弹性连续介质中有限长环向加肋圆柱壳的振动特性分析

基于Flugge薄壳理论,利用环向加肋圆柱壳中力与壳体中面位移关系,运用波传播理论考虑有限长圆柱壳两端边界条件,得到环向加肋圆柱壳结构的运动控制方程。再基于Navier-Stokes波动理论建立圆柱壳周围无限弹性连续介质的运动方程,在此基础上,通过接触面连续条件与Flugge薄壳理论基本条件,建立基于弹性介质与环向加肋圆柱壳结构耦合作用下的圆柱壳振动控制方程,从而得到弹性介质中环向加肋圆柱壳结构的自振特性参数。通过真空中普通圆柱壳、弹性介质中普通圆柱壳、真空中环向加肋圆柱壳以及弹性介质中环向加肋圆柱壳结构的振动特性分析,同时结合三维有限元仿真分析,验证了本文理论方法的正确性,研究成果可为地下管道等相关结构的抗震设计及无损检测提供理论指导。

Vibration characteristics of finite-length ring-stiffened cylindrical shells surrounded by elastic continuum

By utilizing the wave propagation method for considering the boundary conditions at both ends of the finite-length ring-stiffened cylindrical shell, the equation of motion for the cylindrical shell is firstly developed based on the Flugge shell theory and the relationships between internal force and displacement of middle surface of the ring-stiffened cylindrical shell. Secondly, the governing equation for the elastic medium around the cylindrical shell is set up by employing the Navier-Stokes wave theory of homogeneous, isotropic and linear elastic media. After that, following the continuous contact surface conditions and the principle of Flugge thin shell theory, the governing equation for the ring-stiffened cylindrical shell structures considering the dynamic interaction with surrounded elastic medium is developed, and then the free-vibration characteristics of the ring-stiffened cylindrical shell structures surrounded by elastic medium are analyzed. Finally, through the free-vibration analysis of the following four situations, i.e., ordinary cylindrical shell in vacuum, ordinary cylindrical shell in elastic medium, ring-stiffened cylindrical shell in vacuum, and ring-stiffened cylindrical shell in elastic medium, and also combined with three-dimensional finite element simulations, the correctness of the proposed theory is verified. The presented research results can provide theoretical guidance for non-destructive testing and seismic design of underground pipelines and other related engineering structures.