Thermo-mechanical nonlinear forced vibration of sandwich cylindrical microshells with auxetic cores and porous FGM facesheets in flowing fluid

This study investigates the thermo-mechanical nonlinear forced vibration behavior of sandwich cylindrical microshells incorporating butterfly-shaped auxetic cores and temperature-dependent porous functionally graded (PFGM) facesheets. The structure is supported by a nonlinear elastic foundation and conveys an incompressible, inviscid, irrotational internal fluid. Owing to their negative Poisson's ratio, the butterfly-shaped auxetic cores provide enhanced rigidity and stability compared with conventional re-entrant auxetic designs. The PFGM facesheets exhibit temperature-dependent properties and capture realistic material defects. The governing equations are formulated using Hamilton's principle and are based on the modified couple stress theory (MCST) to include size-dependent effects, first-order shear deformation theory (FSDT) and von K & aacute;rm & aacute;n geometric nonlinearity. Fluid-structure interaction is modeled through a velocity-potential formulation with constant internal flow velocity. The Galerkin method reduces the resulting partial differential equations to a set of nonlinear ordinary differential equations, which are solved using the harmonic balance method to obtain nonlinear frequency-amplitude relationships. A parametric study examines the influences of thermal loading, porosity distribution, fluid velocity, nonlinear foundation stiffness, material length-scale parameters, and geometric features of the butterfly-shaped auxetic core on the nonlinear vibration response. The results reveal strong couplings among thermal effects, microstructural parameters, and internal fluid flow, providing valuable guidance for the design and optimization of micro-scale sandwich structures in aeronautical and biomedical applications.