双参数弹性基功能梯度圆柱管自由振动的高阶梁理论解
2024,46(4):86-95
马维力
长安大学 理学院, 陕西 西安 710064，mawilling@163.com
崔辉如
陆军工程大学 国防工程学院, 江苏 南京 210007
申柳雷
国防科技大学 军政基础教育学院, 湖南 长沙 410072
王诗琦
长安大学 理学院, 陕西 西安 710064
彭帆
长安大学 理学院, 陕西 西安 710064
李显方
中南大学 土木工程学院, 湖南 长沙 410075
长安大学 理学院, 陕西 西安 710064，mawilling@163.com
崔辉如
陆军工程大学 国防工程学院, 江苏 南京 210007
申柳雷
国防科技大学 军政基础教育学院, 湖南 长沙 410072
王诗琦
长安大学 理学院, 陕西 西安 710064
彭帆
长安大学 理学院, 陕西 西安 710064
李显方
中南大学 土木工程学院, 湖南 长沙 410075
摘要：
基于高阶剪切变形梁理论,推导了Winkler-Pasternak弹性基径向功能梯度空心圆柱管自由振动行为的控制方程。该方法无须引入剪切修正系数,自动满足空心圆柱管内外表面剪应力自由边界条件。通过引入辅助函数,将关于挠度和转角的耦合控制方程化为单一高阶微分控制方程。给出了典型边界条件下功能梯度空心圆柱管的频率和振型。将计算结果与已有文献结果对比,验证了所提理论的精度。可以为工程中常见的Winkler-Pasternak弹性基梁结构提供更高精度的一维弹性理论解,研究结果表明,功能梯度材料的梯度参数和弹性地基刚度系数对固有频率值影响显著。与高阶固有频率相比,刚度系数对低阶固有频率的影响更加明显。
基于高阶剪切变形梁理论,推导了Winkler-Pasternak弹性基径向功能梯度空心圆柱管自由振动行为的控制方程。该方法无须引入剪切修正系数,自动满足空心圆柱管内外表面剪应力自由边界条件。通过引入辅助函数,将关于挠度和转角的耦合控制方程化为单一高阶微分控制方程。给出了典型边界条件下功能梯度空心圆柱管的频率和振型。将计算结果与已有文献结果对比,验证了所提理论的精度。可以为工程中常见的Winkler-Pasternak弹性基梁结构提供更高精度的一维弹性理论解,研究结果表明,功能梯度材料的梯度参数和弹性地基刚度系数对固有频率值影响显著。与高阶固有频率相比,刚度系数对低阶固有频率的影响更加明显。
基金项目：
国家自然科学基金面上资助项目(12072374)；陕西省自然科学基础研究计划资助项目(2023-JC-QN-0010)
国家自然科学基金面上资助项目(12072374)；陕西省自然科学基础研究计划资助项目(2023-JC-QN-0010)
Free vibration of cylindrical functionally graded tubes on bi-parameter foundation based on a higher-order beam theory
MA Weili
School of Science, Chang′an University, Xi′an 710064, China,mawilling@163.com
CUI Huiru
College of Defense Engineering, Army Engineering University, Nanjing 210007, China
SHEN Liulei
College of Basic Military and Pilitical Education, National University of Defense Technology, Changsha 410072, China
WANG Shiqi
School of Science, Chang′an University, Xi′an 710064, China
PENG Fan
School of Science, Chang′an University, Xi′an 710064, China
LI Xianfang
School of Civil Engineering, Central South University, Changsha 410075, China
School of Science, Chang′an University, Xi′an 710064, China,mawilling@163.com
CUI Huiru
College of Defense Engineering, Army Engineering University, Nanjing 210007, China
SHEN Liulei
College of Basic Military and Pilitical Education, National University of Defense Technology, Changsha 410072, China
WANG Shiqi
School of Science, Chang′an University, Xi′an 710064, China
PENG Fan
School of Science, Chang′an University, Xi′an 710064, China
LI Xianfang
School of Civil Engineering, Central South University, Changsha 410075, China
Abstract：
Based on the theory of high-order shear deformation beam, the governing equations for the free vibration behavior of Winkler-Pasternak elastic foundation radial function gradient hollow cylindrical pipe were derived. This method does not require the introduction of shear correction coefficient and automatically satisfies the free boundary condition of shear stress on the inner and outer surfaces of the hollow cylindrical pipe. By introducing auxiliary functions, the coupled equations for deflection and angle were transformed into a single high-order differential equation. The frequency and mode shapes of the function gradient hollow cylindrical pipe under typical boundary conditions were given. The calculation results were compared with the results in the existing literature to verify the accuracy of the proposed theory. It can provide higher precision one-dimensional elastic theoretical solutions for the common Winkler-Pasternak elastic beam structures in engineering. Research results show that the gradient parameter and elastic foundation stiffness coefficient of the function gradient material have a significant impact on the natural frequency value. Compared with the high-order natural frequency, the stiffness coefficient has a more significant impact on the low-order natural frequency.
Based on the theory of high-order shear deformation beam, the governing equations for the free vibration behavior of Winkler-Pasternak elastic foundation radial function gradient hollow cylindrical pipe were derived. This method does not require the introduction of shear correction coefficient and automatically satisfies the free boundary condition of shear stress on the inner and outer surfaces of the hollow cylindrical pipe. By introducing auxiliary functions, the coupled equations for deflection and angle were transformed into a single high-order differential equation. The frequency and mode shapes of the function gradient hollow cylindrical pipe under typical boundary conditions were given. The calculation results were compared with the results in the existing literature to verify the accuracy of the proposed theory. It can provide higher precision one-dimensional elastic theoretical solutions for the common Winkler-Pasternak elastic beam structures in engineering. Research results show that the gradient parameter and elastic foundation stiffness coefficient of the function gradient material have a significant impact on the natural frequency value. Compared with the high-order natural frequency, the stiffness coefficient has a more significant impact on the low-order natural frequency.
收稿日期：
2022-08-25
2022-08-25
