ResumenEn este trabajo se propone una formulación sistemática que permite resolver el problema dinámico directo de robot paralelos, constituidos por eslabones rígidos y juntas ideales, mediante el uso de las ecuaciones de Gibbs-Appell explícitas, propuestas por Udwadia y Kabala. La metodología permite transformar la resolución del problema dinámico de un sistema mecánico restringido, a la resolución de un sistema conformado por cadenas abiertas, lo cual permite hacer uso de algoritmos eficientes basados en las ecuaciones de Gibbs-Appell. La validación de la metodología se realiza a través de dos ejemplos numéricos. Palabras claves: sistemas multicuerpo, robot paralelos, ecuaciones Gibbs-Appell, dinámica directa Forward Dynamic Problem of Parallel Robot by Using Gibbs-Appell Equations AbstractIn this work the use of efficient open chain algorithms based on Gibbs-Appell equations is extended for solving the forward dynamics problem of parallel robots. This extension is carried out by developing a methodology based on the Explicit Gibbs-Appell dynamic equation of motion. The methodology allows transforming the solution of the dynamic problem corresponding to a restricted mechanical system to the solution of a system formed by open chains that permit using the efficient algorithms based on the Gibbs-Appell equations. The methodology was validated using two numerical examples.
Due to the extensive use of one-dimensional equivalent linear analyses to determine the free-field response of nonlinear soil deposits, dynamic numerical simulations able to reproduce an analogous response to equivalent linear codes are of great value for practical engineering, particularly for dynamic soil-structure interaction problems. An appealing alternative, for problems not close to a failure condition, is to assume a linear elastic behaviour of the soil but with stiffness parameters derived from one-dimensional equivalent linear analyses, i.e. consistent with the level of deformation induced by the input motion. In this approach, energy dissipation has to be artificially incorporated through material damping formulations. In this work, local, Rayleigh, and hysteretic damping formulations in FLAC were assessed to emulate results from one-dimensional equivalent linear analysis. A main feature of the analyses is that they consider a site having a considerably stratified soil deposit, in which the shear wave velocity profile displays significant variations and where the selection of some parameters in the damping formulations is not a trivial task. Results provide relevant insights into the performance of the adopted damping formulations and the selection of material damping parameters to reproduce results of equivalent linear analyses.
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