8 research outputs found
Parallel scanning of implicit surfaces with the simplex algorithm
Solution of mechanical problems often requires the analytical or numerical calculation of equilibrium paths, while solution sets of other dimension than one are rare. From this requirement emerged numerous method for the calculation of bifurcation diagrams. Two large group of the solution methods are the continuation methods and the scanning methods (however hybrid algorithm exists as well). The Simplex Algorithm is a robust approximative technique based on the Piecewise Linearization (PL-)algorithm, which has its application as a continuation and as a scanning algorithm as well. In this paper we will show the extension of the method for finding a 2-dimensional manifold (i.e. surface) with the scanning of the parameter space. We analyze the performance of the algorithm and its parallelization through two simple examples
Csigasorral fĂĽggesztett gerenda szabadrezgĂ©se modálanalĂzissel
Egy csigasorral fĂĽggesztett gerenda szabadrezgĂ©sĂ©t vizsgáljuk. A gerendát Bernoulli-Euler rĂşdkĂ©nt modellezzĂĽk, Ă©s bemutatjuk a szerkezet sajátrezgĂ©salakjait Ă©s sajátkörfrekvenciáit feszĂtett Ă©s feszĂtetlen fĂĽggesztĹ‘kábel esetĂ©n a folytonos rĂşd differenciálegyenletĂ©nek megoldásával. A kábel feszĂtett, vagy feszĂtetlen voltátĂłl fĂĽgg Ě‹oen beszĂ©lĂĽnk aktĂv Ă©s passzĂv fĂĽggesztĂ©sr Ě‹ol. Az aktĂv Ă©s passzĂv fĂĽggesztĂ©s
rezgésalakjai egymásnak megfeleltethet ̋oek, az állapotváltozások során a modális koordináták transzformációja id ̋ofüggetlen módon végezhető.
Numerikus mĂłdszert mutatunk a rezgĂ©s számĂtására, az aktĂv Ă©s passzĂv állapotok közötti váltás kezelĂ©sĂ©re. KĂĽlönbözĹ‘ kezdőállapotokat használva szimuláljuk a tartĂł szabadrezgĂ©sĂ©t. Megmutatjuk, hogy mĂ©g az aktĂv Ă©s passzĂv fĂĽggesztĂ©sek közötti váltás okozta erĹ‘s nemlinearitás
mellett is képes a szerkezet periodikus szabadrezgést végezni
Dynamic analysis of a beam on block-and-tackle suspension system: A continuum approach
In this paper the dynamic analysis of a beam on a block-and-tackle suspension system is accomplished using a continuum approach. The modal shape functions and the natural frequencies of the structure are derived in a dimensionless form for both slacked and stressed cables. A procedure is developed to handle the nonlinearity originated from the consecutive slacking and stressing of the suspension cable. Vibration analysis of the bilinear, multi-degree-of-freedom structure is accomplished for a vortex-shedding generated lift force and for a continuous pedestrian flow
The Effect of Continuous Suspension Constraint on the Free Vibration and Buckling of a Beam
In this paper, the free vibration and the buckling of a continuously suspended simply-supported beam are analyzed. A semi-analytical approach is used to calculate the natural circular frequencies and the critical forces of the beam. The length of the suspension is used as a parameter, and the natural circular frequencies and the critical forces are presented in a frequency map or a buckling map. The maps are analyzed in view of the trivial solutions, and the frequency map is compared to the map of discrete cable-stayed beams. Finally, for the validation of the results a numerical, finite element analysis is performed