Vibration of Quick-Release Bolt–Composite Plate Under Loosening, Missing, and Hygrothermal Conditions

Quick-release bolts (QRBs) are commonly used in electric aircraft for rapid maintenance. However, existing models fail to predict QRB state effects on composite panel vibrations under hygrothermal conditions. This paper proposes an improved orthogonal polynomial solution within the Rayleigh–Ritz framework for composite laminated perforated rectangular plates connected by QRBs. Total energy expressions, including hygrothermal effects, are derived via Kirchhoff plate theory. QRB states—fastened, loosened, and missing—are modeled using artificial springs with nonuniform stiffness. The method supports arbitrary boundary conditions and incorporates composite lay-up angles and hygrothermal variations. Validation through experimental tests and finite-element simulations demonstrates excellent model accuracy, convergence, and efficiency. Frequency errors between theory and the finite-element method stay within 3.3% under hygrothermal conditions. In bolt-state-change experiments, the average theoretical–experimental error remains below 5%. Moreover, the predicted mode shapes show amplified response near altered QRBs, consistent with physical observations. This work offers an efficient analytical tool for vibration analysis and design of QRB-connected composite structures.