Aplicación de la formulación lagrangiana al estudio de las estructuras civiles
Fecha
2017-07-15
Autores
Entenza Boggiano, Victor Antonio
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Editor
Universidad Central “Marta Abreu” de Las Villas
Resumen
La formulación lagrangiana de la mecánica posee ventajas con respecto a la newtoniana. Sin
embargo, en la bibliografía revisada, no es aplicada al estudio de las estructuras civiles.
En este trabajo se desea sistematizar la utilización de la formulación lagrangiana en los problemas
de la dinámica de estructuras. Se procede a la solución, mediante formulación lagrangiana,
de dos problemas semejantes a otros tratados con formulación newtoniana en la bibliografía
consultada: el cálculo de los modos normales de oscilación del sistema mecánico simétrico de
cinco partículas distribuidas a iguales distancias en un eje horizontal, y el cálculo de las ecuaciones
del movimiento de las pequeñas oscilaciones ocurridas en un puente luego de un impacto
en dirección diagonal. Para la resolución del primer problema se hace una implementación del
método en el software Mathematica y se calibran los resultados relativos a las oscilaciones
longitudinales mediante experimentación numérica. El segundo problema se resuelve analíticamente.
Así, para determinadas situaciones del análisis de estructuras, la formulación lagrangiana es
preferible o alternativa a la formulación newtoniana.
The Lagrangian formulation of mechanics has advantages over Newtonian. However, it is not applied to the study of civil structures in the revised literature. In this work it is desired to systematize the use of the Lagrangian formulation in the problems of the dynamics of structures. It is proceed to the solution, by Lagrangian formulation, of two similar problems to other treatises with Newtonian formulation in the bibliography consulted: the calculation of the normal modes of oscillation of the symmetrical mechanical system of five particles distributed at equal distances on a horizontal axis, and The calculation of the equations of motion of the small oscillations occurring in a bridge after an impact in a diagonal direction. For the resolution of the first problem an implementation of the method is made in the software Mathematica and the results relative to the longitudinal oscillations are calibrated through numerical experimentation. The second problem is solved analytically. Thus, for certain situations of structure analysis, the lagrangian formulation is preferable or alternative to the Newtonian formulation.
The Lagrangian formulation of mechanics has advantages over Newtonian. However, it is not applied to the study of civil structures in the revised literature. In this work it is desired to systematize the use of the Lagrangian formulation in the problems of the dynamics of structures. It is proceed to the solution, by Lagrangian formulation, of two similar problems to other treatises with Newtonian formulation in the bibliography consulted: the calculation of the normal modes of oscillation of the symmetrical mechanical system of five particles distributed at equal distances on a horizontal axis, and The calculation of the equations of motion of the small oscillations occurring in a bridge after an impact in a diagonal direction. For the resolution of the first problem an implementation of the method is made in the software Mathematica and the results relative to the longitudinal oscillations are calibrated through numerical experimentation. The second problem is solved analytically. Thus, for certain situations of structure analysis, the lagrangian formulation is preferable or alternative to the Newtonian formulation.
Descripción
Palabras clave
Dinámica de Estructuras, Análisis Dinámico, Formulación Lagrangiana, Cálculo Variacional, Ecuaciones Diferenciales, Análisis Sísmico, Estructuras Civiles, Structural Dynamics, Dynamic Analysis, Lagrangian Formulation, Variational Calculus, Diferential Equations, Sysmological Analysis, Civil Structure