热环境下混凝土矩形薄板在弹性地基上的振动
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摘要
基于刚性板的小挠度理论,考虑混凝土的材料非线性,推导了双参数弹性地基上混凝土矩形薄板热弹性问题的动力方程。采用级数法,导出了热环境下双参数弹性地基上四边简支混凝土矩形薄板的固有频率计算公式和强迫振动下的挠度函数。为便于工程应用,给出了双参数弹性地基上四边简支混凝土矩形薄板在恒向变温和温度均匀变化时的固有频率和均布荷载作用下的挠度函数。针对W inkler弹性地基的情况,讨论了板的材料弹性常数、几何尺寸(长宽比)、相对厚度、刚度系数k和温度对薄板固有频率和挠度函数的影响,从而为工程结构中热环境下弹性地基上混凝土矩形薄板的振动计算提供了理论依据。
Based on the small deflection theory of plate and in consideration of the physical nonlinearity of concrete,the dynamic equation of concrete rectangular plate subjected to thermal environment on two-parameters elastic foundation is derived.Using Galerkin principle,the nonlinear dynamic equation and its closed-form solution for a simply supported concrete rectangular plate on elastic foundation under uniform heat change are presented,and the influences of material constant,length-width ratio,relative thickness,rigidity coefficient and temperature on natural frequencies of plate are discussed.The theoratical base about its dynamic calculation is provided.
Based on the small deflection theory of plate and in consideration of the physical nonlinearity of concrete,the dynamic equation of concrete rectangular plate subjected to thermal environment on two-parameters elastic foundation is derived.Using Galerkin principle,the nonlinear dynamic equation and its closed-form solution for a simply supported concrete rectangular plate on elastic foundation under uniform heat change are presented,and the influences of material constant,length-width ratio,relative thickness,rigidity coefficient and temperature on natural frequencies of plate are discussed.The theoratical base about its dynamic calculation is provided.
引文
[1]Li Shirong.Nonlinear vibration and thermal-buckling of aheated annular plate with a rigid mass[J].Applied Mathe-matics and Mechanics(English Ed),1992,13(8):771—777.
[2]Li Shirong.Nonlinear vibration and thermal-buckling of aheated annular plate with variable thickness[A].Proceedingof ICNM-Ⅱ[C].Peking University Press,1993:535—538.
[3]Li Shirong,Zhou Youhe.Nonlinear vibration of heated ortho-tropic annular plate with immovably hinged edges[J].Jour-nal of Thermal Stresses,2003,26(7):691—700.
[4]杨静宁,李世荣,赵永刚.热过屈曲圆板的非线性自由振动[J].甘肃科学学报,2002.14(1):26—30.
[5]李世荣,周又和,马连生.热过屈曲正交异性圆(环)板的自由振动响应[J].振动工程学报,2005,18(2):184—188.
[6]丁皓江,国凤林,候鹏飞.横观各向同性热电材料简支矩形板的自由振动[J].力学学报,2000,32(4):402—404.
[7]关群,何顺荣.压电、压磁耦合弹性介质圆板的自由振动[J].哈尔滨工业大学学报,2005,37(3):418—422.
[8]黄小林,沈惠申.热环境下功能梯度材料板的自由振动和动力响应[J].工程力学,2005,22(3):224—227.
[9]何建,王善,唐平.爆炸载荷作用下混凝土板的动力响应[J].哈尔滨工业大学学报,2005,37(3):798—800.
[10]时旭东,过镇海.钢筋混凝土结构的温度场[J].工程力学,1996.13(1):35—43.
[11]韩强,黄小清,宁建国.高等板壳理论[M].北京:科学出版社,2002:29—34.
[12]熊渊博,龙述尧,李光耀.弹性地基板分析的局部Petrov-Galerkin方法[J].土木工程学报,2005,38(11):79—83.
[13]过镇海,时旭东.钢筋混凝土的高温性能及其计算[M].北京:清华大学出版社,2003,10—23,106—108.
[14]程选生.热环境作用下钢筋混凝土矩形贮液罐的初探[D].兰州大学,2001.
[15]上海市政工程设计院等编.给水排水工程结构设计手册[M].北京:中国建筑工业出版社,1984:1474—1477.
[16]居荣初,曾心传.弹性结构与液体的耦联振动理论[M].北京:地震出版社,1983:40—92.
[2]Li Shirong.Nonlinear vibration and thermal-buckling of aheated annular plate with variable thickness[A].Proceedingof ICNM-Ⅱ[C].Peking University Press,1993:535—538.
[3]Li Shirong,Zhou Youhe.Nonlinear vibration of heated ortho-tropic annular plate with immovably hinged edges[J].Jour-nal of Thermal Stresses,2003,26(7):691—700.
[4]杨静宁,李世荣,赵永刚.热过屈曲圆板的非线性自由振动[J].甘肃科学学报,2002.14(1):26—30.
[5]李世荣,周又和,马连生.热过屈曲正交异性圆(环)板的自由振动响应[J].振动工程学报,2005,18(2):184—188.
[6]丁皓江,国凤林,候鹏飞.横观各向同性热电材料简支矩形板的自由振动[J].力学学报,2000,32(4):402—404.
[7]关群,何顺荣.压电、压磁耦合弹性介质圆板的自由振动[J].哈尔滨工业大学学报,2005,37(3):418—422.
[8]黄小林,沈惠申.热环境下功能梯度材料板的自由振动和动力响应[J].工程力学,2005,22(3):224—227.
[9]何建,王善,唐平.爆炸载荷作用下混凝土板的动力响应[J].哈尔滨工业大学学报,2005,37(3):798—800.
[10]时旭东,过镇海.钢筋混凝土结构的温度场[J].工程力学,1996.13(1):35—43.
[11]韩强,黄小清,宁建国.高等板壳理论[M].北京:科学出版社,2002:29—34.
[12]熊渊博,龙述尧,李光耀.弹性地基板分析的局部Petrov-Galerkin方法[J].土木工程学报,2005,38(11):79—83.
[13]过镇海,时旭东.钢筋混凝土的高温性能及其计算[M].北京:清华大学出版社,2003,10—23,106—108.
[14]程选生.热环境作用下钢筋混凝土矩形贮液罐的初探[D].兰州大学,2001.
[15]上海市政工程设计院等编.给水排水工程结构设计手册[M].北京:中国建筑工业出版社,1984:1474—1477.
[16]居荣初,曾心传.弹性结构与液体的耦联振动理论[M].北京:地震出版社,1983:40—92.
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