Static and dynamic characteristics of post-buckling of porous functionally graded pipes under thermal shock

The study of thermal post-buckling characteristics of functionally graded pipelines is of great significance for promoting the application of functionally graded materials in spacecraft thermal protection design and marine pipelines. In this study, the static buckling of functionally graded pipes with porosity and the pseudo-linear vibration near the first buckling position of post-buckling are studied. Based on the modified power-law distribution, it is assumed that the material properties of porous FGM pipes change continuously and smoothly along the radial direction. For porosity, it generally occurs in the manufacturing process of functionally graded materials, so the classical Voigt model is selected to describe the material properties of functionally graded material pipelines with pores. Based on Hamilton principle, the nonlinear control equations and corresponding boundary conditions of the pipeline are derived. Firstly, the Routh-Hurwitz criterion is used to discuss the influence of temperature and porosity volume fraction on the critical flow velocity of instability, and then the post buckling structure of the pipeline and the dynamic characteristics of post-buckling are discussed. The numerical results discussed the influence of important parameters such as power law index, porosity volume fraction and temperature on the buckling and post-buckling behaviors of the system.