基于梁函数-Ritz法的圆柱壳模态特性分析

徐港辉,祝长生

Modal characteristics analysis of cylindrical shells based on beam functions-Ritz method

Gang-hui XU,Chang-sheng ZHU

表 1 常用薄壳理论对比

Tab.1 Comparison of common thin shell theories

薄壳理论 $ {\varepsilon _x} $ $ {\varepsilon _\theta } $ $ {\gamma _{x\theta }} $ Donnell $ {\varepsilon _{x_ {\rm{D}}}} $ $ {\varepsilon _{\theta_ {\rm{D}}}} $ $ {\gamma _{x\theta_ {\rm{D}}}} $ Reissner $ {\varepsilon _{x_ {\rm{D}}}} $ ${\varepsilon _{\theta_ {\rm{D}}} }+z\dfrac{1}{ { {r^2} } }\dfrac{ {\partial v} }{ {\partial \theta } }$ ${\gamma _{x\theta_ {\rm{D}}} }+z\dfrac{1}{r}\dfrac{ {\partial v} }{ {\partial x} }$ Sanders $ {\varepsilon _{x_ {\rm{D}}}} $ ${\varepsilon _{\theta_ {\rm{D}}} }+z\dfrac{1}{ { {r^2} } }\dfrac{ {\partial v} }{ {\partial \theta } }$ ${\gamma _{x\theta_ {\rm{D}}} }+z\left(\dfrac{3}{ {2r} }\dfrac{ {\partial v} }{ {\partial x} } - \dfrac{1}{ {2{r^2} } }\dfrac{ {\partial u} }{ {\partial \theta } }\right)$ Love $ {\varepsilon _{x_ {\rm{D}}}} $ ${\varepsilon _{\theta_ {\rm{D}}} }+z\dfrac{1}{ { {r^2} } }\dfrac{ {\partial v} }{ {\partial \theta } }$ ${\gamma _{x\theta_ {\rm{D}}} }+z\dfrac{2}{r}\dfrac{ {\partial v} }{ {\partial x} }$