Guide Nonsmooth Dynamics of Contacting Thermoelastic Bodies: 16 (Advances in Mechanics and Mathematics)

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Dynamical Systems : Lectures Given at the C. Summer School He Chow R. Conti Ray Johnson J. Mallet-Paret Roger D. The Theory of Chaotic Attractors. This study contributes to the development of this? When considered from the mathematical point of view, the method of analysis is reduced to the solution of the system of di? The latter equation is obtained with the use of the Laplace integral transform. Contact Characteristics During Braking Process. Handbook of physiology: Section 2, The cardiovascular system Chapter 1 Introduction.

It is shown that these models include a transport equation for the particulate fluctuation energy, and in more advanced version, for evolution of components of the kinetic stress tensor. The implication of generalized extended thermodynamical principles in modeling particulate flows in a state of rapid motion are described.

J.R.Barber: List of Publications

The special cases of rapid simple shear flows of granular materials is discussed. Comparisons of the model predictions for granular stresses and normal stress differences with the available simulation results are presented. The effects of inter-granular friction, and interstitial fluids on flows of particulate media is also discussed. The influence of harmonic normal loads on sliding friction is investigated through analysis of contacts consisting of spherical sliders of hard materials on softer metal surfaces.

Friction for such contacts is assumed to result from a plowing component and a shearing component. Calculations and experiments show that the relation between the coefficient of friction and normal load is highly nonlinear. In the presence of harmonic variations in normal load, this non-linearity causes a shift in the average coefficient of friction. For ideal lubricated contacts, the shearing component of friction is very small and for this case, it is shown that the maximum average reduction in the coefficient of friction is ten percent.

When the shearing component is more significant, as with dry contacts, the shift is less. For example, when the interfacial shear strength is one-sixth the hardness of the softer material, the maximum average reduction in the coefficient of friction is five percent. A standard system identification technique is used to fit mathematical laws of dynamic friction to experimental data.

The conversion of the data, originally recorded graphically, to discrete time series and their subsequent processing is discussed. Identified friction models are compared on the basis of their accuracy in estimating energy dissipation per cycle of vibration.

Numerical analysis of hemivariational inequalities in contact mechanics

A new Hermite cubic smoothing scheme for the computational description of contact surfaces is outlined. Attention is focused on the two dimensional case, although the scheme is designed to be extendible to three dimensions.

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A numerical result illustrates the utility of the proposed scheme. Study of response of flexible systems due to impact is reported in this paper. The contact forces during impact has been modeled using modified Hertzian relation assuming quasi-static equilibrium. The model incorporates hysteresis damping to explain energy dissipation.

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The developed methodology was then verified with the experimental results. The presence of surface texture on many engineering surfaces results in the contact being more compliant than if the interface were smooth and flat. In this paper we study a model problem, the thermoelastic contact of two steel rings sliding with friction.

Contacts of this type are representative of dry clutches, brakes and seals. We illustrate the importance of including realistic contact stiffness in the thermoelastic analysis of such systems. The stress and temperature fields change significantly as the contact stiffness is varied from rigid to softened, even when the sliding times are of the order of milliseconds in duration.

In this paper we study the design and modelling of a new rotary actuator that has been developed at the University of Waterloo using shape memory alloy springs.

Introduction to Mechanics

Shape memory alloys SMAs have the property that they can be subjected to a large deformation when it is below martensite temperature and it recovers its original shape when it is heated over austenite temperature. In other words, a SMA can directly convert thermal energy to mechanical work!

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It is also interesting to note that among low and medium range actuators SMAs have the highest power to weight ratio. It is modular and large rotations can be obtained using extra modules. The actuator design is first explained and then, the Ikuta's model is modified to derive a mathematical representation of the actuator. Using experimental and simulation results the mathematical model is verified. In this paper we investigate the modelling of an industrial belt-driven gantry robot 1 using graph theoretic modelling GTM.

The design of the robot is such that the kinematic driver is fixed to the base frame while the end-effector is free to move in a straight line relative to the base. This arrangement has the benefit of radically reducing the system inertia, which permits the robot to operate at higher speed. Further increase in the operational speed of the robot is now limited by the induced vibration due to the belt flexibility.

Using graph theoretic modelling we study the robot dynamics considering the base and belt flexibilities. To incorporate the pulley into the formulation, a multi-terminal model is introduced that can be used in the GTM for any simple or compound pulley with fixed or moving shaft.

Limit friction forces between structure constituents are employed to define a practical failure criterion for granular media. An analytical solution is presented to estimate local friction states built up due to given boundary forces on the strocture. The question as to where failure is most likely to initiate is mainly addressed. Experiments were conducted to investigate the effect of the shape of Nitinol strips on shifting the natural frequency of a cantilever beam. Nitinol strips were attached to the cantilever beam in order to reduce the vibration of the beam upon activation.

The results show that Nitinol strips with curved memory are more effective than straight strips in shifting the natural frequency of the system.