Vibration Analysis of 2D Porous Functionally Graded Beams With Inclined Cracks Under Thermo‐Hygro‐Mechanical Coupling

ABSTRACT This work provides an in‐depth investigation into wave propagation in functionally graded material (FGM) beams subjected to coupled thermo‐hygro‐mechanical loading. The proposed model explicitly accounts for the presence of cracks, material porosity, axial pre‐stress, and combined temperature–moisture gradients, which are represented through three distinct distribution schemes: uniform (UTC), linear (LTC), and parabolic (STC). Particular emphasis is placed on crack inclination, as its orientation induces localized stiffness variations that markedly influence both wave velocities and natural frequencies. The mathematical framework is based on classical elasticity theory, augmented by geometric stiffness contributions and thermo‐hygro‐mechanical coupling matrices. A comprehensive parametric study is performed to assess the effects of temperature variation, porosity ratio, crack orientation, wave number, and axial pre‐stress on the vibrational response. The numerical results are benchmarked against existing literature and systematically interpreted through comparative tables and percentage‐based evaluations. Overall, the findings underscore the decisive impact of crack inclination and environmental gradients on the dynamic performance of FGM beams, offering valuable insights for the design of smart and resilient structural systems operating under severe service conditions.