基于特征正交分解的空间变异地震动模拟
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摘要
结合模态截断技术,导出了特征正交分解型谱表示法的随机模拟公式.给出了空间变异地震动的随机描述,并通过引入对地震动谱矩阵的预分解,导出了用于平稳空间变异地震动随机模拟的简化计算公式,避免了较耗时的对复矩阵求特征值的运算.简化公式同样可用快速傅立叶变换算法加速,较之原有模拟方法具有较高的计算效率.最后,模拟了龙潭河特大桥桥址处的空间变异地震动,说明了所推导的方法是正确的,同时形象地说明了地震动特征正交分解模态的物理意义.
By combining with the modal truncation technique,the simulation formulas for proper orthogonal decomposition(POD) based on the spectral representation method were derived.Then,a stochastic model for the spatial variation of seismic ground motions was proposed,and the simplified simulation formulas were obtained by the pre-decomposition of the spectral matrixes of seismic ground motions.As a result,only evaluation of eigenvectors of a real spectral matrix rather than a complex one is involved,and high computation efficiency can be obtained for the elimination of the time-consuming Cholesky decomposition procedure and the uses of the fast Fourier transform(FFT) technique and the modal truncation technique.Finally,an application of the formulas to the Longtan river long-span bridge was included as a numerical example to verify this method and illustrate the physical sense of POD.
By combining with the modal truncation technique,the simulation formulas for proper orthogonal decomposition(POD) based on the spectral representation method were derived.Then,a stochastic model for the spatial variation of seismic ground motions was proposed,and the simplified simulation formulas were obtained by the pre-decomposition of the spectral matrixes of seismic ground motions.As a result,only evaluation of eigenvectors of a real spectral matrix rather than a complex one is involved,and high computation efficiency can be obtained for the elimination of the time-consuming Cholesky decomposition procedure and the uses of the fast Fourier transform(FFT) technique and the modal truncation technique.Finally,an application of the formulas to the Longtan river long-span bridge was included as a numerical example to verify this method and illustrate the physical sense of POD.
引文
[1]ASPASIA Z,VASSILIOS Z.Spatial variation of se ism ic ground motions:An overview[J].App lied M echan ics Reviews,2002,55(3):271-297.
[2]DEODATIS G.S imu lation of ergod ic mu ltivariate stochastic processes[J].Journal of Engineering M echan ics,1996,122(8):778-787.
[3]CHEN X,KAREEM A.Proper orthogonal decomposition-based modeling,analysis and simu lation of dynam ic w ind loadeffects on structures[J].Journal of EngineeringM echan ics,2005,131(4):325-339.
[4]胡亮,李黎,樊剑.基于特征正交分解型谱表示法的桥梁风场数值模拟[C]∥第12届全国结构风工程学术会议论文集.西安:中国土木工程学会桥梁与结构分会风工程委员会,2005:1-5.
[5]SOLAR I G,CARASSALE L.Modal transform ation tools in structural dynam ics and w ind engineering[J].W ind andStructures,2000,3(4):221-241.
[6]D I PAOLA M.D igital simu lation ofw ind field veloc ity[J].Journal ofW ind Engineering and IndustrialAerodynam ics,1998,74-76(1):91-109.
[7]屈铁军,王君杰.空间变化的地震动功率谱的实用模型[J].地震学报,1996,18(1):55-62.QU Tiejun,WANG Jun jie.A practicalmodel for the power spectrum of spatial variant ground motion[J].Acta Se ismologicaS in ica,1996,9(1):69-79.
[8]D I PAOLA M,ZINGALESM.D igital simu lation ofmu ltivariate earthquake ground motions[J].Earthquake Engineering andStructural Dynam ics,2000,29(7):1 011-1 027.
[9]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004:127-134.
[10]史小伟.某大跨连续刚构桥的抗震研究[D].武汉:华中科技大学土木工程与力学学院,2005.
[2]DEODATIS G.S imu lation of ergod ic mu ltivariate stochastic processes[J].Journal of Engineering M echan ics,1996,122(8):778-787.
[3]CHEN X,KAREEM A.Proper orthogonal decomposition-based modeling,analysis and simu lation of dynam ic w ind loadeffects on structures[J].Journal of EngineeringM echan ics,2005,131(4):325-339.
[4]胡亮,李黎,樊剑.基于特征正交分解型谱表示法的桥梁风场数值模拟[C]∥第12届全国结构风工程学术会议论文集.西安:中国土木工程学会桥梁与结构分会风工程委员会,2005:1-5.
[5]SOLAR I G,CARASSALE L.Modal transform ation tools in structural dynam ics and w ind engineering[J].W ind andStructures,2000,3(4):221-241.
[6]D I PAOLA M.D igital simu lation ofw ind field veloc ity[J].Journal ofW ind Engineering and IndustrialAerodynam ics,1998,74-76(1):91-109.
[7]屈铁军,王君杰.空间变化的地震动功率谱的实用模型[J].地震学报,1996,18(1):55-62.QU Tiejun,WANG Jun jie.A practicalmodel for the power spectrum of spatial variant ground motion[J].Acta Se ismologicaS in ica,1996,9(1):69-79.
[8]D I PAOLA M,ZINGALESM.D igital simu lation ofmu ltivariate earthquake ground motions[J].Earthquake Engineering andStructural Dynam ics,2000,29(7):1 011-1 027.
[9]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004:127-134.
[10]史小伟.某大跨连续刚构桥的抗震研究[D].武汉:华中科技大学土木工程与力学学院,2005.
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