A microslip friction model with normal load variation induced by normal motion

A two-dimensional microslip friction model with normal load variation induced by normal motion is presented in this paper. The model is a distributed parameter model, which characterizes the stick-slip-separation of the contact interface and determines the resulting friction force, including its time variance and spatial distribution, between two elastic structures. When the relative motion is simple harmonic motion, the stick-slip-separation transition angles associated with any point in the contact area can be analytically determined within a cycle of motion. In addition, if the relative motion is given, stick-slip-separation transition boundaries inside the contact area and their time variances can be determined. Along with an iterative multi-mode solution approach utilizing harmonic balance method (HBM), the developed model can be employed to determine the forced response of frictionally constrained structures. In the approach, the forced response is constructed in terms of the free mode shapes of the structure; consequently, it can be determined at any excitation frequency and for any type of normal load distribution. Two examples, a one-dimensional beam like damper and a more realistic blade to ground damper, are employed to illustrate the predictive abilities of the developed model. It is shown that while employing a single mode model, transition boundaries for the beam like damper agrees with the results given in the literature, the developed method identifies the phase difference along the slip to stick transition boundary when a multi-mode model is employed. Moreover, while partial slip is illustrated in the two examples, typical softening and hardening effects, due to separation of the contact surface, are also predicted for the blade to ground damper.     

On the phenomenon of the combination type resonance in non-linear two-degree-of-freedom systems

The phenomena of the almost-periodic response, called combination type resonance, is analyzed in two-degree-of-freedom dissipative, non-linear systems subject to sinusoidal excitation. The problem is solved theoretically by means of the modified “small parameter technique” as well as by means of the Ritz-Galerkin method. The results are then compared and checked against an analog computer analysis. Conclusions are drawn about a range of applicability of the two methods. The theoretical investigations are completed by solving the stability problem for both methods.

The results indicate that the phenomenon of the combination resonance might occur in wide regions of initial conditions, since one of the phase angle proves to be arbitrary.     

岩石动态巴西圆盘实验中的过载现象

巴西圆盘实验是国际岩石力学与工程学会（ISRM）推荐的测量岩石静态拉伸强度的方法之一,也是该学会推荐的唯一测量岩石动态拉伸强度的方法。但是巴西圆盘实验得到的静态或者动态拉伸强度往往较真实值偏大,其中一个原因是所谓的过载现象,而且其相应的过载效应在动态巴西圆盘测试中尤为明显。为探究岩石材料动态劈裂拉伸强度的过载效应机理及其率相关性,利用SHPB实验装置开展了不同加载率条件下的动态巴西圆盘实验,对岩石材料劈裂拉伸强度的过载特性进行了定量分析;结合颗粒流程序进行了相关实验的数值模拟,得到了圆盘破裂的微观过程。结果表明:（1）动态巴西圆盘实验得到的岩石拉伸强度存在明显的过载现象,圆盘试样拉伸强度的过载比随加载率增加呈对数形式增加;（2）依据动态拉伸强度实验结果对模型参数引入率相关性后,模拟观察到的过载效应更加贴近实验观测。这些结果表明巴西圆盘实验中拉伸强度的过载现象是客观存在的,其机理与试样的圆盘构型以及测试方法有关。结合实验和数值结果,解释了巴西圆盘实验的过载机理,证明了动态巴西圆盘实验修正的必要性并给出了相应的方案,以获取岩石材料的真实动态拉伸强度。     

Elasto-plastic approach for paper cockling phenomenon: On the importance of moisture gradient

Cockling of paper is a common problem occurring in the production, storage and end-use of paper. It is usually induced by a moisture content change. In many cases, cockling is an irreversible phenomenon; i.e. the initial shape is not obtained although the initial moisture content is restored. This kind of moisture content change occurs in copying machines and in the printing process, for example. In this paper, we present a continuum mechanical model, which is used to study the irreversible cockling of paper. In the model, paper is treated as an orthotropic elasto-plastic material and the model takes into account the small-scale variation of fibre orientation. The model is used to show the importance of the through-thickness moisture gradient on the cockling phenomenon during a cyclic moisture content change. The results suggest that the moisture gradient is a crucial factor for the irreversible cockling.     

High-velocity cumulative gas jets

The author examines the theory of the cumulation effect [1] in axisymmetric inviscid perfect gas flows and the possibility of creating cumulative gas jets with velocities considerably in excess of the speed of sound.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 148–152, July–August, 1989.     

On the directional sensitivity of hot-wires: a new look at an old phenomenon

The directional response of a constant temperature hotwire anemometer to variations in pitch and yaw is reviewed, and a new data reduction technique for obtaining velocity vector data in a steady flow is described. Sequential sampling of the signal as the probe shaft is rotated through 360° provides data to yield a three-dimensional velocity vector. Jorgensen's expression was found to be suitable for the data reduction using independently measured pitch and yaw coefficients. Within the range of velocity and flow direction investigated, the velocity magnitude and direction can be determined to within 2% and 2° respectively if the yaw coefficient is neglected. This measurement method is currently being used to determine velocity distributions on the intake-valve/cylinder boundary for different induction system designs.List of symbols d diameter of hot wire - k ₁ yaw coefficient - k ₂ pitch coefficient - l length of hot wire - V output voltage of hot-wire anemometer - L valve lift - U ₀ free stream velocity - U _e effective measured velocity - variance of the mean - X axial distance parallel to valve stem - square root of the residual - velocity cone angle - probe shaft rotation angle - ₀ velocity phase angle     

Theory of the shimmy phenomenon

The shimmy phenomenon is the appearance of angular self-excited vibrations of the carriage wheels. Such self-excited vibrations provide a serious safety hazard for motion, which explains the great interest of scientists in this phenomenon [1–6]. This problem is most serious for the aircraft fore wheels.     

Elongation coefficient of cumulative jets

To calculate the elongation of cumulative jets, the inertial approximation is generally used [1]. It is assumed that each element of the jet moves with constant velocity. Such an approach is valid for very thin jets for which the internal pressure is nearly atmospheric and therefore the pressure gradient along the jet is approximately equal to zero. In the present paper, in which the model of an ideal incompressible fluid is used, a more accurate approximation taking into account the interaction of neighboring elements of the jet is found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 167–169, November–December, 1983.     

On a new “destabilization” phenomenon: effect of rotary damping

Summary In this note we consider the effect of rotary damping on the instability of Beck's column — almost entirely overlooked in the field of nonconservative problems of elastic stability.

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Zu einem neuen Destabilisierungs-Phänomen: Der Einfluß von Drehdämpfung

Übersicht Behandelt wird der Einfluß von Drehdämpfung auf die Instabilität des Beckschen Stabes, welche bisher bei der Betrachtung nichtkonservativer Probleme der elastischen Stabilität nahezu vollständig unbeachtet blieb.

     

On a localization phenomenon in two types of bio-inspired hierarchically organized oscillatory systems

Nonlinear Dynamics - Linear time-delay feedback method makes the stable system generate the infinite-dimensional hyper-chaos, which possesses more than one positive Lyapunov exponent,...     

Kinematic features of the brittle fracture phenomenon

Summary Normal-fracture surfaces of various high-polymers were investigated with the aid of light microscopy. The common fracture pattern is discussed in relation with the kinematic fracture picture introduced bySmekal (1–3). Attention is paid to radial traces and hyperbolic traces, as well as to other morphological features. With the aid of the morphological picture and results of mechanical surface roughness measurements, the three-dimensional density (volume population) of fracture sources could, at polymethylmethacrylate, be roughly estimated. The geometry of fracture sources of polymethylmethacrylate was elucidated by means of electron microscopy. Supplementary experiments performated at normal-fracture surfaces of polymethylmethacrylate showed the effect of a 90°-rotation of the largest principal stress upon the critical condition of inhomogeneities.

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Zusammenfassung Bruchflächen verschiedener Hochpolymeren wurden lichtmikroskopisch untersucht. Die Bruchfiguren werden an Hand des kinematischen Bildes des Bruchvorgangs, wie esSmekal entwickelte, betrachtet. Besondere Aufmerksamkeit wurde den radialen und hyperbolischen Spuren sowie den anderen morphologischen Zügen gewidmet. Mit Hilfe des morphologischen Bildes und der Ergebnisse von mechanischen Messungen der Oberflächenrauhigkeit konnte grob für Polymethylmethacrylat die 3-dimensionale Dichte (Volumenhäufigkeit) der Quellen für den Bruch abgeschätzt werden. Die geometrische Form der Bruchquellen für Polymethylmethacrylat wurde elektronenmikroskopisch geklärt. Ergänzende Experimente an Normal-Bruchflächen von Polymethylmethacrylat zeigen den Effekt einer 90°-Drehung der größten Hauptspannung auf die kritische Inhomogenitätsbedingung.

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Presented at the conference Flow, Fatigue and Failure held in Leeds on January 8th and 9th, 1959, by the British Society of Rheology.     

Physical mechanisms of the rogue wave phenomenon

A review of physical mechanisms of the rogue wave phenomenon is given. The data of marine observations as well as laboratory experiments are briefly discussed. They demonstrate that freak waves may appear in deep and shallow waters. Simple statistical analysis of the rogue wave probability based on the assumption of a Gaussian wave field is reproduced. In the context of water wave theories the probabilistic approach shows that numerical simulations of freak waves should be made for very long times on large spatial domains and large number of realizations. As linear models of freak waves the following mechanisms are considered: dispersion enhancement of transient wave groups, geometrical focusing in basins of variable depth, and wave-current interaction. Taking into account nonlinearity of the water waves, these mechanisms remain valid but should be modified. Also, the influence of the nonlinear modulational instability (Benjamin–Feir instability) on the rogue wave occurence is discussed. Specific numerical simulations were performed in the framework of classical nonlinear evolution equations: the nonlinear Schrödinger equation, the Davey–Stewartson system, the Korteweg–de Vries equation, the Kadomtsev–Petviashvili equation, the Zakharov equation, and the fully nonlinear potential equations. Their results show the main features of the physical mechanisms of rogue wave phenomenon.     

A stochastic theory of cumulative fatigue damage

A stochastic theory for the cumulative fatigue damage of structural components with random fatigue strength under random loading is proposed on the basis of Stratonovich-Khasminskii theorem. The analytical solutions for the probability densities of the cumulative fatigue damage and fatigue life and for the reliability function are given for steel and reinforced concrete components with constant fatigue strength subject to a narrow band stationary Gaussian stress process with zero mean. The results agree very well with those of digital simulation. It is noted that the theory can be applied, in principle, to both metallic and non-metallic materials, narrow band and wide band stress process, and adapted to a sequence ofn, stationary stress processes or quasi-stationary stress process. The scatter and degradation of fatigue strength and the inspection maintenance can also be incorporated into the theory.     

An exploratory investigation of cumulative shock fatigue

A simple device for producing cumulative shock loading in solids is described. The device uses a ballistic-impact-driven projectile to introduce high-stress waves into a solid. The impact time and load amplitude can be varied to produce fracture in one or several impacts in PMMA rods. The wavefront approached a square wave shape. Materials other than PMMA were loaded to failure to demonstrate the versatility of the device. Fracture morphologies observed with optical and scanning-electron microscopy are described.