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ENERGY BALANCE ANALYSYS IN NON LINEAL DYNAMIC EQUIVALENT SYSTEMS.
Last modified: 2017-12-03
Abstract
This paper introduces a formulation approach for nonlinear dynamic vibrations study as example in concrete building structures. The analysis is performed in time and frequency domain. It could be applied in the first phase to structures with a single degree of freedom (SDOF). In all of the cases, a contrast could be formed using the balance of energy. To validate the model, a quasi-monotonic action is applied in the foundation. The problem is solved both analytically and numerically by evaluating the energies in the time and frequency domain. Subsequently, six calculation accelerograms, all compatible with the energy input, resulting from the adjustment to the same design spectrum, are introduced like general loads.
In all cases the curve derived from the static non-linear push-over analysis is used as a control of lateral rigidity with the displacement. In the case of cyclic loading, the effect derived from hysteresis is also introduced, with special emphasis on the pinching effect by a method based on the Bouc-Wen-Baben-Noori theory [1] and the global damage [2]. It incorporates relevance to the energy balance, in its dissipative part. In all cases, a classical calculation of the resistant capacities of the representative sections of the plastic regions that determine the behavior and the final deformation is incorporated, as well as the relation local curvature - global ductility.
The global energy balance is determined both in the linear and non-linear range. For this, the powers, energies and works developed by the dynamic system in the frequency domain are analyzed. This balance of energies is much more precise and stable than that the forces balance, since the energy enters very selectively in the structure at certain frequencies Hiroshi Akiyama [3].
With this analysis it is possible to predict an equivalent damping coefficient with two components: a) a viscous part and b) a hysteretic part. An adjustment of the variation for the building's modal properties can also be obtained.
With these parameters, it is possible to evaluate the adequateness of the various methods of seismic design and the safety level of the application in several standards, like DDBD [4] or push over method. The operational modal analysis allows us to obtain the frequencies of the structure at a certain moment of time, and its association with the extension to MDOF during the life of the structure while it is used. This methodology can help to establish a systematic of control to different nonlinearities for another type of resistant schemes.
In all cases the curve derived from the static non-linear push-over analysis is used as a control of lateral rigidity with the displacement. In the case of cyclic loading, the effect derived from hysteresis is also introduced, with special emphasis on the pinching effect by a method based on the Bouc-Wen-Baben-Noori theory [1] and the global damage [2]. It incorporates relevance to the energy balance, in its dissipative part. In all cases, a classical calculation of the resistant capacities of the representative sections of the plastic regions that determine the behavior and the final deformation is incorporated, as well as the relation local curvature - global ductility.
The global energy balance is determined both in the linear and non-linear range. For this, the powers, energies and works developed by the dynamic system in the frequency domain are analyzed. This balance of energies is much more precise and stable than that the forces balance, since the energy enters very selectively in the structure at certain frequencies Hiroshi Akiyama [3].
With this analysis it is possible to predict an equivalent damping coefficient with two components: a) a viscous part and b) a hysteretic part. An adjustment of the variation for the building's modal properties can also be obtained.
With these parameters, it is possible to evaluate the adequateness of the various methods of seismic design and the safety level of the application in several standards, like DDBD [4] or push over method. The operational modal analysis allows us to obtain the frequencies of the structure at a certain moment of time, and its association with the extension to MDOF during the life of the structure while it is used. This methodology can help to establish a systematic of control to different nonlinearities for another type of resistant schemes.