基于双参数模型的弹性地基薄板自由振动边界元解析
|
摘要
从双参数弹性地基薄板自由振动的微分方程式出发,通过建立双参数弹性地基薄板的动态基本解,运用边界元法(boundary element method,BEM)对双参数弹性地基板弯曲自由振动的动态特性进行解析研究,建立相应的边界积分方程式及动柔度方程式,采用频率扫描法求解其固有频率。算例研究表明,文中的方法计算简便、可行,具有良好的计算精度,同时该方法也适用于文克尔地基板动态特性解析。
In view of the differential equations for free vibration of plate on two parameter elastic foundation,dynamic fundamental solutions for flexural free vibration of thin plate on two parameter elastic foundation are established.Boundary element method(BEM) is used to analyze the dynamic characteristic of thin plate on two parameter elastic foundation in flexural free vibration.Corresponding boundary integral equations and dynamic flexibility equations are established.The natural frequencies are obtained by using the method of frequency scan.The calculated examples show that the methods suggested are simple,feasible,have good precision and can also be applied to the analysis of Winkler model.
In view of the differential equations for free vibration of plate on two parameter elastic foundation,dynamic fundamental solutions for flexural free vibration of thin plate on two parameter elastic foundation are established.Boundary element method(BEM) is used to analyze the dynamic characteristic of thin plate on two parameter elastic foundation in flexural free vibration.Corresponding boundary integral equations and dynamic flexibility equations are established.The natural frequencies are obtained by using the method of frequency scan.The calculated examples show that the methods suggested are simple,feasible,have good precision and can also be applied to the analysis of Winkler model.
引文
[1]黄义,何芳社.弹性地基上的梁、板、壳[M].北京:科学出版社,2005:3-85.HUANG Yi,HEFangShe.Beams,plates andshells onelasticfoundation[M].Bejing:Science Press,2005:3-85(In Chinese).
[2]Yang TY.Finite element analysis of plate on a two parameter foundationmodel[J].Computers&Structures,1972,2:593-614.
[3]Xie HongYang,Wang YuanHan.Dynamic analysis of elastic plate restingontwo-parameter foundation[J].Rock and Soil Mechanics,2007,28:753-758.
[4]Zhong Yang,Yin JianHua.Free vibration analysis of a plate on founda-tion withcompletelyfree boundary byfiniteintegral transformmethod[J].Mechanics Research Communications,2008,35:268-275.
[5]秦荣,何昌如.弹性地基薄板的静力和动力分析[J].土木工程学报,1988,21(3):71-80.QIN Rong,HEChangRu.Static and dynamic analyses of plates onelasticfoundation[J].Journal of Civil Engineering,1998,21(3):71-80(InChinese).
[6]李刚,丁翔,尚守平.有限条法分析双参数地基板的动静响应[J].湖南大学学报:自然科学版,2008,35(3):7-10.LI Gang,DING Xiang,SHANG ShouPing.Finite stripe method for thestatic and dynamic analysis of plates on two-parameter elastic foundation[J].Journal of Hunan University:Natural Sciences,2008,35(3):7-10(In Chinese).
[7]张广鹏,方英武,张灿果,等.基于边界元法的混联数控机床整机结构动态特性解析[J].机械强度,2005,27(2):140-145.ZHANG GuangPeng,FANG YingWu,ZHANG CanGuo,et al.Dynamicanalysis of a series-parallel NC machine tool structure based on theboundary element method[J].Journal of Mechanical Strength,2005,27(2):140-145(In Chinese).
[8]Brebbia C A,Power H.Boundary elements XXII[M].Boston:WessexInstitute of Technology(WIT)Press,2000:10-66.
[9]Costa Jesus Adjalma Jr.Boundary element method applied to plates onelastic foundations[J].Engineering Analysis,1985,2(4):174-183.
[10]Puttonen Jari,Varpasuo,Pentti.Boundary element analysis of a plate onelastic foundation[J].International Journal for Numerical Methodsin En-gineering,1986,23:287-303.
[11]李正良,邓安福.双参数地基板上弯曲问题的边界积分方程[J].应用数学和力学,1992,13(7):633-642.LI ZhengLiang,DENG AnFu.Boundaryintegral equations for the bend-ingproblemof plates on two parameter foundation[J].Applied Math-ematics and Mechanics,1992,13(7):633-642(In Chinese).
[12]方英武,黄玉美,张广鹏,等.求解薄板频率特性的边界元法解析研究[J].地震工程与工程振动,2004,24(6):27-31.FANG YingWu,HUANG YuMei,ZHANG GuangPeng,et al.Analysisfor frequency characteristics of thin plate by BEM[J].Earthquake Engi-neering and Engineering Vibration,2004,24(6):27-31(In Chinese).
[13]黄玉美,张广鹏,高峰.虚拟样机整机结构特性边界元仿真[M].北京:机械工业出版社,2004:49-51.HUANGYuMei,ZHANGGuangPeng,GAOFeng.Behaviours simulationof the whole virtual prototype machinetools structure bythe boundaryele-ment method[M].Beijing:China Machine Press,2004:49-51(In Chi-nese).
[2]Yang TY.Finite element analysis of plate on a two parameter foundationmodel[J].Computers&Structures,1972,2:593-614.
[3]Xie HongYang,Wang YuanHan.Dynamic analysis of elastic plate restingontwo-parameter foundation[J].Rock and Soil Mechanics,2007,28:753-758.
[4]Zhong Yang,Yin JianHua.Free vibration analysis of a plate on founda-tion withcompletelyfree boundary byfiniteintegral transformmethod[J].Mechanics Research Communications,2008,35:268-275.
[5]秦荣,何昌如.弹性地基薄板的静力和动力分析[J].土木工程学报,1988,21(3):71-80.QIN Rong,HEChangRu.Static and dynamic analyses of plates onelasticfoundation[J].Journal of Civil Engineering,1998,21(3):71-80(InChinese).
[6]李刚,丁翔,尚守平.有限条法分析双参数地基板的动静响应[J].湖南大学学报:自然科学版,2008,35(3):7-10.LI Gang,DING Xiang,SHANG ShouPing.Finite stripe method for thestatic and dynamic analysis of plates on two-parameter elastic foundation[J].Journal of Hunan University:Natural Sciences,2008,35(3):7-10(In Chinese).
[7]张广鹏,方英武,张灿果,等.基于边界元法的混联数控机床整机结构动态特性解析[J].机械强度,2005,27(2):140-145.ZHANG GuangPeng,FANG YingWu,ZHANG CanGuo,et al.Dynamicanalysis of a series-parallel NC machine tool structure based on theboundary element method[J].Journal of Mechanical Strength,2005,27(2):140-145(In Chinese).
[8]Brebbia C A,Power H.Boundary elements XXII[M].Boston:WessexInstitute of Technology(WIT)Press,2000:10-66.
[9]Costa Jesus Adjalma Jr.Boundary element method applied to plates onelastic foundations[J].Engineering Analysis,1985,2(4):174-183.
[10]Puttonen Jari,Varpasuo,Pentti.Boundary element analysis of a plate onelastic foundation[J].International Journal for Numerical Methodsin En-gineering,1986,23:287-303.
[11]李正良,邓安福.双参数地基板上弯曲问题的边界积分方程[J].应用数学和力学,1992,13(7):633-642.LI ZhengLiang,DENG AnFu.Boundaryintegral equations for the bend-ingproblemof plates on two parameter foundation[J].Applied Math-ematics and Mechanics,1992,13(7):633-642(In Chinese).
[12]方英武,黄玉美,张广鹏,等.求解薄板频率特性的边界元法解析研究[J].地震工程与工程振动,2004,24(6):27-31.FANG YingWu,HUANG YuMei,ZHANG GuangPeng,et al.Analysisfor frequency characteristics of thin plate by BEM[J].Earthquake Engi-neering and Engineering Vibration,2004,24(6):27-31(In Chinese).
[13]黄玉美,张广鹏,高峰.虚拟样机整机结构特性边界元仿真[M].北京:机械工业出版社,2004:49-51.HUANGYuMei,ZHANGGuangPeng,GAOFeng.Behaviours simulationof the whole virtual prototype machinetools structure bythe boundaryele-ment method[M].Beijing:China Machine Press,2004:49-51(In Chi-nese).
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心