Aero-thermo-elastic Vibration Analysis of Porous FG Cracked Plates Via the Extended Chebyshev Spectral Method

This study presents a modeling approach for analyzing the aero-thermo-elastic vibration characteristics of porous functionally graded (FG) cracked plates. An extended Chebyshev spectral method is proposed to accurately capture the effects of cracks on the dynamic response by introducing supplementary functions that address local discontinuities while preserving the rapid convergence of Chebyshev polynomials. A thermo-dynamic analysis under steady-state temperature conditions is conducted to determine the internal non-uniform temperature distribution of the plate. The first-order shear deformation theory and supersonic piston theory are integrated to derive the strain energy and kinetic energy expressions for FG cracked plates with non-uniform porosity. Hamilton’s principle is employed to systematically formulate the stiffness, damping, and mass matrices. The proposed method enables high-fidelity modeling of crack-induced discontinuities and effectively captures the coupling between aerodynamic, thermal, and elastic fields. A comprehensive convergence study verifies the stability of the proposed spectral method, and comparisons with published studies and FEM results confirm its accuracy. Finally, a detailed parametric analysis investigates the influence of cracks on the aero-thermo-elastic vibration characteristics of porous FG plates, providing valuable insights into their dynamic behavior under combined aerodynamic and thermal loads.