Matrix Perturbation Method In The Application Of The Damping System Dynamics Problems

Structural dynamic damping is more difficult in the analysis of a problem.With the development of modern structural system,increasing the height of the structure,the increasing span and the application of the new structure and new materials,damping position is becoming more and more important in engineering,which is an indispensable important aspect in the structural dynamic analysis.But in most cases,the damping is often overlooked for continuum structure and the convenience of analysis,this is bound to cause a big error.Modal superposition is one of the most effective methods to solve the dynamic response of the structure.However,considering the structural damping,the damping distribution is complex for many complex structures or structures composed of many components.The modal damping matrix is not Corner matrix,modal superposition method is often not directly solved.In addition,the correct choice of structural damping model can improve the dynamic analysis accuracy of the structural model.How to determine the damping coefficient in the vibration system becomes an important problem in the structural dynamics analysis considering the damping.Therefore,in this paper,we study the dynamic calculation problem and the damping parameters of the damping system with the matrix perturbation theory for the non-proportional damping structure.Through the calculation and experimental analysis,we find out the more accurate damping dynamic system Analytical methods and damping models.The main content of the study is three parts.Firstly,using the matrix perturbation theory,the damping term is used as the perturbation value,and the modal superposition method of the general damping problem is solved.The results show that even in the case of a general damping matrix(or non-proportional damping matrix),the modal superposition method can still be used without the addition of a large amount of computation,using the matrix perturbation method.Through the example,this method is simple and practical,the calculation is small,with good accuracy;Then,when the external load excitation frequency of the system is close to the natural frequency of the system,the damping matrix is directly used as the perturbation matrix,which makes the solution singular and leads to the problem of failure or error,considering to retain some damping in the dynamic equation of the modal coordinates,that is to say,the damping is decomposed,proposed non-singular matrix perturbation method.Through the numerical examples,we obtain the first and second order perturbations,compare it with the exact solution,and the precision is improved obviously,which is basically accurate;Finally,the traditional finite element method and the test technique are used to obtain the frequency difference of the structure with or without damping.Based on the assumption of viscous damping,the similarity between the damping matrix and the mass matrix formed by the finite element method is analyzed,and the weak perturbation system is analyzed and calculated by matrix perturbation theory.Based on the above theory,the relationship between the damping coefficient and the frequency difference is given.