Error Analysis And Updating Of The Forced Decoupling Method Of Damping Matrix

In the field of structural dynamics, until now there are no good solutions for damping matrix decoupling problems. Using damping parameter as a single parameter of the model of global processing, obviously it can not meet the needs of science and engineering. For more than100years, scholars of different countries have long struggled to damping models. In numerous damping models, Rayleigh model is the mainstream of structural dynamic models, due to the perfect mathematical expression. However, people raise doubts about the mandatory linear correlation of damping matrix, mass matrix and stiffness matrix. This model features a perfect mathematical expression and simple calculation, but it has no essential physical basis.Forced decoupling method is the most compelling method of the numerous damping matrix decoupling methods. This method is simple, intuitive and convenient for engineering practical. But the method is still lack of theoretical basis and is rough with high error.Based on the viscous damping model, this paper attempts to propose a new damping matrix forced decoupling method according to some equivalent principle. It can improve Rayleigh model and the classic forced decoupling method.The main works of this paper are as follows:(1) This paper proposes damping force equivalent (or approximate equivalent) principle and a updating forced decoupling method according to damping force equivalent principle.(2) Using the updating forced decoupling method, this paper modifies the recursion expression of the main diagonal elements after the damping matrix forced decoupling.(3) Taking a typical shear frame structure, for example, this paper carries out a numerical comparison between the solutions of the updating forced decoupling method, the classic forced decoupling method, and accurate solutions. The results show that the solutions of the updating forced decoupling method are quite coincident with accurate solutions. The updating forced decoupling method is superior to the classic forced decoupling method.