The Equations of Motion of a Rigid Body with Constraints Explicitly Depending on Time

The general equations of motion of a body for an observer in S ₀ (an inertial frame) or for an observer in S ₁ (an accelerated frame) are derived. They allow us to determine, in any case, the inertial and gyroscopic forces and to find the difference between them. If the vector that determines the position of the body in S ₀ depends explicitly on time in S ₀, the work-energy principle yields a supplementary condition and these equations can be shown to be equivalent to the Painleve integrals in the Lagrange formulation. Since we are dealing with inertial frames, gyroscopic forces rather than inertial forces are taken into account. If another reference frame is used, we can choose it so that the position vector depends implicitly on time in S ₁ and another set of equations can be obtained for the motion of the body in S ₁. The work-energy principle yields a supplementary condition, but inertial forces should be added. Since an explicit time dependence does not exist in S ₁, gyroscopic forces do not exist as well and instead we have Coriolis forces that behave like gyroscopic forces     

Assessment of force models on finite-sized particles at finite Reynolds numbers

Finite-sized inertial spherical particles are fully-resolved with the immersed boundary projection method(IBPM) in the turbulent open-channel flow by direct numerical simulation(DNS). The accuracy of the particle surface force models is investigated in comparison with the total force obtained via the fully-resolved method. The results show that the steady-state resistance only performs well in the streamwise direction, while the fluid acceleration force, the added-mass force, and the shear-induced Saffman lift can effectively compensate for the large-amplitude and high-frequency characteristics of the particle surface forces, especially for the wall-normal and spanwise components. The modified steady-state resistance with the correction effects of the acceleration and the fluid shear can better represent the overall forces imposed on the particles, and it is a preferable choice of the surface force model in the Lagrangian point-particle method.     

Inertial stage of bar buckling under longitudinal compression

The problem of dynamic buckling of a bar under the influence of a compressive force is solved taking into account inertial and elastic forces in different stages of the process. The duration of the inertial stage is determined. It is shown that in solids and gas–liquid media, the duration of the inertial stage for real parameters of structural members can be longer than the duration of impact loading.     

Quasistatic and dynamic instability of one-support cylindrical shells under gyroscopic and nonconservative forces

The paper deals with problem of critical states in single-support rods and cylindrical shells under axial follower forces and centrifugal inertial forces due to rotation. It is shown that depending on the relationship between these forces, loss of stability may be quasistatic or dynamic     

Algorithms for controlling fatigue tests of airplanes

The efficiency of algorithms for automatic control of forces prescribed in the test program is analyzed by an example of a large-aspect-ratio wing considered as a beam loaded by aerodynamic and inertial forces.     

Statistical Foundations of Liquid-Crystal Theory. I: Discrete Systems of Rod-Like Molecules

We develop a mechanical theory for systems of rod-like particles. Central to our approach is the assumption that the external power expenditure for any subsystem of rods is independent of the underlying frame of reference. This assumption is used to derive the basic balance laws for forces and torques. By considering inertial forces on par with other forces, these laws hold relative to any frame of reference, inertial or noninertial. Finally, we introduce a simple set of constitutive relations to govern the interactions between rods and find restrictions necessary and sufficient for these laws to be consistent with thermodynamics. Our framework provides a foundation for a statistical mechanical derivation of the macroscopic balance laws governing liquid crystals.     

Dynamics of a Pipeline under the Action of Internal Shock Pressure

The static and dynamic bending of a pipeline in the vertical plane under the action of its own weight is considered with regard to the interaction of the internal pressure with the curvature of the axial line and the axisymmetric deformation. The pressure consists of a constant and timevarying parts and is assumed to be uniformly distributed over the entire span between the supports. The pipeline reaction to the stepwise increase in the pressure is analyzed in the case where it is possible to determine the exact solution of the problem. The initial stage of bending determined by the smallness of elastic forces as compared to the inertial forces is introduced into the consideration. At this stage, the solution is sought in the form of power series and the law of pressure variation can be arbitrary. This solution provides initial conditions for determining the further process. The duration of the inertial stage is compared with the times of sharp changes of the pressure and the shock waves in fluids. The structure parameters are determined in the case where the shock pressure is accepted only by the inertial forces in the pipeline.     

被动式半捷联稳定平台抗高过载结构设计

针对制导炮弹内部半捷联稳定平台在只有轴承承担高过载时,轴承容易被破坏的问题,设计一种基于对顶半球的半捷联稳定平台抗高过载结构。以半捷联稳定平台工作原理和抗高过载设计要求为基础,设计了基于对顶半球的抗高过载结构,选择所用材料,进行有限元仿真分析;最终制造出该结构并进行地面半物理试验验证。仿真与试验结果表明,半捷联稳定平台在受到高过载时,该结构能起到有效的防护作用,大大减小了轴承的轴向受力,保证了轴承的正常运转,可以确保稳定平台的有效测量。惯性测量系统稳定可靠工作时所承受的过载可达11 000g,具有一定的工程应用价值。     

On the decomposition of forces

We show that any continuously differentiable force is decomposed into the sum of a Rayleigh force and a gyroscopic force. We also extend this result to piecewise continuously differentiable forces. Our result improves the result on the decomposition of forces in a book by David Merkin and further extends it to piecewise continuously differentiable forces.     

摩擦力和摩擦振动的分形行为研究

在不同的摩擦磨损试验机上提取了摩擦磨损过程中摩擦力和摩擦振动的时间序列信号,采用关联维数方法研究了摩擦力和摩擦振动的分形行为．结果表明：摩擦力和摩擦振动信号具有分形特征;随着摩擦磨损过程的进行,信号分形维数的变化出现规律性的递增或递减;对于“收敛”或磨合磨损过程,不同阶段摩擦信号的分形维数趋于增大;对于“发散”的摩擦磨损过程,不同阶段的摩擦信号的关联维数趋于减小．摩擦力和摩擦振动的分形维数的变化规律同摩擦磨损过程中表面形貌分形维数的变化规律相似。     

叶轮机中振动叶片非定常气动力的研究

采用“单一叶片振动方法”代替传统的“全部叶片振动方法”，用线性化的方法推导出计算振动叶片非定常气动力（引起叶片弯曲振动）及力矩（引起叶片扭转振动）方程。通过输入叶型及气流参数，它可以方便有效地估计出作用在振动叶片上的非定常气动力和力矩，以及振动叶片不稳定工况发生的条件和范围。并在氟里昂超音速风洞上进行了实验测量，结果表明，理论计算结果与实验测试结果符合较好。     

Dynamics of an Elastic Four Bar Linkage Mechanism with Geometric Nonlinearities

The geometric nonlinearity due to the large elastic deformations of three flexible links is considered in setting up the dynamic equation of elastic linkages. It is shown that both the quadratic nonlinear terms and the cubic nonlinear terms are included in the model. The analyses with the method of multiple scales demonstrate that the superharmonic resonances caused by the quadratic and cubic nonlinearities, as well as the multi-frequency nature of the inertial force are the reasons causing the critical speed to take place. They also demonstrate that the combination resonances caused by the combined effects of internal resonance in the form of ₂ 2₁, the cubic nonlinearity and the multi-frequency nature of the inertial forces is the reason causing the production of the nonsynchronism of the lower order harmonic resonances of elastic linkages. Meanwhile, the influences of important system parameters on the resonances are investigated.     

Hydrodynamics of flow along the wall of a rotating cup

A study has been carried out of the influence of inertial and Coriolis forces on the hydrodynamics of flow along the inner wall of a rotating cup. It is shown that when these forces are pronounced, the liquid velocity components may be considerably less than those predicted from simple analyses based solely upon a balance of centrifugal and viscous forces, and the velocity at the lip may consequently be critically dependent upon the position of the feed.     

On the shapes of swirling annular jets of a liquid

Annular jets of an incompressible liquid moving in a gas at rest are of interest for applications. A critical analysis of the investigations into jets from centrifugal nozzles is contained in [1]. These investigations elucidated the experimentally observed tulip and bubble jet shapes, and also predict the existence of annular jets of periodic shape. However, simplifications of the flow details are made to obtain the results. For example, in the equations describing the equilibrium of the forces acting on the film, no allowance is made for forces that arise on account of the curving of its shape in the meridional sections nor for the variability of the tangential velocity component in the field of the centrifugal forces. In the present paper, the method of [2] is used to derive equations that describe the flow of swirling annular jets of liquid with uniform profile of the longitudinal velocities in an undisturbed ideal medium with allowance for surface tension and gravity forces and also the pressure difference outside and within the jet. The results of calculations are given that illustrate the dependence of the jet shapes on the relative contributions of the capillary and inertial forces and also the pressure difference, the intensity of the initial swirling, the angle at which the liquid leaves the nozzle, and the gravity force.Translated from Izyestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 144–148, September–October, 1979.I am grateful to V. Ya. Shkadov for interest in the work.     

Stability analysis of gyroscopic systems with integral correction

Stability theorems for gyroscopic systems with integral correction under dissipative and nonconservative positional forces are proved. An inertial vertical gyro is used as an example to illustrate the results obtained     

Solution of Müller's paradox of frame dependence in mixtures of polymeric liquid crystals

Recently, there appeared in this journal a short review article by Müller ((2002), 14: 227–229), in which it was argued that the internal energy of a reacting mixture of liquid crystals should not be an objective quantity (i.e., a quantity independent of the referential frame). Such a paradoxical conclusion has revealed the urging necessity for a better comprehension of the interactions taking place in structured mixtures, specially when referred to non-inertial observers. This work shows that Müller's paradox is avoided when all inertial effects are carefully accounted for. Further, it predicts interesting phenomena without analogue in reacting mixtures of structureless fluids: internal inertial effects, produced by a combination of mass exchanges (e.g. by chemical reactions or phase changes) with the extra degrees of freedom posed by the microstructure. Such effects clarify the reasons why inertial forces and couples acting on a mixture do not always coincide with the sum of the inertial forces and couples exerted upon its individual constituents. The present conclusions establish a reinterpretation of some fundamental concepts of continuum mechanics and thermodynamics, including a deeper understanding of the manner in which total energy and momenta are conserved in complex media. Received: July 25, 2002 / Published online: February 17, 2003 Communicated by Kolumban Hutter, Darmstadt e-mail: faria@mechanik.tu-darmstadt.de     

振荡流中圆柱受力测量研究

本文叙述了测量振荡流中圆柱受力大小和性质的方法和步骤。给出了测量结果,并首次给出这种力的频谱特性。     

Analysis of humidity-dependent adhesion between a probe tip and a surface

Adhesive forces commonly exhibit a monotonic increase or a maximum with increasing relative humidity. However, anomalous behavior has been reported. Here, a numerical model of adhesive forces, comprised mainly of capillary and van der Waals forces, between a tip and a surface is established. It is described by a power law that considers the geometry, the liquid bridge wetting radius, the contact angle, and the separation distance. Capillary forces (sum of surface tension and Laplace pressure) and van der Waals forces are calculated. The latter cannot be neglected in the adhesion even at high humidity. Decrease in adhesion with increasing relative humidity can be attributed to a blunt tip shape, which is validated by experimental data. Specifically, the decrease in adhesion is attributed primarily to a transition from a rounded to a blunt tip shape. Structuring objects at the micro- or nanoscale can either increase or decrease adhesion as a function of relative humidity. This has a wide range of applications in robotic manipulation and can provide a better understanding of adhesion mechanisms in atomic force microscopy in ambient air.     

What do dry granular flows tell us about dense non-Brownian suspension rheology?

Recent years have seen significant progress in our understanding of the rheology of dry granular materials. A scale invariance of equations of motion in the rigid grain limit has helped identifying dimensionless quantities which govern flow. After a review of recent results on dry granular materials, we show how this same dimensional analysis carries over to the case of dense, non-Brownian suspensions. Our review is based on compiled data from various sets of numerical simulations, using both molecular and contact dynamics. It covers the breakdown of kinetic theory, which arises when contact forces dominate collisional forces in inertial flows, and the approach to dense flows up to the quasi-static limit. We show that simple invariance arguments permit to clarify the conditions of occurrence of viscous and inertial scaling in suspensions, and show in particular that both may occur in dense flows even in the presence of significant contact forces, up to the jamming limit. Some implications of the properties of steady uniform quasistatic granular flow under constant pressure for very dense suspensions near the maximum concentration are also discussed.