Geometric stiffening effect on rigid-flexible coupling dynamics of an elastic beam

In the previous work, the authors examined the effect of the geometric stiffness terms on the stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the geometrically non-linear formulations to an elastic beam with free large overall motions. The equations of motion are derived taking into account the foreshortening deformation term, therefore, the equations include the geometric mass and force matrices, which have geometric stiffening effect on the rigid-flexible coupling dynamics of the system. The numerical results obtained in this investigation reveal the significant difference between the deformations with and without stiffening effect. Furthermore, the stiffening effect on the large overall motion is investigated. An influence ratio is employed as a criterion to clarify the application range of the conventional linear modelling method, in which the stiffening effect is neglected. The effectiveness of the criterion is examined by two simulation examples.