Resumen de Análisis dinámico de las tenso estructuras: propuesta de metodología de cálculo y software aplicado
Ernesto Muñiz Martín
Traditionally, the dynamic analysis of Multi degree Systems are based on the study of modal Shapes or energy balances given an established oscillation figure. The expert user of those methods could determine how resonance affects the dynamic behaviour of the analysed structure under time dependent variables as wind, moving loads, human steps, etc. or response spectrums (seismic). This Doctoral thesis propases a calculus methodology whose purpose is to obtain the characteristic modal shapes and energy balances of a tensile structure. Thus, an idealized tensile structure which is modeled using beams with only axial forces could be analyzed in order to get its natural vibrations, modal shapes and tridimensional dynamic behaviour. The expert use of the obtained results conforms the base for the analysis of the most common dynamic situations that can be considered when a tensile structure is designed. Proposed methodology is based on: . Force density method. . Classic analysis of dynamics of structures. . Modal Spectrum Analysis . . Energy balances: Rayleigh Ritz method. Starting from these fundamentals, a sequence of physical and mathematical principies is used to obtain and verify the natural vibration modes for a given tensile structure. The highlights of . the procedure are: . Deduction of the stiffness matrix using the force density method: an adaption of the general method is used to substantiate a stiffness relation among applied forces and displacements on movable nodes. This is possible due to a "static condensation" of part of the system and the deduction of a Dynamic Force Density for each beam that links load and length for a given prestressing level, taking in consideration section, materials and other corrections. Finally, it is concluded that geometry, loads on movable nodes, supports, prestressing loads and beam properties are linked to each other through a "dynamic stiffness matrix" . Classic Dynamic Analysis and Modal Spectrum Methods: taking as the starting point the previous "dynamic stiffness matrix", a relation to the mass of the system (having into consideration geometry, loads and materials) is formulated. Furthermore, it is possible to outline the classic eigenvalue's problem whose resolution is necessary to obtain the modal shapes of a system with multiple degrees of freedom . lt is important to consider the singularities of the problem because X, Y, and Z are independent variables. Synchronization among directions is required because it affects to the tridimensional analysis of the movement when the natural frequencies are studied and the total movement is composed. . Energy balances: They are mostly used to verify results previously obtained. The proposal contains a software as part of the Thesis, whose development is based in the exposed method. The software allows the simulation of the most common tensile structures, showing its modal shapes and natural frequencies
