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 (f_Wet/f_Dry) 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.

基于线性流固相互作用（FSI）模型和经典壳理论，研究了夹心圆柱壳在外部不可压缩或可压缩流体流动下的振动行为。夹层壳包括由碳纳米管 (CNT) 增强复合材料和金属泡沫芯制成的相同外面板和内面板。CNT增强复合材料的有效力学性能是使用混合扩展规则获得的。此外，通过泡沫厚度的孔隙率分布被假定为三角函数的形式。运动方程和相应的边界条件是根据 Donnell、Love 和 Sanders 的理论推导出来的。首次，通过研究质量守恒、广义伯努利方程和线性流固相互作用，提出了沿壳长度的可压缩流动在亚音速和超音速状态下三维压力分布的封闭形式表达式。使用状态空间和伽辽金方法，精确地解析求解控制方程，以开发具有各种边界条件的流体加载夹心壳的固有频率和振型。因此，结合梁模态函数对不同边界条件下伽辽金方法的有效性和准确性进行了研究。此外，还得到了夹心壳动态失稳发生时水流上游临界速度的闭式表达式。结果表明频率比（广义伯努利方程和线性流固耦合。使用状态空间和伽辽金方法，精确地解析求解控制方程，以开发具有各种边界条件的流体加载夹心壳的固有频率和振型。因此，结合梁模态函数对不同边界条件下伽辽金方法的有效性和准确性进行了研究。此外，还得到了夹心壳动态失稳发生时水流上游临界速度的闭式表达式。结果表明频率比（广义伯努利方程和线性流固耦合。使用状态空间和伽辽金方法，精确地解析求解控制方程，以开发具有各种边界条件的流体加载夹心壳的固有频率和振型。因此，结合梁模态函数对不同边界条件下伽辽金方法的有效性和准确性进行了研究。此外，还得到了夹心壳动态失稳发生时水流上游临界速度的闭式表达式。结果表明频率比（使用状态空间和伽辽金方法，精确地解析求解控制方程，以开发具有各种边界条件的流体加载夹心壳的固有频率和振型。因此，结合梁模态函数对不同边界条件下伽辽金方法的有效性和准确性进行了研究。此外，还得到了夹心壳动态失稳发生时水流上游临界速度的闭式表达式。结果表明频率比（使用状态空间和伽辽金方法，精确地解析求解控制方程，以开发具有各种边界条件的流体加载夹心壳的固有频率和振型。因此，结合梁模态函数对不同边界条件下伽辽金方法的有效性和准确性进行了研究。此外，还得到了夹心壳动态失稳发生时水流上游临界速度的闭式表达式。结果表明频率比（得到了夹心壳动态失稳发生时水流上游临界速度的闭式表达式。结果表明频率比（得到了夹心壳动态失稳发生时水流上游临界速度的闭式表达式。结果表明频率比（f _Wet / f _Dry ) 的空气加载夹层壳在亚音速状态随着上游速度略有下降，而在超音速状态下则显着增加（超过 20%）。此外，对于较大的纵横比 ( L / R ) 和壁长细长 ( R / h )值，流动规格对固有频率和临界速度的影响更为明显。结果表明，Love 壳理论对于不同几何比和边界条件的流致夹心圆柱壳的振动分析具有足够的精度，并且可以忽略桑德斯项。