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In order to shorten the design cycle of FOPS and improve the pass rate of FOPS laboratory destructive tests, nonlinear finite element methods of elastic-plastic large displacement were presented to simulate the dynamic displacement, velocity and acceleration of drop hammer during impact process, and the dynamic changing law of these parameters during the whole collision were analyzed. At the same time, the stress and deformation of FOPS happened in the collision process were obtained. Associated with changing law of drop hammer parameters, stress and deformation in FOPS, several laboratory destructive impact tests were conducted, and FOPS deformation patterns and failure modes were acquired. The simulation methods for FOPS were proved to be reasonable and can be the guidance of FOPS design and test.

A numerical study on the dynamic response of a generic rigid water-landing object (WLO) during water impact is presented in this paper. The effect of this impact is often prominent in the design phase of the re-entry project, to determine the maximum force it is subjected to, for material strength determination to ensure structural and equipment integrity, human safety and comfort. The predictive capability of the explicit finite-element arbitrary Lagrangian-Eulerian (ALE) and smoothed particle hydrodynamics (SPH) methods of a state-of-the-art nonlinear dynamic finite-element code for simulation of coupled dynamic fluid structure interaction (FSI) responses of the splashdown event of a WLO were evaluated. The numerical predictions are first validated with experimental data for the maximum impact accelerations and then used to supplement experimental drop tests to establish trends over a wide range of conditions including variations in vertical velocity, entry angle and object weight. The results show that the fully coupled FSI models can capture the water-impact response accurately for all range of drop tests considered and the impact accelerations are practically linearly with the increase in the height of the drop. The reliability of the maximum impact accelerations was calibrated with approximate classical von Karman and Wagner closed-form solutions.Copyright © 2010 by ASME

Together with geological/geophysical studies and laboratory-scale experiments numerical simulations of impacts contribute a great deal to our knowledge of the cratering process. Whereas field studies give information about target conditions and final crater configuration, numerical modeling allow us to follow the evolving process in time and to reconstruct several important features not surviving after the cessation of the impact event and later time.

The valve train system synchronises the engine timing (inlet and exhaust) with the thermodynamics/combustion process. Thus, its optimal operation is vital for the health of the entire engine. The interplay between various forms of dynamics (e.g inertial, structural and impact/contact) and reactions due to loaded tribological conjunctions leads to a complex problem. The solution requires simplifications and assumptions based on careful analysis. The current chapter describes a modelling approach which integrates the fundamental aspects of valve train behaviour in a fast converging methodology.

This chapter deals with the fundamentals of contact mechanics and impact dynamics of ellipsoidal solids of revolution. It provides a brief review of Hertzian contact/impact dynamics with its underlying assumptions. It provides some examples of Hertzian contact/impact conditions for various contact geometries in rolling element bearings and cam-follower pairs. It also introduces the use of finite element analysis to study contact/impact problems in more detail. Other non-Hertzian type contact problems such as in non-conforming thin-layered solid pairs are studied by appropriate analytical approaches. A generic method decomposing pressure waves propagating into the bulk of solid contacting surfaces is also presented with generic results for both soft and hard-coated surfaces.

We extend the analysis, started in a previous work [1], concerning the formation of lunar impact craters due to low-energy trajectories. First, we adopt the Circular Restricted Three- Body Problem and consider different choices of initial conditions inside the stable invariant manifold associated with the central invariant one in the neighborhood of the L2 equilibrium point in the Earth–Moon system. Then we move to the Bicircular Restricted Four- Body Problem to study the effect of the Sun on the distribution of impacts on the Moon’s surface

In order to exert a large force on the environment, it is effective to apply impulsive force. We describe the motions that perform tasks by applying impulsive force as “impact motion.” This paper presents a contact dynamics model of a humanoid robot for such a motion. Multibody dynamics and effect of a servo controller on impulsive force are also considered in the proposed model. The proposed model can estimate impulsive force at low computation cost compared with full-featured dynamics computation methods. The estimation results of each motion are compared with simulation results by OpenHRP3. The maximum error of impulse is about 6 (%). Therefore, the proposed model is useful for estimating dynamics behavior of a humanoid robot.

In this paper we investigate the control of compass gait biped based on its impact dynamics. We use the Receding Horizon Control (RHC) strategy to develop an active control law so as to mimic the passive gait. Our results shows that this control strategy not only mimics the passive gait but can also stabilize it for those initial conditions, which make the passive gait unstable.

The paper highlights the complex issues involved in impact dynamics at nano-scale, prevalent in MEMS. The role of protective layers on the silicon substrate is investigated. It is found that the expected viscoelastic behavior of these layers is not activated due to the very short (almost instantaneous) impact times.Copyright © 2009 by ASME

This paper investigates the control of a bouncing ball using Model Predictive Control. Bouncing ball is a benchmark problem for various rhythmic tasks such as juggling, walking, hopping and running. Humans develop intentions which may be perceived as our reference trajectory and tries to track it. The human brain optimizes the control effort needed to track its reference; this forms the central theme for control of bouncing ball in our investigations., {"references":["R. Ronsse, P. Lefevre, and R. Sepulchre,, \"Rhythmic Feedback\nControl of a Blind Planar Juggler,\" IEEE Transactions on Robotics,\nVol.24,No.4., pp. 790-802, August 2007.","R. Ronsse, P. Lefevre, and R. Sepulchre, \"Sensorless stabilization of\nbounce juggling,\" IEEE Trans. Robot., vol. 22, no. 1, pp. 147-159,\nFeb. 2006.","J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical\nSystems and Bifurcations of Vector Fields. New York: Springer-\nVerlag, 1986.","A. Tiagounov J. Buijs, S. Weiland and B. De Moor. Long horizon\nmodel predictive control for nonlinear industrial processes. In Proc.\nEuropean Control Conference, Cambridge, UK, 2003.","A. Tiagounov, D. van Hessem, M. Balenovic and S. Weiland. From\nstate estimation to long horizon MPC for nonlinear industrial ,\napplications. In INCOOP Workshop materials, D¨usseldorf, Germany,\n2003.","A. Tiagounov and S. Weiland. Model predictive control algorithm for\nnonlinear chemical processes. In Proc. Physics and Control\nConference, St.Petersburg, Russia, 2003.","D. Q. Mayne, J. B. Rawlings, C. V. Rao, P. O. M. Scokaert,\n\"Constrained model predictive control: Stability and optimality\", in\nAutomatica 36 (2000) pp.789-814."]}

This paper presents a novel impact display capable of rendering impact on a fingertip over a range of velocities commonly experienced during everyday manipulation and tactile exploration. An optical range sensor is used to measure the separation between the user?s finger and the contact block in which the sensor is embedded. Ordinarily, impact is rendered by imposing a rigid boundary when contact is made with a virtual object, which is experienced by the user through a thimble interface. Our impact display adds the making and breaking of contact to this experience and allows control over impact dynamics by controlling impact velocity.

High-speed photogrammetric measurements are being used to assess the impact dynamics of the Orion Crew Exploration Vehicle (CEV) for ground landing contingency upon return to earth. Test articles representative of the Orion capsule are dropped at the NASA Langley Landing and Impact Research (LandIR) Facility onto a sand/clay mixture representative of a dry lakebed from elevations as high as 62 feet (18.9 meters). Two different types of test articles have been evaluated: (1) half-scale metal shell models utilized to establish baseline impact dynamics and soil characterization, and (2) geometric full-scale drop models with shock-absorbing airbags which are being evaluated for their ability to cushion the impact of the Orion CEV with the earth s surface. This paper describes the application of the photogrammetric measurement technique and provides drop model trajectory and impact data that indicate the performance of the photogrammetric measurement system.

SUMMARYThis paper suggests a generalized approach to the mathematical modeling of biped locomotion systems (humans or humanoid robots) with special attention paid to impact and contact dynamics. Instead of the usual inductive approach that starts from the analysis of different situations of real motion (walking, running, jumping, climbing the stairs, etc.) and tries to make a generalization, a deductive approach is pursued, whereby an entirely general problem is considered. Impact dynamics is modeled applying the linear complementarity problem (LCP) formulation. General methodology is explained and demonstrated via the synthesis of a spatial biped model. The validity of the modeling approach is proved by experimental measurements on a human subject in the laboratory conditions. Plenty of graphic presentations illustrating experimental results, as well as the results of the corresponding simulation tests are shown.

Non-cohesive granular media exhibit complex responses to sudden impact that often differ from those of ordinary solids and liquids. We investigate how this response is mediated by the presence of interstitial gas between the grains. Using high-speed x-ray radiography we track the motion of a steel sphere through the interior of a bed of fine, loose granular material. We find a crossover from nearly incompressible, fluid-like behavior at atmospheric pressure to a highly compressible, dissipative response once most of the gas is evacuated. We discuss these results in light of recent proposals for the drag force in granular media., Comment: 4 pages, 4 figures, Accepted to PRL

Often the effect of interactions at nano-scale determines the tribological performance of load bearing contacts. This is particularly the case for lightly loaded conjunctions where a plethora of short range kinetic interactions occur. It is also true of larger load bearing conjunctions where boundary interactions become dominant. At the diminutive scale of fairly smooth surface topography the cumulative discrete interactions give rise to the dominance of boundary effects rather than the bulk micro-scale phenomena, based on continuum mechanics. The integration of the manifold localised discrete interactions into a continuum is the pre-requisite to the understanding of characteristic boundary effects, which transcend the physical length scales and affect the key observed system attributes. These are energy efficiency and vibration refinement. This paper strives to present such an approach. It is shown that boundary and near boundary interactions can be adequately described by surface topographical measures, as well the thermodynamic conditions.

We study the dynamic response of stretched thin polymeric films following an impact by a rigid sphere. We vary the sphere radius, the impact velocity, and the film tension, and measure the contact time and the maximum deflection of the film during the impact. The response is sensitive to nonlinearities associated with the additional tension provided by the deformation. A physical model at the scaling level is presented. This allows us (i) to understand qualitatively experimental and numerical results and (ii) to present a diagram mapping different possible impact dynamics for membrane systems, which accounts for the interplay between membrane tension, intrinsic modulus, and geometrical factors such as the frame size and the sphere radius. DOI: 10.1103/PhysRevLett.97.244301

When an electronic device drops to the floor, it usually comes down at an inclination angle. After an initial impact at an uneven level, a clattering sequence occurs in rapid succession. There has been growing recognition that the entire impact sequence, rather than just the initial impact, is important for the shock response of circuits, displays, and disk drives. In a pioneering study by Goyal et al. (see [1] and [2]), it was found that when a two-dimensional rod was dropped at a small angle to the ground, the second impact might be as large as twice the initial impact. This raised the issue of how adequate the current testing procedure and simulation analysis are. Standard fragility tests, which typically involve a single impact with no rotation, are not adequate for that type of drop. Angled dropping tests have been seen in the literature, but they are apparently more complicated in nature. Similarly, including subsequent impacts in numerical simulations increases computational costs. So there is a need for further study of multiple impacts from both analytic and numerical analysis and experimental points of view. Problems of a single impact or first impact are discussed in many articles in mechanics and mathematical literature, (see, for example, [3]–[5] for rigid-body collisions). Even in single-impact cases, the topic remains the focus of much discussion (see [6] and [7]) as many theoretical issues of contact dynamics with friction have started to be resolved. Recent attention has been paid to detecting and calculating the micro-collisions that occur in a short time interval, when the bodies are allowed to be flexible (see [8] and [9]). A whole range of commercial software (ANSYS, etc.) is available to study the single-impact problem, with a rather detailed approach, such as finite element analysis, implemented (see [10] and [11]). The study of multiple impacts, however, is an emerging area. Goyal et al. used in [1] and [2] a transition matrix method to calculate the clattering sequence and its impacts. There, the contact times of impacts are assumed to be instantaneous and time intervals between the impacts are also brief, as

We study the the design of a tracking controller for the popular bouncing ball model: the continuous-time actuation of a table is used to control the impacts of the table with a bouncing ball. The proposed control law uses the impact times as the sole feedback information. We show that the acceleration of the table at impact plays no role in the stability analysis but is an important parameter for the robustness of the feedback system to model uncertainty, in particular to the uncertainty on the coefficient of restitution.

Non-axisymmetric drops impacting on a solid surface can alter impact dynamics significantly, thereby resulting in rebound suppression. Here, we present a method to control the bounce height of drops impacting on heated surfaces with ellipsoidal shaping. Experimental and numerical studies are used to investigate the effects of the geometrical aspect ratio (AR) of the drop on bouncing dynamics, which shows that maximum bounce heights of ellipsoidal drops can be reduced below spherical cases to nearly 40%. Control of bounce height can be explained in terms of a non-axial kinetic energy distribution during retraction. Interestingly, the non-axisymmetric hydrodynamics allows us to reduce contact time below this theoretical limit, which is explored both experimentally and numerically as a function of AR. This work may provide an understanding of bouncing dynamics on non-wetting surfaces for applications in surface cooling and cleaning.

The problem of impact dynamics of space robotic systems that consist of a rigid manipulator supported by a flexible deployable structure is addressed. Due to joint back-drivability and the dynamic coupling between the manipulator and its supporting structure, unknown motion of the system occurs after it makes impulsive contact with the environment. A method that uses the system's dynamic model is proposed to estimate the motion of the system after impact and used to minimize the impact effect and vibrations of the supporting structure. This method is verified experimentally using the MIT Vehicle Emulation System (VES II). The experimental results show that the impact force and the system motion after impact can be reduced if the manipulator configuration prior to impact and the controller gains are properly selected.

Surface damage or material removal during particle target collision is the result of material response to the contact stresses. Energy dissipation under two bodies collision may be estimated by means of the coefficient of velocity restitution and friction. Approach of impact dynamic and experimental study of dynamic coefficients has been applied to clarify the composite material behaviour under conditions of solid particle erosion. It has been shown that the level of energy dissipation during application and value of dynamic coefficient of friction can be a good guide for material selection for the use in conditions of dynamic loading.Copyright © 2005 by ASME

The impact dynamics of full-scale heavy-vehicle rollover events were quantitatively evaluated. Videotapes of a variety of rollover events were collected. One tractor-semitrailer combination was rolled by a sudden steer, two combinations rolled after a barrier impact, and one straight truck was pulled down an embankment. The videotapes were analyzed to estimate the vehicles' roll rates and their vertical velocities upon striking the ground. These experimental values corroborate the results of vehicle dynamic simulations that had been previously conducted to replicate actual rollover crashes. Those crashes were the subject of an NTSB Special Investigation Report that examined the crashworthiness of cargo tank trucks carrying hazardous materials.

In this paper the sensitivity to interference between a robot and its environment is examined. We establish rules for generating robot trajectories which maximize the robots capabilities with respect to exerting forces while minimizing the strain on the drives. Another aspect is the calculation of the maximal tolerable position error that guarantees a certain assembly task to be completed within pre-defined force limits. Applying impact dynamics yields the impact forces when the mating parts come into contact. The transfer behavior of the robot to avoid unwanted oscillations under dynamically varying loads is examined. The dynamical model of the robot includes elasticity, damping, friction and backlash in the joints. The parts to be assembled may be rigid or elastic with Coulomb friction acting between them. The calculation methods are explained in detail and measurements conducted on a PUMA 562 robot complete the approach.

Genetic programming (GP) was used in an experiment to investigate the possibility of learning rules that trigger adaptive mesh refinement. GP detected mesh cells that required refinement by evolving a formula involving cell quantities such as material densities. Various cell variable combinations were investigated in order to identify the optimal ones for indicating mesh refinement. The problem studied was the high speed impact of a spherical ball on a metal plate.

Over the last decades, a lot of attention has been given to the quasi-static behavior of the granular materials. Also, impact problems become important in the field of material engineering and soil mechanics: for example the penetration into the surface of planet by meteorites or projectiles like Nereus Sample Return Project by the Institute of Space and Astronautical Science (ISAS) in Japan. However, only a few attempts have so far been made at impact dynamics of granular materials and shock waves in granular materials and granular layers. The impact behavior of granular materials is quite different from that of other continuous solid materials because of the compressibility and fluidity of granular materials. In this chapter, the dynamic response of granular materials to impact of a spherical projectile is investigated experimentally and also numerically using discrete element method. The two-dimensional granular material comprised of nylon spheres arranged regularly in a rectangular container is collided by a steel sphere at velocities less than 15m/s. The numerical simulations are compared with the measurements using high-speed video camera. The motion of each particle can be traced in detail by discrete element method. Also, it becomes clear that the walls of the container have a significant effect on the impact behavior of granular materials.

Vibro-impact vibration problems with one-degree-of-freedom systems have a long history in mechanics. The problems like stationary subharmonic motions and their stability, the influence of damping and friction on vibro-impact dynamics, elastic and plastic type impacts, time histories and phase portraits of the vibro-impact systems have been considered [1-4].

The foregoing chapters are devoted to investigate the mathematical nature of impact dynamics. Let us note at once that a dynamical problem with the smooth dynamics and the unilateral constraints is not complete, since one needs the knowledge of the behaviour of the system on the constraints surface to investigate global motion. In fact, the behaviour at the impact is generally modeled by a set of coefficients (not necessarily constant) that relate post and pre-collisions values. In this chapter we first investigate in some detail the dynamics of two rigid bodies that collide. Then we review the existing studies on macroscopic models of the shock phenomenon.

We investigate the in-flight dynamics of a simplified model of a supercavitating body. In particular we are interested in the nature and frequency of the impacts which occur as the tail of the body touches the cavity walls. Referring to laboratory experiments conducted at Cal Tech in the 1950’s, we show that the tip force by the fluid is approximately directed along the length of the body. This gives zero moment about the body’s center of mass which leads us to assume that the body moves as if it were a moment-free rigid body pinned at its tip. To simplify the analysis, we assume that the body is not spinning about its symmetry axis. Then the motion between impacts is a plane motion with constant angular velocity. Using elementary fluid mechanics, we model the impact occurring when the tail touches the cavity walls, and we show that it is reasonable to assume that the impact is instantaneous with coefficient of restitution unity. Using this simplified model, we offer a simulation for typical parameters.

The theoretical modeling, numerical simulation, and experimental verification for the impact dynamics of a flexible beam with large overall motion are researched. Based on the rigid-flexible coupling dynamic theory of flexible multibody system, the rigid-flexible coupling dynamic equations of the beam are established. On the use of the continuous contact force method (CCFM) and the contact constraint method (CCM), the respective global impact dynamic equations of the system are derived to achieve dynamic transformation and solution in different stages including impact and unimpact status. The experimental study on the impact dynamics of the flexible beam is investigated, and the dynamic response in the impact process is obtained. The experimental results are compared with the results of the impact dynamic simulation and the finite element method (FEM) simulation. The system's dynamic behaviors in the impact process are analyzed, and the accuracy of the two impact dynamic theories is verified.

The absence of data on the material properties of skeletal muscle has resulted in limitations in the utility of human surrogates in evaluating injury potential during head and neck impact. The purpose of this paper is two fold. First, a quasi-linear viscoelastic model is developed to describe and predict the passive structural response of the New Zealand White rabbit tibialis anterior muscle. Second, the constitutive properties of skeletal muscle and the effect of elongation rate on these properties are determined for both the passive and stimulated states of the muscle. A review of the literature, and recommendations for modeling the effects of skeletal muscle on cervical spine impact dynamics are discussed. Language: en

This paper describes an ongoing effort to develop techniques capable of locating the position of space debris impacts and to quantify the strain energy absorbed by the space structure as a result of these impacts. The techniques under development use optical fiber sensors and neural networks as the primary sensor and decision making components. To date, this project has resulted in the development of (1) a mathematical model of plate impact dynamics for use in sensor and neural network paradigm development, (2) a sensor demodulation system specifically designed for moderate impact energies, (3) several neural network paradigms with the potential to locate impacts, and (4) a test configuration to experimentally confirm the proposed paradigms.

Optimum design of dynamic fracture test rigs demands a thorough appreciation of beam vibration under impact. Analyses invariably presume rigid anvils, and neglect overhang effects. The beam response predicted analytically and numerically in this paper highlights the significant role of anvil rigidity and beam overhangs on the impact dynamics of three point bend (3PB) specimens.

LDA is used to make measurements of the impact and rebound of small particles on metal surfaces. The impact dynamics are investigated in terms of the velocities and angles of the particles on two types of surface. Two experimental rigs designed for low and high velocities are described. Impact and rebound velocities are given for impacts of glass beads at low velocities on aluminium and at higher velocities on aluminium and tool steel.

Use is made of the KRASH program to simulate a simplified car into barrier impact. The objectives are: to outline an approach to the simulation of vehicle structural impact dynamics through the use of a simplified frontal impact model; to identify, through the use of the model, structural features which determine the crash behavior of a car in a frontal barrier impact; to identify current limitations of the approach; and to outline future improvements. A step by step modeling technique is illustrated whose application, at an early stage in the design process, allows an understanding of the contribution of individual components to the overall crash performance of a vehicle.

The authors report the impact response of water droplets impinging on superhydrophobic carbon nanotube arrays and observe that arrays with different wetting properties display significantly different responses. For an array with a static contact angle of 163°, the droplet bounces off the surface several times, while for an array with a reduced contact angle of 140°, the droplet does not rebound and remains pinned. The contact angle hysteresis and contact line pinning for the 140° array suggest that the momentum of the droplet during the initial impact enables it to penetrate and displace the air pockets that are responsible for the superhydrophobicity of the array under static conditions.

This article presents an impact dynamics analysis of the vibratory probe in a microcoordinate measuring machine. The chaotic behavior of the vibratory probe was identified when the driving frequency was changed. A multimode analysis was carried out to investigate the microprobe in both noncontact and contact states. An orthogonal mode transformation was used to maintain continuities when impact occurred. The analytical results indicated that mode coupling and mode coexistence suppressed subbifurcation and pulled down the impact period under particular driving frequencies. To achieve accurate identification of the microprobe in contact with microstructures, the frequency spectra of vibration signals at different contact states were compared. It was shown that the optimum driving frequency should be in the pull-down region. In this region, the dominant frequencies before and after the contact can be clearly separated, resulting in negligible background vibrations.

The dynamic behavior of an air bubble, emanating from a 0.32 mm i.d., 0.64 mm o.d., vertical capillary-tube orifice with a bubble interval of 0.22–0.28 s at constant pressure and adiabatic (T=25°C) conditions, as well as droplet impact and spreading on a hydrophobic surface are characterized. Images of the mili-scale spatial-temporal evolution of bubbles (embryonic appearance at orifice tip → growth and detachment → translation) as well as droplets were acquired using a high-speed (5000 frames/s) digital video camera fitted with a 8× optical zoom lens. It was triggered through a computer interface to record continuous high-speed video from which any desired frame can be captured by digital-video-processing software; the equivalent departure diameter was estimated by area-averaging using image processing software. The impact, spreading, and recoil behaviors of ethanol and water droplets on a horizontal stainless steel surface are depicted in Fig. 1. For constant Weber number (We∼10), the spreading and recoil dynamics in the two cases are significantly different. Higher wettability of ethanol promotes greater spreading and dampens recoil in comparison with that seen in water. Figure 2 depicts the growth of an air bubble in pools of ethanol and water. While displaying similar ebullience, a bubble of smaller size and surface age is produced in low-surface-tension ethanol. Dynamic shape variations of the air bubble as it translates upwards in the pool are seen in Fig. 3. From a nearly spherical, tear-drop bubble, the shape changes to an oblate ellipsoid during translation, and surface tension effects are manifest only in the size of respective bubbles.

The Impact Dynamics Research Facility (IDRF) is a 240-ft.-high gantry structure located at NASA Langley Research Center in Hampton, Virginia. The IDRF was originally built in the early 1960's for use as a Lunar Landing Research Facility. As such, the facility was configured to simulate the reduced gravitational environment of the Moon, allowing the Apollo astronauts to practice lunar landings under realistic conditions. In 1985, the IDRF was designated a National Historic Landmark based on its significant contributions to the Apollo Moon Landing Program. In the early 1970's the facility was converted into its current configuration as a full-scale crash test facility for light aircraft and rotorcraft. Since that time, the IDRF has been used to perform a wide variety of impact tests on full-scale aircraft, airframe components, and space vehicles in support of the General Aviation (GA) aircraft industry, the U.S. Department of Defense (DOD), the rotorcraft industry, and the NASA Space program. The objectives of this paper are twofold: to describe the IDRF facility and its unique capabilities for conducting structural impact testing, and to summarize the impact tests performed at the IDRF in support of the DOD. These tests cover a time period of roughly 2 1/2 decades, beginning in 1975 with the full-scale crash test of a CH-47 Chinook helicopter, and ending in 1999 with the external fuel system qualification test of a UH-60 Black Hawk helicopter. NASA officially closed the IDRF in September 2003; consequently, it is important to document the past contributions made in improved human survivability and impact tolerance through DOD-sponsored research performed at the IDRF.

When a liquid drop lands on a solid surface without wetting it, it bounces with remarkable elasticity. Here we measure how long the drop remains in contact with the solid during the shock, a problem that was considered by Hertz for a bouncing ball. Our findings could help to quantify the efficiency of water-repellent surfaces (super-hydrophobic solids) and to improve water-cooling of hot solids, which is limited by the rebounding of drops as well as by temperature effects.

Heat exchanger tube bundles may be damaged by vibration induced from the cross flow. This damage generally occurs at the tube supports where the tube is only loosely supported. The loose support results in the tube motion being strongly nonlinear with very complicated dynamics. Some theoretical equations for the tube dynamics and wear rates are investigated by using dimensional analysis, physical modeling and numerical simulations. From the analysis of these equations, some simple formulas are developed which show the influence of excitation level and tube-to-support clearance on the tube response.