Parametric Study of a Single Flexible Link Based on Timoshenko and Euler-Bernoulli Beam Theories

Abstract:In this research the sensitivity analysis (SA) of the geometric parameters such as: length, thickness and width of a single link flexible manipulator on maximum deflection (MD) of the end effector and vibration energy (VE) of that point are conducted. The motion equation of the system is developed based on Gibbs-Appel (G-A) formulation. Also for modeling the elastic property of the system the assumption of assumed modes method (AMM) is applied. In this study, two theories are used to obtain the end-point MD and VE of the end effector. Firstly, the assumption of Timoshenko beam theory (TBT) has been applied to consider the effects of shear and rotational inertia. After that, Euler-Bernoulli beam theory (EBBT) is used. Then Sobol’s sensitivity analysis method is applied to determine how VE and end-point MD is influenced by those geometric parameters. At the end of the research, results of two mentioned theories are compared.