DYNAMIC SUBSTRUCTURE TECHNIQUE FOR MULTIPLE-IMPACT RESPONSES OF BEAM WITH VARIABLE CROSS-SECTION

A dynamic substructure method for the analysis of multiple-impact responses of beams with variable cross-section is presented with the consideration of structural damping and effects of impact and separation. The dynamic governing equations for variable cross-section beam impacting against springs are derived in modal coordinates. The Newmark implicit integration method is applied to solve numerically the dynamic governing equations. The impact process of the valve slice against the lift limiter and the valve seat during valve opening and closure is studied. The multiple-impact phenomenon, impacting dynamic responses of the beam and effects of the valve thickness and the hollow window size on valve opening and valve closure are investigated numerically. The results of numerical convergence and the comparison with the three-dimensional dynamic finite element solution show that the presented dynamic substructure method is reasonable and valid for the analysis of multiple-impact responses of variable cross-section beams, especially when the multiple-impact responses take long period of time. Moreover, the presented method is suitable for the numerical simulations of optimal design of valve structures.