Research On Dynamic Substructure Method For Transient Multiple-impact Responses Of Flexible Beam-Rod Systems

The multiple-impact problems of flexible structural systems have wide engineering background and are of important theoretical significance. In the process of multiple impacts, the transient impact response is not only concerned with the motion, local deformation and global deformation of each part, and concerned with the impact-induced transient wave propagation in each part and wave interaction at interfaces, but also related to the various forms of energy conversion between each part. Therefore, the way of using coefficient of restitution to study impact behavior in the rigid-rigid models is not suitable for flexible-flexible models. Furthermore, comparing with the rigid-flexible models, the flexible-flexible models are much more complex in the theoretical analysis and numerical calculation of multiple impactsThis thesis studies three typical impact systems:rod-rod, beam-rod and variable section beam-flexible support. A dynamic substructure method is presented to investigate the flexible-flexible model of multiple-impact problems; subsequently this mehod is applied to other typical impact systems. The main research work and achievements are shown as follows:(1) A basic theory of dynamic substructure method is developed to account for multiple-impact dynamics of flexible-flexible models. The present dynamic substructure method can be adopted to solve multiple-impact problems and calculate the propagation of the impact-induced transient waves in flexible-flexible models.(2) According to the problems of the substructure groups sharing the same contact point and the multiple contact points located in the same substructure, a constraint addition-deletion technique considering the interaction of the transient impact-contact effect is proposed, to ensure the effective applications of dynamic substructure method in the multi-point and multiple-impact problems.(3) The present dynamic substructure method is firstly applied to investigate the propagation of the impact-induced transient waves in flexible-flexible models. By the comparison with the theoretical solution and the three-dimensional dynamic finite element solution, it is shown that the present method is convergent in numerical calculation and of high numerical precision. The applications include several typical impact systems:rod-rod, beam-rod, variable section beam-flexible support, multiple beam-rod and micro cantilever tip impacting sample surface in tapping mode atomic force microscopy.(4) A new dynamic substructure method is proposed to study multiple-impact problems of micro/nano flexible bodies with the consideration of surface effect, which can study the multiple impacts between micro cantilever tip and sample surface in tapping mode atomic force microscopy. An adhesive contact model is used to treat the contact constrain between the cantilever tip and sample surface. The method correctly calculates the transient multiple-impact response, the propagation of the impact-induced transient waves in the micro/nano structures and the sub-impact phenomenon; it indicates that the present method is suitable for the numerical simulations of multiple impacts between the micro cantilever tip and the sample surface in tapping mode atomic force microscopy.(5) In the flexible-flexible multiple-impact systems, the impact mechanism is influenced significantly by the wave propagations. As the impact-induced transient waves travel along the all flexible bodies, the characteristics of waves are affected by the boundary condition, impact interface and wave internal interaction that influence directly on the impact force response and the beginning and ending of impacts. Its impact mechanism is greatly different from that of rigid-body impact and rigid-flexible body impact.