正交各向异性圆柱壳静动态特性分析及比较研究
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摘要
圆柱壳是工程实际中经常使用的结构形式,深入研究它的静动力性能具有实际的工程意义。
本文首先对圆柱壳的稳定性、自由振动、瞬态和稳态动力响应研究进行了简要回顾和评述。
从Flügge壳体理论出发,推导出正交各向异性圆柱壳在静水压力作用下的平衡方程,把弹性失稳问题转化成为求解广义特征值问题,并讨论了正交各向异性、L/R和h/R等因素对临界失稳压力的影响。本文还使用Love-Timoshenko和Donnell壳体理论分析了临界压力,给出了3种壳体理论在平衡微分方程式、内力表达式、三个位移表达式的差异,并且使用解析方法精确计算了失稳压力,讨论了3种理论之间的差异,分析了产生差异的原因。
基于正交各向异性圆柱壳在静水压力作用下的自由振动平衡方程,推导出在简支边界条件下壳体自由振动特征方程。分析了正交各向异性圆柱壳的自由振动特性以及静水压力对其自由振动频率的影响,详细讨论了壳体几何参数和材料特性参数对自振频率的影响,给出了最低频率随L/R变化的包络线。本文还使用Love-Timoshenko和Donnell壳体理论计算了自由振动频率。
本文基于Flügge壳体理论,从正交各向异性圆柱壳在轴向压力作用下的自由振动平衡方程出发,推导出在简支边界条件下壳体自由振动的特征方程,分析了正交各向异性圆柱壳在轴向压力作用下的稳定和自由振动特性以及轴向压力对其自由振动频率的影响,详细讨论了壳体几何参数和材料特性参数对于自振频率的影响,给出了最低频率随L/R变化的包络线。
使用Flügge壳体理论和振型叠加方法,分析了正交各向异性圆柱壳在静水压力作用下受到径向冲击时的瞬态动力响应问题,并且讨论了结构尺寸变化以及材料特性对响应量的影响。对振型叠加法的精度和收敛性也进行了讨论,还使用Timoshenko壳体理论分析了动力响应,讨论了2种理论之间的差异。
Flügge壳体理论和振型叠加方法还用于正交各向异性圆柱壳受到径向简谐力作用时稳态动力响应问题分析,并且讨论了结构尺寸以及材料特性对响应量的影响。文中给出了位移和应变的响应历程。
Shell structures have been widely used in so many engineering areas; it is interesting and challengeable to study the static and dynamic characteristics of shells. Brief reviews about elastic stability, free vibration, transient dynamic response and harmonic dynamic response of circular cylindrical shells are given first.
According to Flügge shell theory, the equations for orthotropic circular cylindrical shells under external hydrostatic pressure are given. A characteristic equation for stability can be obtained for both simply supported at the ends. Divergence loads of shell are calculated from this equation. Jacobi method is used to solve this eigenvalue problem. The effects of orthotropicity, L/R ratio and h/R ratio on the divergence load are discussed in detail. Love-Timoshenko shell theory and Donnell shell theory are also used to calculate the same example. The differences of equilibrium equations, expressions of forces and moments of these 3 theories are given in tables. The accuracy of these two theories is examined in this paper.
An analysis is presented for the free vibration of an orthotropic circular cylindrical shell subjected to hydrostatic pressure. Based on Flügge shell theory, the equations of free vibrations of an orthotropic circular cylindrical shell under hydrostatic pressure are obtained. For shear diaphragms at both ends, the resulting characteristic equations about pressure and frequency are given. The effect of shell’s parameters (L/R, h/R) and material properties on the free vibration characteristics have been studied in detail. Differences between Love-Timoshenko, Donnell equations and that of Flügge theory are examined too.
A study for an orthotropic circular cylindrical shell subjected to axial load is present. The effect of shell’s parameters (L/R, h/R) and material properties on the free vibration characteristics have been studied.
Following Flügge’s exact derivation for the buckling of cylindrical shells, the equations of motion for dynamic loading of an orthotropic circular cylindrical shell under external hydrostatic pressure have been formulated. The normal mode theory is used to provide transient dynamic response for the equations of motion.
The effect of shell’s parameters, external hydrostatic pressure and material properties on the shell response has been studied in detail. A part of tables and figures are given. The responses of displacements, strain and stress are obtained for the area of impact, while those outside the area of impact are also calculated. The accuracy of normal mode theory and Timoshenko shell theory are examined in this paper.
The harmonic responses of an orthotropic circular cylindrical shell under external hydrostatic pressure are studied. There is a slight shift in the locations of the resonant peaks, an example is illustrated for this phenomena. The resonant response of displacements and strain are obtained.
本文首先对圆柱壳的稳定性、自由振动、瞬态和稳态动力响应研究进行了简要回顾和评述。
从Flügge壳体理论出发,推导出正交各向异性圆柱壳在静水压力作用下的平衡方程,把弹性失稳问题转化成为求解广义特征值问题,并讨论了正交各向异性、L/R和h/R等因素对临界失稳压力的影响。本文还使用Love-Timoshenko和Donnell壳体理论分析了临界压力,给出了3种壳体理论在平衡微分方程式、内力表达式、三个位移表达式的差异,并且使用解析方法精确计算了失稳压力,讨论了3种理论之间的差异,分析了产生差异的原因。
基于正交各向异性圆柱壳在静水压力作用下的自由振动平衡方程,推导出在简支边界条件下壳体自由振动特征方程。分析了正交各向异性圆柱壳的自由振动特性以及静水压力对其自由振动频率的影响,详细讨论了壳体几何参数和材料特性参数对自振频率的影响,给出了最低频率随L/R变化的包络线。本文还使用Love-Timoshenko和Donnell壳体理论计算了自由振动频率。
本文基于Flügge壳体理论,从正交各向异性圆柱壳在轴向压力作用下的自由振动平衡方程出发,推导出在简支边界条件下壳体自由振动的特征方程,分析了正交各向异性圆柱壳在轴向压力作用下的稳定和自由振动特性以及轴向压力对其自由振动频率的影响,详细讨论了壳体几何参数和材料特性参数对于自振频率的影响,给出了最低频率随L/R变化的包络线。
使用Flügge壳体理论和振型叠加方法,分析了正交各向异性圆柱壳在静水压力作用下受到径向冲击时的瞬态动力响应问题,并且讨论了结构尺寸变化以及材料特性对响应量的影响。对振型叠加法的精度和收敛性也进行了讨论,还使用Timoshenko壳体理论分析了动力响应,讨论了2种理论之间的差异。
Flügge壳体理论和振型叠加方法还用于正交各向异性圆柱壳受到径向简谐力作用时稳态动力响应问题分析,并且讨论了结构尺寸以及材料特性对响应量的影响。文中给出了位移和应变的响应历程。
Shell structures have been widely used in so many engineering areas; it is interesting and challengeable to study the static and dynamic characteristics of shells. Brief reviews about elastic stability, free vibration, transient dynamic response and harmonic dynamic response of circular cylindrical shells are given first.
According to Flügge shell theory, the equations for orthotropic circular cylindrical shells under external hydrostatic pressure are given. A characteristic equation for stability can be obtained for both simply supported at the ends. Divergence loads of shell are calculated from this equation. Jacobi method is used to solve this eigenvalue problem. The effects of orthotropicity, L/R ratio and h/R ratio on the divergence load are discussed in detail. Love-Timoshenko shell theory and Donnell shell theory are also used to calculate the same example. The differences of equilibrium equations, expressions of forces and moments of these 3 theories are given in tables. The accuracy of these two theories is examined in this paper.
An analysis is presented for the free vibration of an orthotropic circular cylindrical shell subjected to hydrostatic pressure. Based on Flügge shell theory, the equations of free vibrations of an orthotropic circular cylindrical shell under hydrostatic pressure are obtained. For shear diaphragms at both ends, the resulting characteristic equations about pressure and frequency are given. The effect of shell’s parameters (L/R, h/R) and material properties on the free vibration characteristics have been studied in detail. Differences between Love-Timoshenko, Donnell equations and that of Flügge theory are examined too.
A study for an orthotropic circular cylindrical shell subjected to axial load is present. The effect of shell’s parameters (L/R, h/R) and material properties on the free vibration characteristics have been studied.
Following Flügge’s exact derivation for the buckling of cylindrical shells, the equations of motion for dynamic loading of an orthotropic circular cylindrical shell under external hydrostatic pressure have been formulated. The normal mode theory is used to provide transient dynamic response for the equations of motion.
The effect of shell’s parameters, external hydrostatic pressure and material properties on the shell response has been studied in detail. A part of tables and figures are given. The responses of displacements, strain and stress are obtained for the area of impact, while those outside the area of impact are also calculated. The accuracy of normal mode theory and Timoshenko shell theory are examined in this paper.
The harmonic responses of an orthotropic circular cylindrical shell under external hydrostatic pressure are studied. There is a slight shift in the locations of the resonant peaks, an example is illustrated for this phenomena. The resonant response of displacements and strain are obtained.
引文
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