建筑膜结构非线性振动及其预张力测量理论和试验研究
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摘要
随着科技的进步和社会的发展，薄膜结构在许多领域，尤其是在建筑工程领域，得到了广泛的应用与发展。建筑膜结构是最近几十年才兴起的一种建筑结构体系，它被广泛应用于大型体育场馆、展览会场、娱乐场等建筑中。建筑膜结构自重轻、刚度较小，因而对外荷载的作用非常敏感，容易发生振动，甚至导致工程事故。因此，研究建筑膜结构在暴风雨、冰雹、风卷残物等作用下的振动特性，把握其一般规律，对合理地进行建筑膜结构的设计和施工，防止或减少建筑膜结构工程事故等，具有重要意义。另外，将建筑膜结构非线性振动的研究应用于建筑膜结构预张力测量方法的研究中，也具有较大的工程实践意义；通过所研究的方法测量建筑膜结构的预张力，控制实际张力值与设计值相符合，保证工程质量；并适时检测建筑膜结构在使用过程中的张力值是否变化，以采取有效的措施调整预张力，防止或减少工程事故。
本论文主要对正交异性矩形薄膜结构的大挠度非线性自由振动及其在冲击荷载作用下的非线性受迫振动进行理论和应用研究。首先采用解析方法研究正交异性矩形膜结构几何非线性自由和受迫振动问题，求得其近似解析解；然后将理论研究应用于工程实际，提出测量建筑膜结构预张力的新方法——“弹射法”，推导出测量的理论公式，并进行数值分析和试验研究，验证“弹射法”测量建筑膜结构预张力的有效性。本文的具体研究内容如下：
①运用冯卡门大挠度理论结合达朗贝尔原理建立正交异性矩形薄膜结构无阻尼和有阻尼大挠度非线性自由振动偏微分控制方程组；采用直接积分法和L-P摄动法对无阻尼自由振动控制方程组进行求解，得到其振动频率和挠度函数的近似解析解；采用KBM摄动法对有阻尼自由振动控制方程组进行求解，得到其振动频率和挠度函数的近似解析解。
②以正交异性矩形薄膜结构大挠度非线性自由振动研究为基础，建立正交异性矩形薄膜结构在冲击荷载作用下的无阻尼和有阻尼受迫振动控制方程组；采用L-P摄动法对无阻尼受迫振动控制方程进行求解，得到其振动频率和挠度函数的近似解析解；采用KBM摄动法对有阻尼受迫振动控制方程进行求解得其振动频率和挠度函数的近似解析解；采用ANSYS/LS-DYNA有限元分析软件对正交异性矩形薄膜结构在冲击荷载作用下的受迫振动进行数值分析，并将数值分析结果与理论结果进行对比分析，分析结果表明理论计算和数值结果吻合较好。
③将正交异性矩形薄膜结构大挠度非线性振动的理论研究应用于建筑膜结构工程实际，提出测量建筑膜结构预张力的新方法——“弹射法”，建立测量的理论模型，并按照能量守恒原理推导出测量的理论公式；采用ANSYS/LS-DYNA有限元分析软件建立“弹射法”测量建筑膜结构预张力的有限元分析模型，进行数值分析；将数值分析结果与理论结果进行对比，从数值分析上佐证了“弹射法”测量建筑张拉膜结构预张力的有效性。
④根据“弹射法”的理论研究，制定“弹射法”测量建筑膜结构预张力的试验方案；按照试验方案研制了十字形螺杆式双轴张拉装置对膜材试件进行张拉；选用建筑工程中常用的三种膜材进行经纬等荷和经纬不等荷弹射试验；将获得的各组试验数据代入测量的理论公式求得膜材的试验计算预张力，并将试验计算预张力与膜材实际预张力进行对比分析；分析表明，膜材试验计算预张力与实际预张力比较吻合，从试验上验证了采用“弹射法”测量建筑膜结构预张力的有效性。
With the progress of science and technology and the development of society, themembrane structure has been widely applied in many areas, especially in the buildingengineering area. The building membrane structure is a new structure system, which hasbeen rising during the recent several dozens of years. It is widely applied in large-scalestadium, exhibition center, casino, and so on. Because the building membranestructure’s dead weight is light and the rigidity is small, it is very sensitive under theimpact load and easy to engender vibration, thus results in engineering accident.Therefore, it is quite necessary to study the vibration characteristics of the buildingmembrane structure under impact loading (such as rainstorm, hail, the waste picked upby the wind, and so on) to obtain the general laws of them. These studies haveimportant significance for the reasonable design and construction of building membranestructure, thus to prevent or reduce the engineering accident of building membranestructure. In addition, applying the theoretical studies of nonlinear vibration of buildingmembrane structure into the studies of pretension measurement method of buildingmembrane structure has a great significance for engineering practice. We can use thestudied measurement method to measure the actual pretension, thus to control the actualpretension accord with the design pretension and guarantee the construction quality.Meanwhile, we can use this method to detect whether the pretension has changed in theworking process, thus to adopt effective measures to adjust the pretension to prevent orreduce engineering accident.
This dissertation mainly studied the theory and application of the nonlinear freevibration of orthotropic rectangular membrane structure and its forced vibration underimpact loading. Firstly, analytical method was applied to study the large deflectiongeometrical nonlinear free and forced vibration problem of orthotropic rectangularmembrane structure and the general analytical solution was obtained. Then, we appliedthe theoretical studies into actual building membrane engineering to develop a newmethod—Ejection Method for monitoring the pretension of building membranestructure and the theoretical measurement formula was derived and obtained. Finally,the numerical analysis and ejection experiment were carried out for the EjectionMethod and the numerical and experiment results proved the Ejection Method is valid.The concrete study contents are as follows:
①The partial differential governing equations of damped and undamped nonlinear free vibration of orthotropic rectangular membrane were established bycombining the Von Kármán’s large deflection theory with the D’Alembert’s principle.The undamped free vibration governing equations were solved by direct integrationmethod and L-P perturbation method, and the approximate analytical solution of thefrequency and deflection function were obtained. The damped free vibration governingequations were solved by t KBM perturbation method, and the approximate analyticalsolution of the frequency and deflection function were obtained.
②Based on the studies of nonlinear free vibration of orthotropic rectangularmembrane structure, the governing equations of the damped and undamped forcedvibration of orthotropic rectangular membrane structure under concentrated impact loadwere established. The undamped forced vibration governing equations were solved byL-P perturbation method, and the approximate analytical solutions of the frequency anddeflection function of were obtained. The damped forced vibration governing equationswere solved by KBM perturbation method, and the approximate analytical solution ofthe frequency and deflection function were obtained. The ANSYS/LS-DYNA finiteelement analysis software was adopted to carry out the numerical analysis of the forcedvibration of orthotropic rectangular membrane structure under the impact load. Thecomparison and analysis of the theoretical and numerical results indicate that thetheoretical results coincide well with the numerical results.
③Applying the theoretical studies of this dissertation into actual buildingmembrane engineering, a new method—Ejection Method was developed for monitoringthe pretension of building membrane structure. The theoretical model of this methodwas established, and the theoretical measurement formula was derived and obtainedaccording to the principle of conservation of energy. The finite element analysis modelof Ejection Method was established and the numerical computation was carried out bythe ANSYS/LS-DYNA finite element analysis software. The theoretical and thenumerical results were compared and analyzed and the compared results prove that useEjection Method to measure the pretension of building membrane structure is feasibleand valid.
④The experimental scheme was constituted for measuring the pretension ofmembrane structure by Ejection Method according to the theoretical studies of EjectionMethod. According to the experimental scheme, the crisscross screw biaxial stretchingdevice was prepared for stretching the membrane test specimens. Three kinds ofmembrane material were selected to carry out the ejection experiment. The ejection experiments with equal loading and unequal loading in the warp and weft directionswere carried out and the experimental data was recorded. Put each group ofexperimental data into the theoretical measurement formula to obtain the experimentalcomputational pretensions, and compared the experimental computational pretensionsto the actual pretensions. The comparing analysis results indicate that the most ofexperimental computational pretensions tallied with the actual pretensions. This alsoproved that use Ejection Method to measure the pretension of building membranestructure is feasible and valid.
本论文主要对正交异性矩形薄膜结构的大挠度非线性自由振动及其在冲击荷载作用下的非线性受迫振动进行理论和应用研究。首先采用解析方法研究正交异性矩形膜结构几何非线性自由和受迫振动问题，求得其近似解析解；然后将理论研究应用于工程实际，提出测量建筑膜结构预张力的新方法——“弹射法”，推导出测量的理论公式，并进行数值分析和试验研究，验证“弹射法”测量建筑膜结构预张力的有效性。本文的具体研究内容如下：
①运用冯卡门大挠度理论结合达朗贝尔原理建立正交异性矩形薄膜结构无阻尼和有阻尼大挠度非线性自由振动偏微分控制方程组；采用直接积分法和L-P摄动法对无阻尼自由振动控制方程组进行求解，得到其振动频率和挠度函数的近似解析解；采用KBM摄动法对有阻尼自由振动控制方程组进行求解，得到其振动频率和挠度函数的近似解析解。
②以正交异性矩形薄膜结构大挠度非线性自由振动研究为基础，建立正交异性矩形薄膜结构在冲击荷载作用下的无阻尼和有阻尼受迫振动控制方程组；采用L-P摄动法对无阻尼受迫振动控制方程进行求解，得到其振动频率和挠度函数的近似解析解；采用KBM摄动法对有阻尼受迫振动控制方程进行求解得其振动频率和挠度函数的近似解析解；采用ANSYS/LS-DYNA有限元分析软件对正交异性矩形薄膜结构在冲击荷载作用下的受迫振动进行数值分析，并将数值分析结果与理论结果进行对比分析，分析结果表明理论计算和数值结果吻合较好。
③将正交异性矩形薄膜结构大挠度非线性振动的理论研究应用于建筑膜结构工程实际，提出测量建筑膜结构预张力的新方法——“弹射法”，建立测量的理论模型，并按照能量守恒原理推导出测量的理论公式；采用ANSYS/LS-DYNA有限元分析软件建立“弹射法”测量建筑膜结构预张力的有限元分析模型，进行数值分析；将数值分析结果与理论结果进行对比，从数值分析上佐证了“弹射法”测量建筑张拉膜结构预张力的有效性。
④根据“弹射法”的理论研究，制定“弹射法”测量建筑膜结构预张力的试验方案；按照试验方案研制了十字形螺杆式双轴张拉装置对膜材试件进行张拉；选用建筑工程中常用的三种膜材进行经纬等荷和经纬不等荷弹射试验；将获得的各组试验数据代入测量的理论公式求得膜材的试验计算预张力，并将试验计算预张力与膜材实际预张力进行对比分析；分析表明，膜材试验计算预张力与实际预张力比较吻合，从试验上验证了采用“弹射法”测量建筑膜结构预张力的有效性。
With the progress of science and technology and the development of society, themembrane structure has been widely applied in many areas, especially in the buildingengineering area. The building membrane structure is a new structure system, which hasbeen rising during the recent several dozens of years. It is widely applied in large-scalestadium, exhibition center, casino, and so on. Because the building membranestructure’s dead weight is light and the rigidity is small, it is very sensitive under theimpact load and easy to engender vibration, thus results in engineering accident.Therefore, it is quite necessary to study the vibration characteristics of the buildingmembrane structure under impact loading (such as rainstorm, hail, the waste picked upby the wind, and so on) to obtain the general laws of them. These studies haveimportant significance for the reasonable design and construction of building membranestructure, thus to prevent or reduce the engineering accident of building membranestructure. In addition, applying the theoretical studies of nonlinear vibration of buildingmembrane structure into the studies of pretension measurement method of buildingmembrane structure has a great significance for engineering practice. We can use thestudied measurement method to measure the actual pretension, thus to control the actualpretension accord with the design pretension and guarantee the construction quality.Meanwhile, we can use this method to detect whether the pretension has changed in theworking process, thus to adopt effective measures to adjust the pretension to prevent orreduce engineering accident.
This dissertation mainly studied the theory and application of the nonlinear freevibration of orthotropic rectangular membrane structure and its forced vibration underimpact loading. Firstly, analytical method was applied to study the large deflectiongeometrical nonlinear free and forced vibration problem of orthotropic rectangularmembrane structure and the general analytical solution was obtained. Then, we appliedthe theoretical studies into actual building membrane engineering to develop a newmethod—Ejection Method for monitoring the pretension of building membranestructure and the theoretical measurement formula was derived and obtained. Finally,the numerical analysis and ejection experiment were carried out for the EjectionMethod and the numerical and experiment results proved the Ejection Method is valid.The concrete study contents are as follows:
①The partial differential governing equations of damped and undamped nonlinear free vibration of orthotropic rectangular membrane were established bycombining the Von Kármán’s large deflection theory with the D’Alembert’s principle.The undamped free vibration governing equations were solved by direct integrationmethod and L-P perturbation method, and the approximate analytical solution of thefrequency and deflection function were obtained. The damped free vibration governingequations were solved by t KBM perturbation method, and the approximate analyticalsolution of the frequency and deflection function were obtained.
②Based on the studies of nonlinear free vibration of orthotropic rectangularmembrane structure, the governing equations of the damped and undamped forcedvibration of orthotropic rectangular membrane structure under concentrated impact loadwere established. The undamped forced vibration governing equations were solved byL-P perturbation method, and the approximate analytical solutions of the frequency anddeflection function of were obtained. The damped forced vibration governing equationswere solved by KBM perturbation method, and the approximate analytical solution ofthe frequency and deflection function were obtained. The ANSYS/LS-DYNA finiteelement analysis software was adopted to carry out the numerical analysis of the forcedvibration of orthotropic rectangular membrane structure under the impact load. Thecomparison and analysis of the theoretical and numerical results indicate that thetheoretical results coincide well with the numerical results.
③Applying the theoretical studies of this dissertation into actual buildingmembrane engineering, a new method—Ejection Method was developed for monitoringthe pretension of building membrane structure. The theoretical model of this methodwas established, and the theoretical measurement formula was derived and obtainedaccording to the principle of conservation of energy. The finite element analysis modelof Ejection Method was established and the numerical computation was carried out bythe ANSYS/LS-DYNA finite element analysis software. The theoretical and thenumerical results were compared and analyzed and the compared results prove that useEjection Method to measure the pretension of building membrane structure is feasibleand valid.
④The experimental scheme was constituted for measuring the pretension ofmembrane structure by Ejection Method according to the theoretical studies of EjectionMethod. According to the experimental scheme, the crisscross screw biaxial stretchingdevice was prepared for stretching the membrane test specimens. Three kinds ofmembrane material were selected to carry out the ejection experiment. The ejection experiments with equal loading and unequal loading in the warp and weft directionswere carried out and the experimental data was recorded. Put each group ofexperimental data into the theoretical measurement formula to obtain the experimentalcomputational pretensions, and compared the experimental computational pretensionsto the actual pretensions. The comparing analysis results indicate that the most ofexperimental computational pretensions tallied with the actual pretensions. This alsoproved that use Ejection Method to measure the pretension of building membranestructure is feasible and valid.
引文
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