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Frictional Forces (frictional + force)

Distribution by Scientific Domains
Engineering66%
Physics and Astronomy33%

Selected Abstracts

Finite element modelling of frictional instability between deformable rocks

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2003
H. L. Xing
Abstract Earthquakes are recognized as resulting from a stick,slip frictional instability along faults. Based on the node-to-point contact element strategy (an arbitrarily shaped contact element strategy applied with the static-explicit algorithm for modelling non-linear frictional contact problems proposed by authors), a finite element code for modelling the 3-D non-linear friction contact between deformable bodies has been developed and extended here to analyse the non-linear stick,slip frictional instability between deformable rocks with a rate- and state-dependent friction law. A typical fault bend model is taken as an application example to be analysed here. The variations of the normal contact force, the frictional force, the transition of stick,slip instable state and the related relative slip velocity along the fault between the deformable rocks and the stress evolution in the total bodies during the different stages are investigated, respectively. The calculated results demonstrate the usefulness of this code for simulating the non-linear frictional instability between deformable rocks. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Tracking control of a piezo-actuated stage based on a frictional model,

ASIAN JOURNAL OF CONTROL, Issue 3 2009
Yi-Cheng Huang
Abstract The tracking control accuracy of a piezoelectric actuator (PEA) is limited due to the actuator's inherent hysteretic nonlinearity. Direct drive of PEA on a positioning stage with friction force will cause control problems. An approximated dynamic model of PEA with consideration of friction force is novel synthesized for control. This model is based on a second-order transfer function with two parameterization terms. The first time delay term consists of the hysteresis of piezo effect combined with frictional force lag with varying velocity. The second term is comprised of both presliding and sliding regimes. The H-infinite tracking controller is designed to compensate for the structural uncertainty associated with time delay and the unstructured frictional force in the PEA stage. Iterative Learning Control is implemented to reduce the unmodeled repetitive error by a factor of 20. Numerical simulations and experimental tests consolidate the root mean square (RMS), positioning error close to the hardware reproducibility and accuracy level. Experimental results show the controlled stage can be potentially used for precise positioning. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

A discrete model for the dynamic propagation of shear bands in a fluid-saturated medium

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2007
Julien Réthoré
Abstract The first part of this manuscript discusses a finite element method that captures arbitrary discontinuities in a two-phase medium by exploiting the partition-of-unity property of finite element shape functions. The fluid flow away from the discontinuity is modelled in a standard fashion using Darcy's relation, and at the discontinuity a discrete analogy of Darcy's relation is used. Subsequently, dynamic shear banding is studied numerically for a biaxial, plane-strain specimen. A Tresca-like as well as a Coulomb criterion is used as nucleation criterion. Decohesion is controlled by a mode-II fracture energy, while for the Coulomb criterion, frictional forces are transmitted across the interface in addition to the cohesive shear tractions. The effect of the different interface relations on the onset of cavitation is studied. Finally, a limited quantitative study is made on the importance of including a so-called dynamic seepage term in Darcy's relation when considering dynamic shear banding. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Tidal dissipation in rotating fluid bodies: a simplified model

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2009
Gordon I. Ogilvie
ABSTRACT We study the tidal forcing, propagation and dissipation of linear inertial waves in a rotating fluid body. The intentionally simplified model involves a perfectly rigid core surrounded by a deep ocean consisting of a homogeneous incompressible fluid. Centrifugal effects are neglected, but the Coriolis force is considered in full, and dissipation occurs through viscous or frictional forces. The dissipation rate exhibits a complicated dependence on the tidal frequency and generally increases with the size of the core. In certain intervals of frequency, efficient dissipation is found to occur even for very small values of the coefficient of viscosity or friction. We discuss the results with reference to wave attractors, critical latitudes and other features of the propagation of inertial waves within the fluid, and comment on their relevance for tidal dissipation in planets and stars. [source]

Comparison of analytical and numerical solution for optimal vortex diffuser design

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005
Andreas H. Mehrle
The contribution deals with optimization of wing tip devices, so called vortex diffusers. A comparison is given between an analytical approach for obtaining the optimal circulation loading and the results of a numerical investigation using a lifting line method. The purpose of most wing tip devices is to reduce the induced drag of the main wing by converting vortex energy into thrust. In order to achieve an optimal design, a variational formulation originally proposed by Betz and Prandtl for air screws is applied to the circulation distribution of the diffuser blades. In extension to the inviscid formulation, a viscous correction is applied in order to account for frictional forces. In an effort to validate the analytical results, a comparison is given with numerical solutions from a lifting line method. The loading of the diffuser blades is parametrized and optimized with respect to resulting thrust by use of a quasi-Newton gradient method. Comparison shows that, knowing the velocity distribution in the near wake of the wing, considerable decrease of induced drag may be achieved making use of vortex diffusers. Although actual circulation loading may differ between the analytical and numerical estimation, resulting thrust agrees within a few percent. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Mechanics with variable-order differential operators

ANNALEN DER PHYSIK, Issue 11-12 2003
C.F.M. Coimbra
Abstract This work presents the novel concept of Variable-Order (VO) Calculus through the description of a simple problem in Mechanics. A mathematical definition for the VO-differential operator that is suitable to mechanical modelling is proposed, and an example concerning the effect of nonuniform viscoelastic frictional forces is described. A numerical method for the solution of Variable Order Differential Equations (VODEs) is proposed. The physical model under study requires mathematical tools that lie beyond the traditional methods of Constant-Order (CO) differential equations. The VO-Calculus formulation is compared to a CO-Calculus model in order to show the limitations of the latter in resolving the transition between the relevant dynamic regimes. [source]