Ritz向量法在结构与土相互作用分析中的应用
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摘要
为了提高地震作用下结构与土相互作用体系分析效率,对应用Ritz向量法求解SSI体系地基子结构主模态及进行地震反应计算的适用性与有效性进行了分析研究.根据地基土主模态分布较为分散的特点,考察外部动荷载的空间分布与地基自身振动特性的对应关系,滤除对地基振动贡献较小的低阶振型.算例分析结果表明,Ritz向量法自振特性计算效率较传统模态向量有明显提高,同等动力反应分析精度条件下截取的模态数量仅为后者的1/7,大大降低了地基子结构的计算规模,该方法应用于地基土的主模态分析十分有效.
In order to improve the computational efficiency of dynamic analysis of structure-soil interaction system,the application of Ritz vectors in the modal analysis and seismic analysis of foundation sub-structure is comprehensively analyzed in this paper.As a replacement of traditional modal vectors,Ritz vectors may automatically filter the lower-ranking modals of negligible contribution to the foundation vibration by taking the spatial distribution of external loading into consideration.The results of sample analysis indicate that Ritz vectors can notably boost the solution efficiency of natural frequencies.The amount of Ritz vectors employed in the calculation is only 1/7 of that of traditional modal vectors with the same accuracy,which is very helpful to the reduction of computational scale of substructure matrixes.The efficiency of Ritz vectors in the solution of foundation modals is proved by trail and error.
In order to improve the computational efficiency of dynamic analysis of structure-soil interaction system,the application of Ritz vectors in the modal analysis and seismic analysis of foundation sub-structure is comprehensively analyzed in this paper.As a replacement of traditional modal vectors,Ritz vectors may automatically filter the lower-ranking modals of negligible contribution to the foundation vibration by taking the spatial distribution of external loading into consideration.The results of sample analysis indicate that Ritz vectors can notably boost the solution efficiency of natural frequencies.The amount of Ritz vectors employed in the calculation is only 1/7 of that of traditional modal vectors with the same accuracy,which is very helpful to the reduction of computational scale of substructure matrixes.The efficiency of Ritz vectors in the solution of foundation modals is proved by trail and error.
引文
[1]Chopra A K,Reviewer F N.Dynamics of Structures:Theory and Applications to Earthquake Engineering[M].Englewood Cliffs,NJ:Prentice-Hall,1995.
[2]楼梦麟.结构振动模态分析的Wilson-Ritz向量法[J].地震工程与工程振动,1992,12(4):40-48.Lou Menglin.Wilson-Ritz vector method for modalanalysis of structures[J].Earthquake Engineering andEngineering Vibration,1992,12(4):40-48(in Chi-nese).
[3]Wilson E L,Yuan Mingwu,Dickens J M.Dynamicanalysis by direct superposition of Ritz vectors[J].Earthquake Engineering and Structural Dynamics,1992,10(6):813-821.
[4]陈波,武岳,沈世钊,等.Ritz-POD法及其在大跨度屋盖结构风振分析中的应用[J].沈阳建筑大学学报:自然科学版,2005,21(6):601-605.Chen Bo,Wu Yue,Shen Shizhao,et al.A new load-dependent Ritz vector method for wind-induced responseanalysis of large span roofs:Ritz-POD method[J].Journal of Shenyang Architectural and Civil EngineeringInstitute:Natural Science,2005,21(6):601-605(inChinese).
[5]汪梦甫,沈蒲生.Ritz向量叠加法的改进及其应用[J].湖南大学学报:自然科学版,1996,23(3):109-115.Wang Mengfu,Shen Pusheng.Improvement of Ritzvector superstructure method and its application[J].Journal of Hunan University:Natural Science,1996,23(3):109-115(in Chinese).
[6]楼梦麟.子结构Ritz向量综合法[J].应用力学学报,1996,13(4):126-130.Lou Menglin.Ritz vectors synthesis technique for sub-structuring[J].Chinese Journal of Applied Mechanics,1996,13(4):126-130(in Chinese).
[7]曲乃泗,吴全军.改进Ritz向量法在动态子结构分析中的应用[J].大连理工大学学报,1991,31(5):529-536.Qu Naisi,Wu Quanjun.Application of improved Ritzvector method in vibrational characteristic analysis ofsubstructure[J].Journal of Dalian University of Tech-nology,1991,31(5):529-536(in Chinese).
[8]Wilson E L,Bayo E P.Use of special Ritz vectors indynamic substructure analysis[J].Journal of StructureEngineering,1986,112(8):1944-1954.
[9]Abdallah A A,Huckelbridge A A.Boundary flexibilitymethod of component mode synthesis using static Ritzvectors[J].Computers and Structure,1990,35(1):51-61.
[10]Gladwell G M L.Branch mode analysis of vibrating sys-tems[J].Journal of Sound and Vibration,1964,1(1):41-59.
[2]楼梦麟.结构振动模态分析的Wilson-Ritz向量法[J].地震工程与工程振动,1992,12(4):40-48.Lou Menglin.Wilson-Ritz vector method for modalanalysis of structures[J].Earthquake Engineering andEngineering Vibration,1992,12(4):40-48(in Chi-nese).
[3]Wilson E L,Yuan Mingwu,Dickens J M.Dynamicanalysis by direct superposition of Ritz vectors[J].Earthquake Engineering and Structural Dynamics,1992,10(6):813-821.
[4]陈波,武岳,沈世钊,等.Ritz-POD法及其在大跨度屋盖结构风振分析中的应用[J].沈阳建筑大学学报:自然科学版,2005,21(6):601-605.Chen Bo,Wu Yue,Shen Shizhao,et al.A new load-dependent Ritz vector method for wind-induced responseanalysis of large span roofs:Ritz-POD method[J].Journal of Shenyang Architectural and Civil EngineeringInstitute:Natural Science,2005,21(6):601-605(inChinese).
[5]汪梦甫,沈蒲生.Ritz向量叠加法的改进及其应用[J].湖南大学学报:自然科学版,1996,23(3):109-115.Wang Mengfu,Shen Pusheng.Improvement of Ritzvector superstructure method and its application[J].Journal of Hunan University:Natural Science,1996,23(3):109-115(in Chinese).
[6]楼梦麟.子结构Ritz向量综合法[J].应用力学学报,1996,13(4):126-130.Lou Menglin.Ritz vectors synthesis technique for sub-structuring[J].Chinese Journal of Applied Mechanics,1996,13(4):126-130(in Chinese).
[7]曲乃泗,吴全军.改进Ritz向量法在动态子结构分析中的应用[J].大连理工大学学报,1991,31(5):529-536.Qu Naisi,Wu Quanjun.Application of improved Ritzvector method in vibrational characteristic analysis ofsubstructure[J].Journal of Dalian University of Tech-nology,1991,31(5):529-536(in Chinese).
[8]Wilson E L,Bayo E P.Use of special Ritz vectors indynamic substructure analysis[J].Journal of StructureEngineering,1986,112(8):1944-1954.
[9]Abdallah A A,Huckelbridge A A.Boundary flexibilitymethod of component mode synthesis using static Ritzvectors[J].Computers and Structure,1990,35(1):51-61.
[10]Gladwell G M L.Branch mode analysis of vibrating sys-tems[J].Journal of Sound and Vibration,1964,1(1):41-59.
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