Explainable AI based prediction of natural frequencies and modal damping in multi-delaminated MWCNT/GFRP composite plates

This study presents a comprehensive investigation of vibrational behavior in multi-walled carbon nanotube (MWCNT) reinforced glass fiber reinforced polymer (GFRP) composite plates featuring multiple delaminations using explainable artificial intelligence techniques. A displacement-based finite element model incorporating third order shear deformation theory (TSDT) was developed to analyze natural frequencies and modal damping factors in composite plates with double and triple delamination configurations. The mathematical framework considers 12-ply symmetric laminate configurations [(0/90)3]s with clamped boundary conditions, examining 71,280 systematic cases for double delamination and 109,200 cases for triple delamination across six interfaces. The finite element analysis reveals complex frequency-damping interdependencies where MWCNT reinforcement (0.005-0.01 wt%) consistently increases natural frequencies by 1.751-3.53% while simultaneously reducing modal damping factors by 3.003-7.484%. Double delamination configurations exhibit frequency ranges from 134.8-174.82 Hz, while triple delamination scenarios demonstrate more severe degradation with frequencies spanning 124.44-168.75 Hz, representing up to 26.3% reduction between optimal and damage locations. To overcome computational challenges associated with extensive parametric studies, an advanced machine learning framework was implemented using XGBoost regression models achieving exceptional performance with R2 values of 0.993 for natural frequency predictions and 0.997 for modal damping factor predictions for double delaminated case. The explainable AI implementation through SHAP and LIME analysis reveals that interface position dominates frequency behavior while MWCNT concentration significantly influences damping characteristics. The framework enables rapid dual-parameter predictions in less than 0.001 seconds compared to 45 minutes required for finite element analysis, facilitating efficient design space exploration and multi-objective optimization for damage-tolerant composite structures in aerospace, automotive, and marine applications.