一种计算非比例阻尼结构地震响应的新方法
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摘要
在非比例阻尼结构地震响应分析中,直接积分法和强迫解耦法均具有鲜明的优缺点,考虑到计算精度和计算效率的均衡,提出了一种可用于非比例阻尼结构地震响应计算的新方法——多自由度模态方程方法.同时,通过推导指出了直接积分法和强迫解耦法是所提出方法的两种特殊形式,从而构建了非比例阻尼结构地震响应计算方法的完整理论体系.最后采用数值算例验证了多自由度模态方程方法在非比例阻尼结构地震响应计算中的有效性,并说明其可以通过合理划分结构分区来调节计算精度和计算效率.
For seismic response analysis of structures with non-proportional damping characteristic,the derived and presented traditional calculation methods based on proportional damping will no longer be accurate in theory,and in some cases even produce incorrect results.In view of such problems,engineering and academia often adopt the direct integration method for exact solution,which would need relatively large computation cost,and the forced decoupling method with high efficiency for approximate solution which would introduce unknown error.Taking into account the equilibrium of accuracy and efficiency,a new method for calculating non-proportionally damped structure's seismic response is presented,which is named as multiple-degree-of-freedom modal equation method.The derivation also points out that the direct integration method and forced decoupling method are two special extreme forms which can be obtained from the proposed method,and thereby the integrated theory system for non-proportionally damped structure's seismic response calculation is established.Finally,numerical study is carried out to verify the availability of the proposed method in the calculation of seismic response of non-proportionally damped structures,and it shows that along with the changing of dimension number of equation and partitioned mode of structure the efficiency and accuracy of the proposed method also gradually change and can be adjusted.
For seismic response analysis of structures with non-proportional damping characteristic,the derived and presented traditional calculation methods based on proportional damping will no longer be accurate in theory,and in some cases even produce incorrect results.In view of such problems,engineering and academia often adopt the direct integration method for exact solution,which would need relatively large computation cost,and the forced decoupling method with high efficiency for approximate solution which would introduce unknown error.Taking into account the equilibrium of accuracy and efficiency,a new method for calculating non-proportionally damped structure's seismic response is presented,which is named as multiple-degree-of-freedom modal equation method.The derivation also points out that the direct integration method and forced decoupling method are two special extreme forms which can be obtained from the proposed method,and thereby the integrated theory system for non-proportionally damped structure's seismic response calculation is established.Finally,numerical study is carried out to verify the availability of the proposed method in the calculation of seismic response of non-proportionally damped structures,and it shows that along with the changing of dimension number of equation and partitioned mode of structure the efficiency and accuracy of the proposed method also gradually change and can be adjusted.
引文
1 Elishakaff I,Lyon HR.Random Vibration-Status Recent Developments.New York:Elsevier Science Publishers, 1986
2 Shahruz SM,Mahavamana PA.An upper bound on response of non-classically damped linear systems.Journal of Sound and Vibration,1998,218(5):883-891
3 Foss KA.Coordinates which uncouple the equation of motion of damped linear dynamic systems.Journal of Applied Mechanics-ASME,1958,25(1):361-364
4 Lou ML,Duan Q,Chen GD.Modal perturbation method and its applications in structural systems.Journal of Engineering Mechanics,ASCE,2003,169(8):935-943
5 Karen K,Mohsen GA.New approaches for non-classically damped system eigenanalysis.Earthquake Engineering and Structural Dynamics,2005,34(9):1073-1087
6 Fernando C,Maria JE.Computational methods for complex eigenproblems in finite element analysis of structural systems with viscoelastic damping treatments.Computer Methods in Applied Mechanics and Engineering,2006, 195(44-47):6448-6462
7 Lbrahtmbegovic A,Wilson EL.Simple numerical algorithms for the mode superposition analysis of linear structural systems with non-proportional damping.Computers and Structures,1989,33(2):523-531
8 Lin FB,Wang YK,Cho YS.A pseudo-force iterative method with separate scale factors for dynamic analysis of structures with non-proportional damping.Earthquake Engineering and Structural Dynamics,2003,32(2):329- 337
9 Bilbaoa A,Agirrebeitiab J,Ajuria G.Proportional damping approximation for structures with added viscoelastic dampers.Finite Elements in Analysis and Design,2006, 42(6):492-502
10 Lin JL,Tsai KC.Simplified seismic analysis of one-way asymmetric elastic systems with supplemental damping. Earthquake Engineering and Structural Dynamics,2007, 36(6):783-800
11 Lin JL,Tsai KC.Seismic analysis of two-way asymmetric building systems under bi-directional seismic ground motions. Earthquake Engineering and Structural Dynamics, 2008,37(2):305-328
12 Guo W,Yu ZW,Xu HY.Application of three-degree-of-freedom modal equation in seismic analysis of storey isolated structure.IEEE International Workshop on Architecture, Civil and Environmental Engineering,Wuhan,China, 2011
2 Shahruz SM,Mahavamana PA.An upper bound on response of non-classically damped linear systems.Journal of Sound and Vibration,1998,218(5):883-891
3 Foss KA.Coordinates which uncouple the equation of motion of damped linear dynamic systems.Journal of Applied Mechanics-ASME,1958,25(1):361-364
4 Lou ML,Duan Q,Chen GD.Modal perturbation method and its applications in structural systems.Journal of Engineering Mechanics,ASCE,2003,169(8):935-943
5 Karen K,Mohsen GA.New approaches for non-classically damped system eigenanalysis.Earthquake Engineering and Structural Dynamics,2005,34(9):1073-1087
6 Fernando C,Maria JE.Computational methods for complex eigenproblems in finite element analysis of structural systems with viscoelastic damping treatments.Computer Methods in Applied Mechanics and Engineering,2006, 195(44-47):6448-6462
7 Lbrahtmbegovic A,Wilson EL.Simple numerical algorithms for the mode superposition analysis of linear structural systems with non-proportional damping.Computers and Structures,1989,33(2):523-531
8 Lin FB,Wang YK,Cho YS.A pseudo-force iterative method with separate scale factors for dynamic analysis of structures with non-proportional damping.Earthquake Engineering and Structural Dynamics,2003,32(2):329- 337
9 Bilbaoa A,Agirrebeitiab J,Ajuria G.Proportional damping approximation for structures with added viscoelastic dampers.Finite Elements in Analysis and Design,2006, 42(6):492-502
10 Lin JL,Tsai KC.Simplified seismic analysis of one-way asymmetric elastic systems with supplemental damping. Earthquake Engineering and Structural Dynamics,2007, 36(6):783-800
11 Lin JL,Tsai KC.Seismic analysis of two-way asymmetric building systems under bi-directional seismic ground motions. Earthquake Engineering and Structural Dynamics, 2008,37(2):305-328
12 Guo W,Yu ZW,Xu HY.Application of three-degree-of-freedom modal equation in seismic analysis of storey isolated structure.IEEE International Workshop on Architecture, Civil and Environmental Engineering,Wuhan,China, 2011
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