Subsonic and supersonic flow-induced vibration of sandwich cylindrical shells with FG-CNT reinforced composite face sheets and metal foam core

Based on the linear fluid-solid interaction (FSI) model and classical shell theories, vibration behavior of sandwich cylindrical shells subjected to external incompressible or compressible fluid flow is investigated. The sandwich shell includes the same outer and inner face sheets made of carbon nanotube (CNT) reinforced composites and a metal foam core. The effective mechanical properties of CNT reinforced composites are obtained using the extended rule of mixture. Also, the porosity distribution through the foam thickness is assumed to be in the form of a trigonometric function. Equations of motion and corresponding boundary conditions are derived according to the Donnell's, Love's and Sanders' theories. For the first time, a closed-form expression of three-dimensional pressure distribution in both subsonic and supersonic regimes of compressible flow passing along the length of shell is presented by studying conservation of mass, generalized Bernoulli equation and linear fluid-solid interaction. The governing equations are exactly and analytically solved to develop natural frequencies and mode shapes of fluid-loaded sandwich shells with various boundary conditions using the state-space and Galerkin's methods. So the validity and accuracy of the Galerkin's method in conjunction with beam modal functions for different boundary conditions are investigated. In addition, a closed-form expression is obtained for critical upstream speed of water flow at which the dynamic instability of sandwich shells occurs. Findings indicate the frequency ratio (fWet/fDry) of air-loaded sandwich shells decreases slightly with upstream speed in the subsonic regime, while a significant increase is seen in the supersonic regime (more than 20%). Also, the effect of flow specifications on the natural frequency and critical speed are much more pronounced for larger values of aspect (L/R) and wall slenderness (R/h) ratios. It is shown that Love's shell theory is accurate enough for vibration analysis of flow-induced sandwich cylindrical shells with different geometric ratios and boundary conditions and the sanders' terms can be neglected.