Transient Dynamic Analysis of Rotating Beams Using Second-Order Theory: A Finite Difference Approach

Finite difference method is used to perform transient dynamic analysis for a rotating flexible beam via nonlinear geometrically-exact approach with second-order strain theory. The responses obtained are in good agreement with those obtained by Simo et al. using nonlinear finite element approach. In the case of rotating beam, traditional approach based on linear beam theory may lead to grossly inaccurate results: instability of a physically stable system. For this reason, one needs to employ higher order beam theories to account for the foreshortening as well as centrifugal effect, even if the deformation remains small. Our results indicate that while the discretization of the linear partial differential equation yields the correct responses for both flexural deflection and sectional rotation, the second order terms must be included for finite difference discretization in order to obtain the correct transient response for the extensional deformation.