Nonlinear dynamic analysis of a variable angle tow composite diving board

This paper investigates the nonlinear dynamic response and energy transfer mechanisms of a Variable Angle Tow (VAT) composite springboard featuring an intermediate unilateral support. While conventional straight-fiber composites are limited by their constant stiffness profiles, VAT composites enable spatial stiffness tailoring to optimize kinematic performance. A fully coupled nonlinear mathematical model is developed utilizing the Timoshenko beam theory and von Kármán geometric nonlinearities to account for large deformations. The governing equations are derived via Hamilton’s principle, discretized using the Galerkin method, and integrated numerically with a penalty approach modeling the unilateral contact. A comparative dynamic analysis between a tailored VAT (45 ∘ -90 ∘ ) and a straight-fiber composite springboard demonstrates that the VAT configuration significantly reduces the fundamental natural frequency while amplifying the maximum tip vertical velocity by over 145% (reaching 2.7 m/s). The results reveal that the variable fiber orientation induces a strong bend-twist coupling ( \(\:{D}_{16}\) ), triggering pronounced torsional oscillations and activating dominant geometric nonlinearities, which are evidenced by asymmetric phase portraits and higher-order harmonics in the frequency spectrum. Furthermore, energy analysis confirms that the VAT springboard possesses a vastly superior mechanical energy capacity, storing approximately 380 J of strain energy and releasing over 300 J of kinetic energy, compared to just 125 J and 50 J in the straight-fiber counterpart. These findings indicate that VAT composites provide substantial dynamic tailorability, alongside enhanced mechanical energy storage and energy return capacity for high-performance diving structures.