EXTRACTING SIGNATURES FOR RIGID BODY MOTION AND MODES OF COUPLED VIBRATION IN ELASTIC MULTI-ROD MECHANISMS BY POD PROCESSING OF THE FINITE ELEMENT DYNAMICS

摘要

The method of Proper Orthogonal Decomposition for coupled dynamic fields is applied to systematically analyze the free dynamics, approximated by the method of finite elements, of a set of moving flexible rods and a two-rod flexible mechanism. The POD analysis identifies unique optimum degrees-of-freedom, Proper Orthogonal (PO) modes, for these systems. For moving stiff rods, the single dominant PO mode involves weak coupling of rigid body motion to deformation motion. The shapes of the PO modes for rigid body motion and vibration have invariant characteristic signatures for rigid body motion coupled to deformation motion. These signatures remain almost the same when two stiff rods are connected to form a slider-crank mechanism. The two dominant POMs of the mechanism represent rigid body mode of motion, which are coupled weakly to higher order PO modes. The weak coupling is due to the high rigidity of the rods in the mechanism.