Vibration of Euler–Bernoulli and Timoshenko beams in large overall motion on flying support using finite element method

The equations of motion for a beam on a flying support for Euler–Bernoulli and Timoshenko Beam Theories is derived. In modeling and attempting to have an accurate model at high speeds, a stretch variable instead of conventional axial deformation is used. For a planar rotating beam and a spatial rotating beam, equations of motion are lineralized and verified. Finite element and Newmark direct integration methods are employed for numerical simulations.