The Block Lanczos Method And Its Application To Analysis Of Wind-induced Response For Long-span Roofs

Recent years, along with the development of science and technology, long-span roofs havebeen widely applied for various long-span public buildings, such as gymnasiums, hangars andexhibition pavilions. These structures are light, flexible and they also possess small dampingfactor and low vibration frequencies. They are always in low atmospheric boundary layer withhigh turbulence. They are sensitive to fluctuating wind load more and more, and the wind loadhas become a dominant problem among all kinds of loads in structural design. But the presentwind load code doesn't provide specific formula like the tall building or high-rise structure. It isnecessary to do more research on the wind-resistant design of long-span roofs. Therefore it isimportant to study on wind load and wind-induced response for long-span roofs in theory andengineering practice.In general, the most widely used is mode superposition method, in which method, generallyconsidered high model have little effect on structure and is neglected. It is easy have a greatererror if we calculate the response only use previous orders. The calculation of power spectrumalso requires a lot of computation when the long-span roofs have a lot of freedom degrees. Andthe actual engineering design efficiency is easily affected.This paper proposes a block Lanczos vector direct superposition method to calculate thewind-induced response of long-span roofs .The POD technology is used to decomposefluctuating wind so as to obtain the eigenmodes only related to the space, with this as the initialiterative vector block Lanczos method. The Lanczos vectors orthogonal with the mass make theequation into a three-diagonal form, solving this equation bringing greater convenience tocalculate this equation.This method solve the problem existing in the traditional modesuperposition method of neglecting higher-order mode which possibly make a large contributionto the structure response.With the pressure data testing in the wind tunnel synchronously, the wind-induced responseof different long-span roofs structures is analyzed using the traditional mode superpositionmethod. The eigenvectors of fluctuating wind with POD are regarded as spatial distribution ofthe loading to generate Lanczos vectors. The wind-induced response is analyzed with BlockLanczos vector superposition method, and which is compared with the traditional modesuperposition method and the single-load as the initial vector iterative Lanczos method. The concept of mode contribution is introduced to determine the order mode participation.