Forced Vibration of Flexible Body Systems: A Dynamic Stiffness Method

Due to the development of high speed machinery, robots, and aerospace structures, the research of flexible body systems undergoing both gross motion and elastic deformation has seen increasing importance. The finite element method and modal analysis are often used in formulating equations of motion for dynamic analysis of the systems which entail time domain, forced vibration analysis. This study develops a new method based on dynamic stiffness to investigate forced vibration of flexible body systems. In contrast to the conventional finite element method, shape functions and stiffness matrices used in this study are derived from equations of motion for continuum beams. Hence, the resulting shape functions are named as dynamic shape functions. By applying the dynamic shape functions, the mass and stiffness matrices of a beam element are derived. The virtual work principle is employed to formulate equations of motion. Not only the coupling of gross motion and elastic deformation, but also the stiffening effect of axial forces is taken into account. Simulation results of a cantilever beam, a rotating beam, and a slider crank mechanism are compared with the literature to verify the proposed method.