Seismic Transient Response Analysis Of The Quasi-Structures For Vertical-Stacking Multibody Systems

There are plenty of mechanism systems in engineering that consist of several vertical-stacking parts,such as quayside crane,overhead crane and recycling platform for rockets,et al.For the mechanism view,unilateral constraint characteristic can be found between different parts.Under the base excitation,such as earthquake and wave,slide,transient detachment and even derailment can occur between different parts or the overall structure and the foundation.Traditional structural dynamics cannot describe the unilateral constraint,in order to use the quasi-static analysis strategy(such as response spectrum method),the relationship between different parts are always being treated as binding.However,this simplified strategy can not reflect the actual movements.Plenty of achievements have been obtained for the constraints in the context of multibody system dynamics.Therefore,it's a good reason to analyze the vertical-stacking mechanisms in the theoretical frame of multibody system dynamics.However,these system not only contains many common problem,but also present some vivid characteristic as their own.From the structural view,the dimension of these structure is large and should been treated as flexible bodies,which is the research field of the flexible multibody system contact-impact dynamics.From the view of architecture,the parts of these structures should be maintained in there initial position,therefore,the overall rigid motions are always small,but change fast.From the view of structural design,the dynamic equations should be rebuilt if the design changes.Based on above facts,this paper discusses the specific modeling strategy for vertical-stacking mechanisms in the context of flexible multibody systems,the solution strategy for dynamic contact force between flexible bodies and the fine adjustment strategy for long time simulation in complex cases.The main works are as follows:(1)A general mode superposition method has been proposed for transient analysis of vertical-stacking mechanism.In this paper,the flexible multibody system contact impact problem has been introduced to deal with the vertical-stacking mechanism,this kind of mechanism have been classified as "quasi-structures for vertical-stacking multibody systems".The rigid modes have been proved to be used to reflect the rigid motion,a model smoothing method,combined with the modal superposition method,have been used to rewrite the equations of motion of the vertical-stacking system as modal coordinate equations.On the one hand,one need not to simplify the unilateral constraint but can also reflect the actual movements between different parts,the modeling efficiency can be improved with a reliable accuracy.On the other hand,the high frequency components can be filtered effectively in the modeling stage,the stiffness of the system can be reduced in the meantime.The disturbance of the contact force solution can also be reduced.(2)A numerical strategy and analysis model for transient contact force in the frame of flexible multibody systems have been proposed in this paper.The numerical solution of the contact force between different flexible bodies become more difficult as the FEM discretization.In this paper,the linear complementarity prolem(LCP)has been used to describe the unilateral constraint.The normal gap functions between contacting points has been replaced by their time-averaged value in a short time interval.In the following,the LCP equations bave been built up by using the time-averaged gap function and the normal contact force.The normalized stragety has been proposed to improve the numerical stability.By using this method,the transient contact forces have been modified in a smoothed manner.Therefore,the proposed method can take into account of smooth contact and impact,without changing different models in different contact stage.Furthermore,the amplitude of the contact force can be determined by the real constitutive law of the flexible bodies,other than the virtual constitutive law.(3)A fast matching method of artificial seismic wave is proposed in this paper.In this approach,the analytical solution of harmonic response of the single freedom system are obtained first.In the following,the artificial seismic wave matching problem aimed at the goal response spectrum have been transferred to a set of nonlinear equations about the combination coefficient.The efficient algorithm of the nonlinear equations can be used to solve the resulting equations.In order to filter the "zero drift" problem,the displacement wave has been written by the multiplication of the envelope function and the trigonometric series.The velocity and acceleration results can then be obtained by the derivation of the displacement wave.According to the conditions that must be satisfied in the initial segment,sustained segment and the attenuation segment,the envelope function can be determined by quintic polynomial.(4)A numerical simulation strategy is proposed in this paper to improve the computational efficiency for transient analysis of the nuclear polar crane,which is a typical vertical-stacking multibody system,the contact-impact problem,which lead to a spatial and temporal multi-scale features,increase the numerical difficulties for lone-time simulation.The parameters of ODE(ordinary differential equation)integrator have been discussed in this paper,the time-step size that satisfy the numerical stability have been obtained by calculating some typical cases,in the following,the integral span have been divided into several segments,the maximum step size of each segment have been adjusted to reduce the useless searching process.The numerical efficiency can be improved remarkably without disturbing the numerical simulation.Numerical examples detects the slide,detachment and horizontal impact phenomenons which can not be easily obtained by traditional structural dynamics methods.