Sharif Digital Repository

The equations of motion for a beam on a flying support for EulerBernoulli 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  

In this paper, a two-link flexible manipulator is considered. For a prescribed motion, Timoshenko and Euler-Bernoulli beam models are considered. Using the Galerkin method, nonlinear equations of motion are solved. The Runge-Kutta method is employed for the time response integration method. A comparative study is made between the Euler-Bernoulli and Timoshenko beam models, with and without foreshortening effects. It is demonstrated that for two-link manipulators, both theories provide good models, and the results for both theories are very similar for all ranges of slenderness ratio. The findings suggest that for two-link manipulators with relatively high slenderness ratios, there is a...