Nonlinear dynamic analysis and multi-objective optimization of composite bicycle suspensions for high-performance sports applications

The application of composite materials in modern bicycle suspension systems offers significant advantages in terms of weight reduction and flexibility; however, the resulting large deformations necessitate a rigorous nonlinear dynamic analysis. In this study, a comprehensive mathematical model based on the Timoshenko beam theory is developed to capture the transverse shear deformations inherent in thick composite laminates. Geometric nonlinearities are incorporated using von Karman membrane stretching strains. The governing continuous equations are discretized via the Galerkin method, leading to the precise analytical determination of the nonlinear stiffness parameter. The nonlinear dynamic responses are subsequently analyzed using time-history and Fast Fourier Transform (FFT) techniques over a 0.5 s simulation span. The results reveal a pronounced tension-stiffening effect, demonstrating a 38 % reduction in the maximum transverse deflection—from 34mm in the linear assumption to 21mm in the nonlinear model. Furthermore, amplitude-dependent frequency shifts are clearly observed, with the resonance frequency shifting from 29.1 Hz to approximately 38.0 Hz at a deflection amplitude of 15mm, while the primary nonlinear FFT peak is identified within the 31.5 − 32.0 Hz range. Finally, a multi-objective optimization using the NSGA-II algorithm is conducted to extract the Pareto optimal design points, considering phase velocities up to ± 2.0 m/s. The findings underscore the critical necessity of incorporating both shear deformations and geometric nonlinearities for the robust and reliable design of composite bicycle suspensions.