An Application Of Ritz Vectors Method In The Wind-induced Response On Dome-like Roof

Roof structures with new types, large spans, low-rise, low-frequency and high flexibility are generally in high turbulent regions, then wind loads become important to these structures. Commonly, wind-induced response is analysed in frequency domain method. How to choose proper modes is an important job.The solution of the eigenvalue or modal problem for large-span roof structure is of the most costly phase of a dynamic response analysis. And some special modals, which have dominant contributions to the structure, are easily overlooked because of their higher position of modal order while using the traditional mode superposition. In this paper as a typical example of a large-span dome-like curve roof, the direct superposition of Ritz vectors and Lanczos vectors, known as load depend Ritz vectors method, are used in the solution of the eigenvalue problem and wind-response analysis combined with the result of "X-mode" method and traditional modal superposition, the direct superposition of Ritz vectors and Lanczos vectors turn out to yield more accurate results with fewer vectors and the modals with higher order are not overlooked. Based on error minimization, this algorithm is presented for the generation of a sequence of orthogonal Ritz vectors. These orthogonal vectors are used to reduce the size of the system. This direct superposition of Ritz vector is more efficient than the traditional mode superposition and "X-mode" method. The proposed method not only reduces computer time requirements significantly but provides an error estimation for the dynamic analysis. From the result in this paper it can be seen that Ritz vectors and Lanczos vectors can replace the traditional modes to compute structure response to some extent, especially, they are suit to solve wind-induced response. on roof structure.In this paper, still, a deduction of Matrix Calculation Method, which is more practical than FEM, is offered. The formulae and parameters in MCM are immediately related to notions such as generalized mass and generalized force. So that it is very conventional for experiment convey and calculation analysis and it is very clear for its physics notions. Then MCM is used in wind-response analysis on dome-like roofs and yields more reasonable outputs than traditional SRSS method.