中文摘要：

使用Gram-Schmidt正交化构造了满足圆柱壳自由边界条件的一组正交多项式,并以此为基函数构造圆柱壳的振动位移表达式;在此基础上,基于Sanders壳体理论,利用Rayleigh-Ritz法,提出了一种用于分析弹性边界约束的正交加肋圆柱壳振动特性的方法。利用该方法,求解了两端简支的正交加肋圆柱壳的自由振动固有频率,将其与文献结果对比,验证了文中方法的正确性;该文还分析了边界各方向约束刚度对正交加肋圆柱壳振动特性的影响。研究表明,本文的方法收敛性好,计算效率高,且可用于分析受经典边界约束的加肋壳振动特性,具有很强的通用性。

英文摘要：

A set of characteristic orthogonal polynomials satisfying free-free boundary condition is constructeddirectly by employing Gram-Schmidt procedure, and then is employed to represent the general formulationsfor the displacements in any axial mode of free vibrations for shells. Based on Sanders＊ shell theory,a method using to analyze vibration characteristics for orthogonal stiffened cylindrical shells constrainedby elastic boundary is proposed by employing Rayleigh-Ritz method. Comparing with the availableanalytical results for a simply supported orthogonal stiffened cylindrical shell, the method proposed in thispaper is verified and it is proved that this method can also be used to analyze vibration characteristics ofshells with classical boundaries. Strong convergence is observed from convergence study. Further, the effectsof the restraint stiffness for elastic boundary in axial, circumferential, radial and rotational directions,on the natural frequencies are studied.