动态子结构高效集成的主动力和界面力处理方法
|
摘要
在现有的船舶水弹性子结构分离与集成方法中,主船体结构的振动采用以模态广义坐标为变量的动力学方程进行描述,船内子结构的振动采用以空间物理位移为变量的动力学方程进行描述。通过两者的边界连接条件进行综合集成时,会遇到模态空间与物理空间的转换集成问题。针对该问题,提出了"虚拟模态"方法,一方面可以使动态子结构集成计算精确,另一方面可大幅减少子结构集成的计算量。理论上,该"虚拟模态"方法适用于其他领域类似的动态子结构集成计算问题。最后,通过数值算例,对该"虚拟模态"方法的正确性和适用性进行了验证。
In the hydroelastic substructure separation and integration method,the structural vibration of the main hull is described by dynamic equations in terms of the generalized modal coordinates,while the vibration of the internal substructure is expressed with dynamic equations in terms of the geometric coordinates of displacements.When carrying out a synthesis analysis in the light of the boundary connection conditions,there exist compatibility problems between the modal space and the geometric space.In order to deal with this problem,a virtual modal method is proposed in this work.This method will greatly reduce the computational effort for structural integration,with the calculation precision guaranteed at the same time.Theoretically speaking,this virtual modal method is also applicable to problem analogous in some other research areas.Finally,the correctness and applicability of this method are validated through a numerical example.
In the hydroelastic substructure separation and integration method,the structural vibration of the main hull is described by dynamic equations in terms of the generalized modal coordinates,while the vibration of the internal substructure is expressed with dynamic equations in terms of the geometric coordinates of displacements.When carrying out a synthesis analysis in the light of the boundary connection conditions,there exist compatibility problems between the modal space and the geometric space.In order to deal with this problem,a virtual modal method is proposed in this work.This method will greatly reduce the computational effort for structural integration,with the calculation precision guaranteed at the same time.Theoretically speaking,this virtual modal method is also applicable to problem analogous in some other research areas.Finally,the correctness and applicability of this method are validated through a numerical example.
引文
[1]王文亮,杜作润.结构振动与动态子结构方法[M].上海:复旦大学出版社,1985.Wang Wenliang,Du Zuorun.Structure Vibration and Dynamic Substructure Analysis Method[M].Shanghai:Fudan University Press,1985.
[2]殷学纲,陈淮,蹇开林.结构振动分析的子结构方法[M].北京:中国铁道出版社,1991.Yin Xuegang,Chen Huai,Jian Kailin.Substructure Method for Structure Vibration Analysis[M].Beijing:China Railway Publishing House,1991.
[3]向树红,邱吉宝,王大钧.模态分析与动态子结构方法新进展[J].力学进展,2004,34(3):289-303.Xiang Shuhong,Qiu Jibao,Wang Dajun.The resent progresses on modal analysis and dynamic sub-structure methods[J].Advances in Mechanics,2004,34(3):289-303.
[4] Suarez L E,Singh M P.Improved fixed interface method for model synthesis[J].AIAA Journal,1992,30(12):2952-2958.
[5]骞朋波,尹晓春,沈煜年,等.碰撞激发弹塑性波传播的动态子结构方法[J].力学学报,2012,44(1):184-188.Qian Pengbo,Yin Xiaochun,Shen Yunian,et al.Dynamic substructure method for propagation of elasticplastic wave induced by impact[J].Chinese Journal of Theoretical and Applied Mechanics,2012,44(1):184-188.
[6]诸赟,张美艳,唐国安.一种基于子结构界面动刚度的模态综合法[J].振动工程学报,2015,28(3):345-351.Zhu Yun,Zhang Meiyan,Tang Guoan.A modal synthesis method based upon dynamic stiffness on interface[J].Journal of Vibration Engineering,2015,28(3):345-351.
[7]白斌,白广忱,费成巍,等.改进的混合界面子结构模态综合法在失谐叶盘结构动态特性分析中的应用[J].机械工程学报,2015,51(9):73-81.Bai Bin,Bai Guangchen,Fei Chengwei,et al.Application of improved hybrid interface substructural component modal synthesis method in dynamic characteristics analysis of mistuned bladed disk assemblies[J].Journal of Mechanical Engineering,2015,51(9):73-81.
[8]邹春平,陈端石,华宏星.船舶结构振动模态综合法[J].上海交通大学学报,2003,37(8):1213-1218.Zou Chunping,Chen Duanshi,Hua Hongxing.Modal synthesis method of structural vibration analysis of ship[J].Journal of Shanghai Jiaotong University,2003,37(8):1213-1218.
[9] Soize C.A model and numerical method in medium frequency range for vibroacoustic predictions using the theory of structural fuzzy[J].J.Acoust.Soc.Am.,1993,94(2):849-865.
[10]Franzoni L P,Park C D.An illustration of analytical/numerical matching with finite-element analysis for structure vibration problems[J].J.Acoust.Soc.Am.,2000,108(6):2856-2864.
[11]Park C D.Analytical-numerical matching for fluidloaded structures with discontinuities[J].J.Acoust.Soc.Am.,2004,116(5):2956-2968.
[12]邹明松,吴有生.水弹性子结构分离及集成方法[J].船舶力学,2014,18(5):574-580.Zou Mingsong,Wu Yousheng.A method used for separating and coupling substructure based on hydroelasticity theory and dynamic substructural theory[J].Journal of Ship Mechanics,2014,18(5):574-580.
[13]邹明松,吴有生,沈顺根,等.考虑航速及自由液面影响的声介质中三维结构水弹性力学研究[J].船舶力学,2010,14(11):1304-1311.Zou Mingsong,Wu Yousheng,Shen Shungen,et al.Three-dimensional hydroelasticity with forward speed and free surface in acoustic medium[J].Journal of Ship Mechanics,2010,14(11):1304-1311.
[14]邹明松.船舶三维声弹性理论[D].无锡:中国船舶科学研究中心,2014.Zou Mingsong.Three-dimensional sono-elasticity of ships[D].Wuxi:China Ship Scientific Research Center,2014.
[15]Wu Y S.Hydroelasticity of floating bodies[D].London:Brunel University,1984.
[16]Bishop R E D,Price W G,Wu Y S.A general linear hydroelasticity theory of floating structures moving in a seaway[J].Philosophical Transactions of the Royal Society of London A,1986,316(1538):375-426.
[17]恽伟君,段根宝,胡仲根.模态综合超单元法及其在船舶动态计算中的应用[J].上海力学,1982,(4):8-18.Yun Weijun,Duan Genbao,Hu Zhonggen.Superelement method of modal synthesis and its application to the dynamic calculation of ship structures[J].Shanghai Mechanics,1982,(4):8-18.
[2]殷学纲,陈淮,蹇开林.结构振动分析的子结构方法[M].北京:中国铁道出版社,1991.Yin Xuegang,Chen Huai,Jian Kailin.Substructure Method for Structure Vibration Analysis[M].Beijing:China Railway Publishing House,1991.
[3]向树红,邱吉宝,王大钧.模态分析与动态子结构方法新进展[J].力学进展,2004,34(3):289-303.Xiang Shuhong,Qiu Jibao,Wang Dajun.The resent progresses on modal analysis and dynamic sub-structure methods[J].Advances in Mechanics,2004,34(3):289-303.
[4] Suarez L E,Singh M P.Improved fixed interface method for model synthesis[J].AIAA Journal,1992,30(12):2952-2958.
[5]骞朋波,尹晓春,沈煜年,等.碰撞激发弹塑性波传播的动态子结构方法[J].力学学报,2012,44(1):184-188.Qian Pengbo,Yin Xiaochun,Shen Yunian,et al.Dynamic substructure method for propagation of elasticplastic wave induced by impact[J].Chinese Journal of Theoretical and Applied Mechanics,2012,44(1):184-188.
[6]诸赟,张美艳,唐国安.一种基于子结构界面动刚度的模态综合法[J].振动工程学报,2015,28(3):345-351.Zhu Yun,Zhang Meiyan,Tang Guoan.A modal synthesis method based upon dynamic stiffness on interface[J].Journal of Vibration Engineering,2015,28(3):345-351.
[7]白斌,白广忱,费成巍,等.改进的混合界面子结构模态综合法在失谐叶盘结构动态特性分析中的应用[J].机械工程学报,2015,51(9):73-81.Bai Bin,Bai Guangchen,Fei Chengwei,et al.Application of improved hybrid interface substructural component modal synthesis method in dynamic characteristics analysis of mistuned bladed disk assemblies[J].Journal of Mechanical Engineering,2015,51(9):73-81.
[8]邹春平,陈端石,华宏星.船舶结构振动模态综合法[J].上海交通大学学报,2003,37(8):1213-1218.Zou Chunping,Chen Duanshi,Hua Hongxing.Modal synthesis method of structural vibration analysis of ship[J].Journal of Shanghai Jiaotong University,2003,37(8):1213-1218.
[9] Soize C.A model and numerical method in medium frequency range for vibroacoustic predictions using the theory of structural fuzzy[J].J.Acoust.Soc.Am.,1993,94(2):849-865.
[10]Franzoni L P,Park C D.An illustration of analytical/numerical matching with finite-element analysis for structure vibration problems[J].J.Acoust.Soc.Am.,2000,108(6):2856-2864.
[11]Park C D.Analytical-numerical matching for fluidloaded structures with discontinuities[J].J.Acoust.Soc.Am.,2004,116(5):2956-2968.
[12]邹明松,吴有生.水弹性子结构分离及集成方法[J].船舶力学,2014,18(5):574-580.Zou Mingsong,Wu Yousheng.A method used for separating and coupling substructure based on hydroelasticity theory and dynamic substructural theory[J].Journal of Ship Mechanics,2014,18(5):574-580.
[13]邹明松,吴有生,沈顺根,等.考虑航速及自由液面影响的声介质中三维结构水弹性力学研究[J].船舶力学,2010,14(11):1304-1311.Zou Mingsong,Wu Yousheng,Shen Shungen,et al.Three-dimensional hydroelasticity with forward speed and free surface in acoustic medium[J].Journal of Ship Mechanics,2010,14(11):1304-1311.
[14]邹明松.船舶三维声弹性理论[D].无锡:中国船舶科学研究中心,2014.Zou Mingsong.Three-dimensional sono-elasticity of ships[D].Wuxi:China Ship Scientific Research Center,2014.
[15]Wu Y S.Hydroelasticity of floating bodies[D].London:Brunel University,1984.
[16]Bishop R E D,Price W G,Wu Y S.A general linear hydroelasticity theory of floating structures moving in a seaway[J].Philosophical Transactions of the Royal Society of London A,1986,316(1538):375-426.
[17]恽伟君,段根宝,胡仲根.模态综合超单元法及其在船舶动态计算中的应用[J].上海力学,1982,(4):8-18.Yun Weijun,Duan Genbao,Hu Zhonggen.Superelement method of modal synthesis and its application to the dynamic calculation of ship structures[J].Shanghai Mechanics,1982,(4):8-18.