On the stability of Lamb modes

We prove analytically, in two steps, that Lamb modes in a homogeneous waveguide are stable for arbitrary admissible values of Lame constants. First, by using an energy-type method we show that, for real wavenumbers #kappa#, #omega#"2 is real, where #omega# is a frequency. Then it is shown that for a purely imaginary frequency #omega# the dispersion relation D(k, #omega#)=0 does not have real roots in #kappa#. This result provides a theoretical support for the physical relevance of the signalling problem in a homogeneous waveguide to seismology. An implementation of the mathematical formalism for treating the spatial response of an open homogeneous system to a localized harmonic oscillator, i.e., for treating the signalling problem, is carried out by computing numerically the wavenumbers of Lamb modes and applying the Briggs causality condition. In the computations, we first discretize the boundary value problem for Lamb modes by using a Chebyshev collocation method, and then, for a given complex #omega#, find all solutions in #kappa# of the resulting algebraic eigenvalue problem. the companion-matrix method and a standard global eigenvalue solver are used. It is also shown that an unstable inhomogeneous waveguide is always absolutely unstable. Thus, the signalling problem is physically meaningful only for stable waveguides. (orig.)SIGLEAvailable from TIB Hannover: RR 6943(95/02) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Contribution to the dynamic contact/impact problem

Machines, mechanisms, vehicles, robots, manipulators are multibody configurations with many dependent contacts including impulsive and stick-slip processes, dynamic sliding, chattering; etc. Some of these phenomena are generated by the imperfect coupling between the elements. Applications of impact mechanics can require linear and onlinear combination of friction, thermal effects, dynamic plasticity, wave propagation, etc.. Even low speed collisions can be complicated although finite element analysis now provide expanded solution capabilities. In some problems, the main interest lies not in the stresses and displacements in the contact region but rather the dynamics (velocity changes and energy loss) of the colliding objects. For problems that involve intermittent motions due to an impact prediction of the response is more difficult. In an impact, nonlinear contact forces of unknown nature are created, which act and disappear over a short period of time. Practically, in several situations simple models are advantageous. Thus, if a designer is interested in the effect upon a control strategy of a collision of a robot's end effector or an automotive engineer wishes to simulate highway speed collisions for arbitrary vehicle orientations they need fast and accuracy models. A simple model is usually sufficient to model chaotic dynamics of vibration impact. (orig.)SIGLEAvailable from TIB Hannover: RR 6943(98-09) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

On the regularity of weak solutions of a shear thinning fluid of power-law type

SIGLEAvailable from TIB Hannover: RR 6943(2003,23) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Unstetige Kontakte in Mehrkoerpersystemen. Randelementrechnungen und erste Experimente

Available from TIB Hannover: RR 6943(97-22) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Screen magnetic type problem for vector Helmholtz equation

SIGLEAvailable from TIB Hannover: RR 6943(97-07) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Mixed boundary value problems for the Stokes equation

The paper deals with mixed type three-dimensional boundary value problems of Hydrodynamics, particularly with mixed problems for the Stokes linear equation in a domain either exterior or interior to an arbitrary, closed, two-dimensional, smooth surface with a smooth boundary. On one part of the boundary the Dirichlet type condition (the velocity field) is prescribed, while on the other part the Neumann type condition (the stress vector) is given. With the help of the theory of boundary integral (pseudodifferential) equations uniqueness and existence theorems are proved in the Bessel-potential and Besov spaces, and C"#alpha#-smoothness (with #alpha#<1/2) of solution is established in a neighbourhood of the curve where different boundary conditions collide. (orig.)SIGLEAvailable from TIB Hannover: RR 6943(97-06) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A model and a general problem on plastic flow under great deformations

SIGLEAvailable from TIB Hannover: RR 6943(99-07) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Orthogonal projections onto convex sets and the application to problems in plasticity

We review the classical theory of static and quasi-static plasticity in an abstract framework of convex analysis. It can be shown that the extended use of orthogonal projections onto closed convex sets simplifies the analysis substantially. We present new characterizations of the primal problem in plasticity. The abstract setting is applied to problems in perfect plasticity and to plasticity with nonlinear hardening. Furthermore, our approach leads to a better understanding of the radial return algorithm which is commonly used in computational plasticity. (orig.)Available from TIB Hannover: RR 6943(99-15) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Experimental and theoretical investigation of a rigid body striking an elastic rod

Available from TIB Hannover: RR 6943(2000,12) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

On a hybrid boundary element method

In this paper we study a symmetric boundary element method based on a hybrid discretization of the Steklov-Poincare operator. The representation used involves only single and double layer potentials and does not require the discretization of the hypersingular integral operator as in the symmetric formulation. The stability of the hybrid Galerkin discretization is based on a BBL-like stability condition for the trial spaces used. Then the error estimates follow by the application of a generalized Strang lemma. For the resulting symmetric stiffness matrix we can construct efficient preconditioners to use the preconditioned conjugate gradient method as iterative solver. Due to the symmetry, this approach is already used in engineering applications for the symmetric coupling of boundary and finite elements. (orig.)SIGLEAvailable from TIB Hannover: RR 6943(97-50) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman