随机风浪作用下结构的动力响应分析方法研究
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摘要
随着我国经济建设的迅猛发展,很多海洋工程结构不断涌现。例如,近期已建成东海大桥、杭州湾大桥、青岛海湾大桥等多座跨海大桥。另外,琼州海峡大桥、渤海海峡大桥和台湾海峡大桥也正在酝酿规划之中。这些跨海峡桥梁不但跨径大,而且桥位处水深,浪高,气候、水文、地质、地震等海洋环境因素异常复杂。台风以及台风掀起的巨浪破坏力极大,而且两者之间在强度、方向以及频谱等方面具有复杂的相关关系,对跨海峡桥梁的作用具有强烈的动态特性、随机性和耦合性。在许多情况下,通常将瞬态的强风和波浪激励看作等效静力作用。但对于跨海峡桥梁,台风以及台风掀起的巨浪动态特性显著且具有强烈的耦合效应。因此,考虑台风以及台风掀起巨浪这种破坏性环境荷载的实际动力特征、随机性和耦合性,发展风和波浪作用下结构的随机响应分析方法,对跨海峡桥梁的设计和建造来说有着重要的意义。
本文以上述海洋工程结构为背景,研究了结构在随机风浪作用下动力响应的理论与数值计算方法。主要研究内容包括：
1)基于设计波法,利用ANSYS软件中的PIPE59单元模拟桥墩桥塔结构,用Airy波理论和Stokes五阶波理论分别计算了规则波下的响应时间历程。
2)根据圆柱波浪力谱的计算方法,利用FORTRAN语言编写了计算波浪力谱的程序,并与ANSYS的随机振动响应分析方法结合来计算结构的动力响应。通过与文献中的算例的比较,验证了该方法的可靠性。利用该方法计算了桥墩桥塔结构在两种波浪力谱JONSWAP谱与P-M谱的作用下响应的功率谱,并且积分得到响应的方差。基于虚拟激励法,以大连理工大学自主开发的结构分析软件DDJ-W为基础,开发随机波浪响应分析功能,计算了相同波浪荷载条件下桥墩桥塔随机响应,并与ANSYS程序的计算结果进行比较。
3)按照随机振动虚拟激励法的基本思想,通过构造虚拟激励,发展了风和波浪作用下结构的随机响应分析方法。应用Morison方程计算构件的波浪力,构件波浪力采用投影面积法转化为节点荷载,按Borgman假定处理非线性动水阻尼,然后进行迭代修正,并精确地处理非正交阻尼阵。该方法可以考虑风沿任意作用方向作用以及波浪沿任意方向的传播。以大连理工大学结构分析软件DDJ-W为基础,开发了结构在随机风浪作用下动力响应分析程序系统。最后以桥墩和桥塔结构为算例,对该方法进行了初步验证。
With the rapid development of China's economy, more and more ocean engineering structures are built. For example, many cross-sea bridges such as the East Sea Bridge, the Hangzhou Bay Bridge and the Qingdao Bay Bridge have been built recently. In addition, the Qiongzhou Strait Bridge, the Bohai Strait Bridge and the Taiwan Strait Bridge are also in planning. The over-strait bridge not only has a long span, but also locates in deep water. Its environment factors such as wave, climatic, hydrology, geology and earthquake are exceedingly complicated. The wind and wave have great power. Moreover, they have complicated relationship in intensity, direction, frequency spectrum and so on. The action on the over-strait bridge has intensive dynamic characteristic, randomness and coupling. Under many circumstances, the transient strong wind and wave excitation are regarded as equivalent static loads. But for the over-strait bridge, wind and wave have distinctive dynamic characteristic and coupling effect. It's significant to considering the actual dynamic characteristic of wind and wave for the design and construction of the over-strait bridge. Therefore, it is important to develop an appropriate method for the random response of structures under wind and wave loads.
A numerical method for the dynamic response analysis of the structures mentioned above subjected to wind and wave loads is developed in this article, and it includes:
First, based on the designing wave method, the dynamic response analysis of a pier and a bridge tower is fulfilled by using ANSYS. The pier and tower are modeled by the PIPE59 element. Two different wave theories, i.e., the Airy wave theory and the fifth Stokes wave theory are used for comparison.
Second, a Fortran Program is developed for obtaining the wave load spectrum of a cylinder from the wave spectrum. The wave load spectrum is then used in ANSYS for random vibration analysis of structures. This method is verified through a simple example. Moreover, it is used to obtain the response spectrum and mean square deviation of a pier and a bridge tower under JONSWAP wave spectrum and P-M wave spectrum. A random vibration method is developed for the response of structures under wave loads based on pseudo-excitation method. The corresponding program is developed in the structural analysis program DDJ-W of Dalian University of Technology. The random responses of a pier and a tower are implemented and compared with those obtained by ANSYS.
Third, a random vibration method for analyzing the random responses of structures under wind and wave loads is developed. The wind and wave are taken as random loads while their spectra are regarded as basic inputs. This method is based on the pseudo-excitation method. The wave loads which are computed by Morison equation is translated to node loads by the projection area method. The nonlinear dynamic water damping is handled iteratively based on Borgman assumption. The non-orthogonal damping matrix can be dealt with precisely. This method can consider wind and wave which spread along arbitrary directions. Based on the structural analysis software DDJ-W of Dalian University of Technology, a program is developed to analyze dynamic responses of structures under random wind and wave loads. Finally, a pier and a bridge tower are analyzed to make a preliminary verification of the proposed method.
本文以上述海洋工程结构为背景,研究了结构在随机风浪作用下动力响应的理论与数值计算方法。主要研究内容包括：
1)基于设计波法,利用ANSYS软件中的PIPE59单元模拟桥墩桥塔结构,用Airy波理论和Stokes五阶波理论分别计算了规则波下的响应时间历程。
2)根据圆柱波浪力谱的计算方法,利用FORTRAN语言编写了计算波浪力谱的程序,并与ANSYS的随机振动响应分析方法结合来计算结构的动力响应。通过与文献中的算例的比较,验证了该方法的可靠性。利用该方法计算了桥墩桥塔结构在两种波浪力谱JONSWAP谱与P-M谱的作用下响应的功率谱,并且积分得到响应的方差。基于虚拟激励法,以大连理工大学自主开发的结构分析软件DDJ-W为基础,开发随机波浪响应分析功能,计算了相同波浪荷载条件下桥墩桥塔随机响应,并与ANSYS程序的计算结果进行比较。
3)按照随机振动虚拟激励法的基本思想,通过构造虚拟激励,发展了风和波浪作用下结构的随机响应分析方法。应用Morison方程计算构件的波浪力,构件波浪力采用投影面积法转化为节点荷载,按Borgman假定处理非线性动水阻尼,然后进行迭代修正,并精确地处理非正交阻尼阵。该方法可以考虑风沿任意作用方向作用以及波浪沿任意方向的传播。以大连理工大学结构分析软件DDJ-W为基础,开发了结构在随机风浪作用下动力响应分析程序系统。最后以桥墩和桥塔结构为算例,对该方法进行了初步验证。
With the rapid development of China's economy, more and more ocean engineering structures are built. For example, many cross-sea bridges such as the East Sea Bridge, the Hangzhou Bay Bridge and the Qingdao Bay Bridge have been built recently. In addition, the Qiongzhou Strait Bridge, the Bohai Strait Bridge and the Taiwan Strait Bridge are also in planning. The over-strait bridge not only has a long span, but also locates in deep water. Its environment factors such as wave, climatic, hydrology, geology and earthquake are exceedingly complicated. The wind and wave have great power. Moreover, they have complicated relationship in intensity, direction, frequency spectrum and so on. The action on the over-strait bridge has intensive dynamic characteristic, randomness and coupling. Under many circumstances, the transient strong wind and wave excitation are regarded as equivalent static loads. But for the over-strait bridge, wind and wave have distinctive dynamic characteristic and coupling effect. It's significant to considering the actual dynamic characteristic of wind and wave for the design and construction of the over-strait bridge. Therefore, it is important to develop an appropriate method for the random response of structures under wind and wave loads.
A numerical method for the dynamic response analysis of the structures mentioned above subjected to wind and wave loads is developed in this article, and it includes:
First, based on the designing wave method, the dynamic response analysis of a pier and a bridge tower is fulfilled by using ANSYS. The pier and tower are modeled by the PIPE59 element. Two different wave theories, i.e., the Airy wave theory and the fifth Stokes wave theory are used for comparison.
Second, a Fortran Program is developed for obtaining the wave load spectrum of a cylinder from the wave spectrum. The wave load spectrum is then used in ANSYS for random vibration analysis of structures. This method is verified through a simple example. Moreover, it is used to obtain the response spectrum and mean square deviation of a pier and a bridge tower under JONSWAP wave spectrum and P-M wave spectrum. A random vibration method is developed for the response of structures under wave loads based on pseudo-excitation method. The corresponding program is developed in the structural analysis program DDJ-W of Dalian University of Technology. The random responses of a pier and a tower are implemented and compared with those obtained by ANSYS.
Third, a random vibration method for analyzing the random responses of structures under wind and wave loads is developed. The wind and wave are taken as random loads while their spectra are regarded as basic inputs. This method is based on the pseudo-excitation method. The wave loads which are computed by Morison equation is translated to node loads by the projection area method. The nonlinear dynamic water damping is handled iteratively based on Borgman assumption. The non-orthogonal damping matrix can be dealt with precisely. This method can consider wind and wave which spread along arbitrary directions. Based on the structural analysis software DDJ-W of Dalian University of Technology, a program is developed to analyze dynamic responses of structures under random wind and wave loads. Finally, a pier and a bridge tower are analyzed to make a preliminary verification of the proposed method.
引文
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[2]Neumann G. On ocean wave spectra and a new method of forecasting wind-generated sea [J].ch Erosion Board, U.S. Army Corps. Of Engineers Tch.Mem,1953,43:42.
[3]Longuet-Higgins M S. The statistical analysis of a random moving surface [J].Phis. Trans. Roy. Soc. London. Ser. A.,1957,249:321-387.
[4]Borgman L E. Random hydrodynamic forces on objects. Annals of Mathematics Statistics, 1967,38:37-51.
[5]Borgman L E. Spectral analysis of ocean wave forces on piling [J].Proc. ASCE, 1967,93(WW2):129-156.
[6]Malhorta A K, Penien J. Response of offshore structures to random wave forces [J]. ASCEJ. Structural Div,1970,October:2155-2173.
[7]Malhorta A K, Penien J. Non-determinostic analysis of offshore structures [J]. ASCEJ. Engng. Mechanics Div,1970, December:985-1003.
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[10]Brebbia CA, Walker S. Dynamic analysis of offshore structures [M]. London: Butterrworths,1979.
[11]Curley K R, Kareem A. Simulation of ringing on offshore systems under viscous loads [J]. Journal of Engineering mechanics ASCE,1998,124(5):582-586.
[12]Han S M, Benaroya H. Comparison of linear and nonlinear responses of a compliant tower to random wave forces [J]. Chaos, Solitons and Fractals,2002,14:269-291.
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[17]梁剑青,欧进萍.大跨度斜拉桥桥面风致抖振的粘滞阻尼控制分析[J].地震工程与工程振动,2006,26(1)：139-144.
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[21]Peeters B, Roeck G. Reference-Based Stochastic Subspace Identification for Output-Only Modal Analysis [J]. Mechanical System and Signal Processing, 1999,13(6):855-878.
[22]杨洁,涂光备,张旭.干扰效应对高层住宅建筑风压系数的影响[J].同济大学学报,2004,32(11)：1442-1446.
[23]彪仿俊.建筑物表面风荷载的数值模拟研究[D].杭州：浙江大学,2005.
[24]Schmidt S, Thiele F. Comparison of numerical methods applied to the flow over wall-mounted cubes [J]. International Journal of Heat and Fluid Flow,2002,23:330-339.
[25]Kasperski M. Extreme wind load distribution for linear and nonlinear design [J].Eng. Structure,1992,14(1):27-34.
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[28]叶丰,顾明.估算高层建筑顺风向等效风荷载和响应的简化方法.工程力学.2003,20(1)：63-67.
[29]李国亮等.杭州湾大桥南岸超长施工栈桥设计中风、浪、流荷载的确定[J].公路交通科技,2007,24(10)：100-108.
[30]Watanabe E et al. Design and construction of a floating swing bridge in Osaka [J]. Marine Structures,2000,13(4-5):437-458.
[31]聂孟喜等.风、浪、流联合作用下系统系泊力的时域计算方法[J].清华大学学报,2004,44(9)：1214-1217.
[32]邹志利等.风浪流作用下系泊船系缆力和碰撞力的数值模拟[J].中国海洋平台,2002,17(2)：22-27.
[33]Bisht RS, Jain AK. Wind and wave induced behaviour of offshore guyed tower platforms [J]. Ocean Engineering,1998,25(7):501-519.
[34]Datta TK, Jain AK. Response of articulated tower platforms to random wind and wave forces [J]. Computers and Strucutures,1990,34(1):137-144.
[35]Li YS, Kareem A. Stochastic response of tension leg platforms to wind and wave fields [J]. Journal of Wind Engineering and Industrial Areodynamics,1990,36:915-926.
[36]陆文发,李林普,高明道.近海导管架平台北京[M].北京：海洋出版社,1992：391-480.
[37]竺艳蓉.海洋工程波浪力学[M].天津：天津大学出版社,1991.
[38]尚晓江,邱峰,赵海峰等.ANSYS结构有限元高级分析方法范例应用[M].北京：中国水利水电出版社,2008.
[39]王新敏.ANSYS工程结构数值分析[M].北京：人民交通出版社,2007.
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[2]Neumann G. On ocean wave spectra and a new method of forecasting wind-generated sea [J].ch Erosion Board, U.S. Army Corps. Of Engineers Tch.Mem,1953,43:42.
[3]Longuet-Higgins M S. The statistical analysis of a random moving surface [J].Phis. Trans. Roy. Soc. London. Ser. A.,1957,249:321-387.
[4]Borgman L E. Random hydrodynamic forces on objects. Annals of Mathematics Statistics, 1967,38:37-51.
[5]Borgman L E. Spectral analysis of ocean wave forces on piling [J].Proc. ASCE, 1967,93(WW2):129-156.
[6]Malhorta A K, Penien J. Response of offshore structures to random wave forces [J]. ASCEJ. Structural Div,1970,October:2155-2173.
[7]Malhorta A K, Penien J. Non-determinostic analysis of offshore structures [J]. ASCEJ. Engng. Mechanics Div,1970, December:985-1003.
[8]Clough R W, Pensien J. Dynamic of structures [M]. New York:Mc Graw Hill Book Co. Inc., 1974.
[9]Pierson W J, Moscowitz L. A proposed spectral from for fully developed wind seas based on the similarity theory of Kitaigorodskii [J].S. A. J. Geophys Res., 1964,69 (24):5181-5190.
[10]Brebbia CA, Walker S. Dynamic analysis of offshore structures [M]. London: Butterrworths,1979.
[11]Curley K R, Kareem A. Simulation of ringing on offshore systems under viscous loads [J]. Journal of Engineering mechanics ASCE,1998,124(5):582-586.
[12]Han S M, Benaroya H. Comparison of linear and nonlinear responses of a compliant tower to random wave forces [J]. Chaos, Solitons and Fractals,2002,14:269-291.
[13]Davenport A G. Gust Loading Factors [J].Journal of Structural Duvision,1967, 93(3):11-34.
[14]张相庭.结构风压和风振计算[M].上海：同济大学出版社,1985.
[15]黄本才.结构抗风分析原理及应用[M].上海：同济大学出版社,2001.
[16]Gu M, Zhang R X, Xiang H F. Identification of flutter derivatives of bridge decks [J]. Journal of Wind Engineering and Industrial Aerodynamics,2000,84:151-162.
[17]梁剑青,欧进萍.大跨度斜拉桥桥面风致抖振的粘滞阻尼控制分析[J].地震工程与工程振动,2006,26(1)：139-144.
[18]Johnson E A, Christenson R E, Spencer B F et al. Semi-active Damping of Cables with Sag [J]. International Conference of Advances in structure dynamics, Elservier Science Ltd.2000, (1):327-334.
[19]陈艾荣,项海帆.大跨刚构桥梁气动弹性试验及分析[J].振动工程学报,1999,12(4)：535-539.
[20]Jakobsen J B, Hansen E. Determination of the aerodynamic derivatives by a system identification method [J]. Journal of Wind Engineering and industrial Aerodynamics, 1995,57:295-395.
[21]Peeters B, Roeck G. Reference-Based Stochastic Subspace Identification for Output-Only Modal Analysis [J]. Mechanical System and Signal Processing, 1999,13(6):855-878.
[22]杨洁,涂光备,张旭.干扰效应对高层住宅建筑风压系数的影响[J].同济大学学报,2004,32(11)：1442-1446.
[23]彪仿俊.建筑物表面风荷载的数值模拟研究[D].杭州：浙江大学,2005.
[24]Schmidt S, Thiele F. Comparison of numerical methods applied to the flow over wall-mounted cubes [J]. International Journal of Heat and Fluid Flow,2002,23:330-339.
[25]Kasperski M. Extreme wind load distribution for linear and nonlinear design [J].Eng. Structure,1992,14(1):27-34.
[26]Holmes J D. Along-wind of latticetowers.Ⅲ:Effective load distribution [J]. Engineering Structure,1996,18:483-488.
[27]徐安,谢壮宁,倪振华.用瞬态测压法研究高层建筑的等效设计风荷载[J].土木工程学报,2004,37(9)：11-16,26.
[28]叶丰,顾明.估算高层建筑顺风向等效风荷载和响应的简化方法.工程力学.2003,20(1)：63-67.
[29]李国亮等.杭州湾大桥南岸超长施工栈桥设计中风、浪、流荷载的确定[J].公路交通科技,2007,24(10)：100-108.
[30]Watanabe E et al. Design and construction of a floating swing bridge in Osaka [J]. Marine Structures,2000,13(4-5):437-458.
[31]聂孟喜等.风、浪、流联合作用下系统系泊力的时域计算方法[J].清华大学学报,2004,44(9)：1214-1217.
[32]邹志利等.风浪流作用下系泊船系缆力和碰撞力的数值模拟[J].中国海洋平台,2002,17(2)：22-27.
[33]Bisht RS, Jain AK. Wind and wave induced behaviour of offshore guyed tower platforms [J]. Ocean Engineering,1998,25(7):501-519.
[34]Datta TK, Jain AK. Response of articulated tower platforms to random wind and wave forces [J]. Computers and Strucutures,1990,34(1):137-144.
[35]Li YS, Kareem A. Stochastic response of tension leg platforms to wind and wave fields [J]. Journal of Wind Engineering and Industrial Areodynamics,1990,36:915-926.
[36]陆文发,李林普,高明道.近海导管架平台北京[M].北京：海洋出版社,1992：391-480.
[37]竺艳蓉.海洋工程波浪力学[M].天津：天津大学出版社,1991.
[38]尚晓江,邱峰,赵海峰等.ANSYS结构有限元高级分析方法范例应用[M].北京：中国水利水电出版社,2008.
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