Three approaches to the dynamic problem of a pendulum and a rotating flexible beam

FERNANDO BUEZAS; RUBENS SAMPAIO; CARLOS P. FILIPICH; MARTA B. ROSALES

Brasilia, Brasil

Congreso; COBEM 2007 19th. International Congress of Mechanical Engineering; 2007

The dynamic characteristics of a rotating beam play a significant role in the overall performance and design of various engineering systems, such as turbo-machinery, wind turbines, etc. In this work the dynamic problem of a flexible pendulum and a beam rotating around an axis perpendicular to its plane is addressed taking into account the gravitational effect. The dynamics of pendulums and rotating beams is studied according to three approaches, two of them related with the Strength of Materials theory (SM) and the other one with nonlinear Theory of Elasticity (TE). The stiffening effect due to the centrifugal forces is taken into account only in the case of the rotating beam subjected to high rotating speeds and neglected in the case of a pendulum under self-weight due to the low values of the speed, when addressed with SM theory. The derivation of the governing equations is done by superposition of the deformations to the rigid motion for the first approach (SM). The second approach with SM theory is through the application of Hamilton´s principle. The  lagrangian form is employed with the nonlinear TE.   Comparison of the three models allows to determine advantages and drawbacks of each of them.