Bibliographic citations
Misaico, K., (2021). Estudio de la respuesta estructural de edificios tipo corte simple mediante métodos de análisis cualitativo de ecuaciones diferenciales [Tesis, Universidad Nacional de Ingeniería]. http://hdl.handle.net/20.500.14076/22362
Misaico, K., Estudio de la respuesta estructural de edificios tipo corte simple mediante métodos de análisis cualitativo de ecuaciones diferenciales [Tesis]. PE: Universidad Nacional de Ingeniería; 2021. http://hdl.handle.net/20.500.14076/22362
@misc{sunedu/3927411,
title = "Estudio de la respuesta estructural de edificios tipo corte simple mediante métodos de análisis cualitativo de ecuaciones diferenciales",
author = "Misaico Sairitupac, Kevin Luis",
publisher = "Universidad Nacional de Ingeniería",
year = "2021"
}
The simulation of the structural response to seismic events in buildings requires solving differential equations using traditional quantitative methods, obtaining purely numerical responses, but without any analysis that shows us the stable behavior of the solution. In this research it is proposed to analyze the solution of the problem in two ways: quantitative numerical (using Matlab) and qualitative. The latter provides tools for the analysis of the stability of the system solution, through its phase plane the behavior of the solution can be observed in its proximity to the critical point, Lyapunov's theorem that allows us to obtain a function that give stability conditions, the Hartman-Grobman theorem that allows a nonlinear system to be approximated to linear near the equilibrium point and corresponding additional theorems of the qualitative theory of ordinary differential equations. As a result, we will have three types of solutions; unstable (lack of stability), stable and asymptotically stable, the last two of vital importance in civil engineering works, the dynamic behavior of the structures must be safe and stable during and after the action of the earthquake, or another type of external force (wind, explosion, tsunami). Finally, the theory of control will be studied that will allow us to stabilize linear systems, incorporating into the dynamic system a control that sends an electrical signal to the actuator (example: active magneto-rheological dissipator) counteracting the movement that comes from external forces (seismic, wind etc.) and thus ensuring the stability of the dynamic system.
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