A finite element structural dynamics model of a beam with an arbitrary moving base—part I: formulations

Abstract A general lumped mass finite element structural dynamics model was developed for a three-dimensional elastic beam with an arbitrary and large base movement. The six degrees of freedom of the base movement can incorporate either a prescribed arbitrary motion of the base or as coupling of the beam with other substructures. The beam can be pretwisted and have a mass centre offset from the elasticity centre in order to model some specific structures such as helicopter blades. The equations of motion were derived using the virtual work principle. Large deflections and small strains of the beam were assumed so that the geometrical nonlinearities are included. The centrifugal stiffness terms caused by the large base movement were specifically considered so that the dynamics model is applicable for both nonlinear and linear analyses. This dynamics model is expected to provide a general and fundamental element for rotating beams and beam-like multibody structures. Numerical examples are presented to validate the model and demonstrate its great modelling flexibility in a companion paper.

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