Modal Vibration Sensitivity to Anisotropic Stiffness Degradation in Composite Laminates: Implications for Fatigue Damage Assessment

Abstract

Fatigue-induced damage in laminated composites can degrade individual elastic properties at different rates, producing mode-dependent changes in structural vibration characteristics. This study investigates whether intact-state modal sensitivities can predict the frequency response to finite anisotropic stiffness degradation without repeated degraded-state eigenvalue analyses. A component-resolved modal-sensitivity framework is derived from the generalized eigenvalue problem and extended to finite stiffness loss by integrating a logarithmic frequency–stiffness relation. The formulation is implemented using a first-order shear deformation theory (FSDT) finite-element model with nine-node quadratic elements. A unidirectional [0]₁₀ GFRP laminate is used to identify stiffness–mode relationships, while a symmetric cross-ply [0/90]_s laminate assesses predictor transferability. The numerical implementation and modal sensitivities are verified through analytical beam-limit comparisons and finite-difference calculations. For the unidirectional laminate, bending-dominated modes exhibit E₁ sensitivities of 0.493–0.498, whereas twisting-mode frequencies are primarily sensitive to G₁₂, with values of 0.443–0.459. For prescribed stiffness reductions up to 30%, conventional linear extrapolation produces maximum errors of approximately 1.4–1.6% for the dominant stiffness–mode combinations, whereas the integrated formulation limits the corresponding errors to 0.147%. For the cross-ply laminate, integrated prediction errors remain below 0.16% across all investigated cases. The results demonstrate that intact-state sensitivities can provide an accurate reduced-order mapping from prescribed anisotropic stiffness degradation to multimode frequency changes. The formulation does not model fatigue-damage evolution or predict fatigue life, but provides a mechanics-based basis for vibration-informed assessment of fatigue-related stiffness deterioration.