Abstract: Coupling terms of elastic general coordinates are employed to describe a deformation field of a flexible body in order to obtain the consistent linearization dynamic model of flexible mechanical systems. Nonlinear strain-displacement relations of the flexible body are introduced to determine new mode functions, and an approximate linear relation between general deformation coordinates and strains of the body is obtained. So the strain energy of the flexible body can be given by using the conventional linear strain-displacement relation. The nonlinear terms of deformation coordinates in kinematic analysis can be linearized until partial velocities and partial angular ones, are given. A consistent linearization dynamic model of the systems is developed by using Kane’s equation. Dynamic responses of a flexible beam in a quick return, mechanism are studied by using the model. Simulating results show that the behaviors of the beam are unstable at the certain angular velocities of the rigid crank, and an interesting periodic pattern is observed for some cases.

Key words: Dynamics, Flexible mechanical system, Rigid-flexible coupling