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Wed, 21 Jul 2010 13:45:54 +0200Wed, 21 Jul 2010 13:45:54 +0200A discrete mechanics approach to Cosserat rod theory – Part 1: static equilibria
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2206
A theory of discrete Cosserat rods is formulated in the language of discrete Lagrangian mechanics. By exploiting Kirchho's kinetic analogy, the potential energy density of a rod is a function on the tangent bundle of the conguration manifold and thus formally corresponds to the Lagrangian function of a dynamical system. The equilibrium equations are derived from a variational principle using a formulation that involves null{space matrices. In this formulation, no Lagrange multipliers are necessary to enforce orthonormality of the directors. Noether's theorem relates rst integrals of the equilibrium equations to Lie group actions on the conguration bundle, so{called symmetries. The symmetries relevant for rod mechanics are frame{indierence, isotropy and uniformity. We show that a completely analogous and self{contained theory of discrete rods can be formulated in which the arc{length is a discrete variable ab initio. In this formulation, the potential energy density is dened directly on pairs of points along the arc{length of the rod, in analogy to Veselov's discrete reformulation of Lagrangian mechanics. A discrete version of Noether's theorem then identies exact rst integrals of the discrete equilibrium equations. These exact conservation properties confer the discrete solutions accuracy and robustness, as demonstrated by selected examples of application. Copyright c 2010 John Wiley & Sons, Ltd.P. Jung; S. Leyendecker; J. Linn; M. Ortizreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2206Wed, 21 Jul 2010 13:45:54 +0200Discrete Lagrangian mechanics and geometrically exact Cosserat rods
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2093
Inspired by Kirchhoff’s kinetic analogy, the special Cosserat theory of rods is formulatedin the language of Lagrangian mechanics. A static rod corresponds to an abstract Lagrangian system where the energy density takes the role of the Lagrangian function. The equilibrium equations are derived from a variational principle. Noether’s theorem relates their first integrals to frame-indifference, isotropy and uniformity. These properties can be formulated in terms of Lie group symmetries. The rotational degrees of freedom, present in the geometrically exact beam theory, are represented in terms of orthonormal director triads. To reduce the number of unknowns, Lagrange multipliers associated with the orthonormality constraints are eliminated using null-space matrices. This is done both in the continuous and in the discrete setting. The discrete equilibrium equations are used to compute discrete rod configurations, where different types of boundary conditions can be handled.P. Jung; S. Leyendecker; J. Linn; M. Ortizreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2093Wed, 20 May 2009 14:51:18 +0200Brillouin Light Scattering from Surface Phonons in Hexagonal and Cubic Boron Nitride Films
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/932
Phase velocities of surface acoustic waves in several boron nitride films were investigated by Brillouin light scattering. In the case of films with predominantly hexagonal crystal structure, grown under conditions close to the nucleation threshold of cubic BN, four independent elastic constants have been determined from the dispersion of the Rayleigh and the first Sezawa mode. The large elastic anisotropy of up to c11/c33 = 0.1 is attributed to a pronounced texture with the c-axes of the crystallites parallel to the film plane. In the case of cubic BN films the dispersion of the Rayleigh wave provides evidence for the existence of a more compliant layer at the substrate-film interface. The observed broadening of the Rayleigh mode is identified to be caused by the film morphology.Thomas Wittkowski; P. Cortina; Jörg Jorzick; K. Jung; Burkard Hillebrandspreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/932Tue, 08 Feb 2000 00:00:00 +0100