DYNAMIC MODELING OF BEAMS WITH FLEXIBLE SUPPORT

The beams with flexible support have translational androtational degrees of freedom. The classical model of the beams with flexiblesupport can be adopted only when the flexibility of the support is verysmall. In the present work, the nonlinear and linear coupling dynamic models ofthe Euler-Bernoulli's beam with flexible support are established byemploying the modeling method of flexible multi-body systems. The models areapplicable to the beams with any flexible support and can describe thecoupling vibration of the bending of the beam and the overall motionsdue to the flexibility of the support. Furthermore, the models can besimplified as the dynamic models of the cantilever beam and the rigidbeam, and the bending vibration equation of the linear coupling modelcan be linearly transformed as that of the classic linear model of the beams withflexible support. As an example, vibration frequencies of two linear modelsare calculated by employing Assumed Modes Method. The results indicatethat the linear coupling model is better than the classical model forbeams with flexible support.