的迟滞特性,但对俯仰力矩和法向力的迟滞特性影响不大。     

Distinctive Features of the Distributions of the Body Force Produced by a Plasma Actuator

Basing upon the assumption on the solenoidality of the field of the time-average body force produced by a surface dielectric barrier discharge analytical expressions for the spatial distributions of the components of this force are proposed. The calculations of the dischargegenerated near-surface jet are in good agreement with the experiment. The distinctive features of spatial distributions of the body force components calculated from the data of the velocity field measurements are physically explained.     

动态激光散斑测超小型物体动态特性

本文基于动态散斑场的相关统计特性,发展了一种系统识别技术,这是一条有效的用来分析超小型物体动态特性的途径.我们对重为8g的微型悬臂梁,实时记录了梁振动的自由响应时间域信号,对其进行了动态特性计算机分析和实验研究。     

滑块在平面上是如何运动的

滑块在平面上的运动在完全刚性地基假设下其运动方程存在内在的矛盾.在将地基看作弹性的前提下求解了这个问题,并根据所得解的物理意义,解释了摩擦激振的基本原理.     

Variational Characterization of a Quasi-rigid Body

The rigidity of a body usually is characterized by the kinematical assumption that the mutual distance between any two of its particles remains unaltered in any possible deformation. However, from this alone nothing can be said about the internal contact forces exerted between adjacent sub-bodies. Therefore, the determination and form of an internal state of stress for a rigid body is problematical. Here, we will show that by considering such a kinematical characterization as an internal constraint for an elastic body, the constrained body inherits the mechanical structure of the elastic parent theory, i.e., the internal constraint generates an associated set of Lagrange multiplier fields which can be interpreted as an internal constraint reaction pseudo-stress field with the same structure as the state of stress in the parent elastic body. Thus, although the final deformation is the same for both the rigid body and the rigidly constrained elastic body, the latter corresponds to a richer model and, to emphasize this distinction, we refer to it as a quasi-rigid body. While in equilibrium the pseudo-stress field of a quasi-rigid body will satisfy equations identical to the equilibrium equations for the stress field in the elastic parent theory, such equations are not, in general, sufficient to assure uniqueness. In order to overcome this indeterminacy, we consider the quasi-rigid body as the limit of a sequence of deformable bodies, where each member of the sequence is identified by a material parameter such that, as this parameter tends to infinity, the body to which it refers is rigidified. Our approach is variational, i.e., we consider a sequence of minimization problems for hyperelastic bodies whose elastic strain energy is multiplied by a penalty term, say 1/ε . As ε→?0, body distortions are more and more penalized so that the sequence of the displacement fields tends to a rigid displacement field, whereas the sequence of the associated stress fields tends to a definite non-zero limit. It will be shown that among all pseudo-stress fields that satisfy the equilibrium equations for the quasi-rigid body, the unique limit of the sequence as ε→0 minimizes a functional analogous to the complementary energy functional in classical linearized elasticity. This result permits its unique determination without having to consider the whole sequence of penalty problems.     

The Arithmetic Mean Theorem of Eshelby Tensor for a Rotational Symmetrical Inclusion

In 1997, H. Nozaki and M. Taya found numerically that for any regular polygonal inclusion except for a square, both the Eshelby tensor at the center and the average Eshelby tensor over the inclusion domain are equal to the Eshelby tensor for a circular inclusion and independent of the orientation of the inclusion. Then in 2001, these remarkable properties were mathematically justified by Kawashita and Nozaki. In this paper, a more radical property is presented for a rotational symmetrical inclusion: For any N-fold (N is an integer greater than 2 and unequal to 4) rotational symmetrical inclusion, the arithmetic mean of the Eshelby tensors at N rotational symmetrical points in the inclusion is the same as the Eshelby tensor for a circular inclusion and independent of the orientation of the inclusion. It follows that the Eshelby tensor at the center and the average Eshelby tensor over the rotational symmetrical inclusion domain are identical to the Eshelby tensor for a circular inclusion and independent of the orientation of the inclusion as well. This paper shows that although the Eshelby property does not hold for non-ellipsoidal inclusions, the Eshelby tensor for a rotational symmetrical inclusion satisfies the arithmetic mean property. Mathematics Subject Classifications (2000) 73C02.     

Rotational Symmetries of Crystals with Defects

I use the theory of Lie groups/algebras to discuss the symmetries of crystals with uniform distributions of defects.      

组合旋转壳体的安定上限分析

对旋转组合壳体的各个子区的位移场进行双三次Ｂ样条插值，同时对子区交界处的广义力向量以单三次Ｂ样条展开，推导出以广义向量表示的组合壳体的平衡方程，然后从Ｂｅｔｉ互换定理和虚功原理出发推导出离散的壳体结构中可能的塑性应变率循环，从而给出了组合壳体安定上限分析的有限元列式，把组合壳体的安定上限分析归结为求解一个数学规划问题，文末给出了算例     

Rotational Galloping of Two Coupled Oscillators

Abstract. We will consider nonlinear rotational galloping for two mechanically coupled seesaw oscillators in steady cross-flow, where mechanical coupling consists of a torsion spring. This oscillator system may be viewed as a mechanical two d.o.f. model for the study of rotational galloping of a continuous elastic structure. Using a quasi-steady modelling approach as model equations two coupled nonlinear oscillators are obtained. Depending on the stiffness of the torsion spring and the natural frequencies of the two oscillators either a non-resonant or 1:1 internal resonant system is found. Assuming the windforce to be relatively small an asymptotic analysis based on averaging is presented for both cases.Sommario: Vengono considerate le oscillazioni galoppanti rotazionali non lineari di due oscillatori disposti in bilico su un fulcro (seesaw oscillators) soggetti a un flusso trasversale stazionario e accoppiati meccanicamente attraverso una molla di torsione. Questo sistema oscillatorio può essere interpretato come un modello meccanico a due gradi di libertà per studiare il galoppo rotazionale di una struttura continua elastica. Modellando le azioni indotte dal flusso in modo quasi-statico, si ottengono due oscillatori non lineari accoppiati. A seconda della rigidezza della molla di torsione e delle frequenze naturali dei due oscillatori, si ottiene un sistema non risonante o in risonanza interna 1:1. Assumendo che le forze del vento siano relativamente piccole, viene presentata per entrambi i casi un'analisi asintotica basata sul metodo della media.