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Resumen

 

FREQUENCIES AND NATURAL MODES OF FREE VIBRATION WITHOUT DAMPING OF A CANTILEVER BEAM

FRECUENCIAS Y MODOS NATURALES DE VIBRACION LIBRE SIN AMORTIGUAMIENTO DE UNA VIGA EN CANTILEVER
MSc. Elkin G. Florez S.
Ing. Raquel Irene Laguado R.

Abstract: The present paper refers to the analysis of free vibrations without damping in a beam in cantilever, using an analytical development. For the solution of the partial differentials equations of second and fourth order that governs the movement of the beam, in the axial and cross-sectional direction respectively, was used the method of separation of variables and the application of the respective boundary conditions in two-way directions. For the analyzed beam, we have done the following assumptions: area of
uniform section, the material of the beam is homogenous and isotropic and the existing deformations in the beam are within limits elastic. The analytical development used in the present work allows to know the mathematical principles more commonly used in the
development of solutions to the problems of analysis of vibrations in continuous systems such as beams, axes, columns so on.

Resumen: Este artículo trata sobre el análisis de las vibraciones libres sin amortiguamiento de una viga en Cantilever utilizando un desarrollo analítico. Para la solución de las ecuaciones diferenciales parciales de segundo y cuarto orden, las cuales describen el movimiento de la viga. En las direcciones axial y transversal respectivamente. Fue aplicado el método de separación de variables y la condición de frontera respectiva en ambas direcciones. Para analizar la viga, se tomaron las siguientes condiciones: el área de sección es uniforme, el material de la viga es homogéneo y isotrópico, y las deformaciones existentes en la viga están en sus límites elásticos. El desarrollo analítico utilizado en este trabajo permite conocer los principios matemáticos comúnmente utilizados en las soluciones de los problemas de análisis de vibraciones en sistemas continuos como las vigas, ejes, columnas, entre otros.

Keywords: Vibration, Beam, Natural frequency, Modes of vibration, Continuous systems.