<p>The in-wheel motor skateboard chassis has emerged as a promising platform for high-level autonomous driving and multi-degree-of-freedom controllability. Nevertheless, the nonlinear dynamics considering the nonlinear time-varying parameters from suspension and skateboard is still regarded as a significant challenge. In this paper, a nonlinear 11-degree-of-freedom (11-DOF) chassis model is established based on multibody system dynamics theory, considering the nonlinear cubic and quadratic mechanics from the suspension and the skateboard platform. The nonlinear relationship between suspension force and displacement is defined up to the cubic term, while the nonlinear relationship between the flexible deformation of the skateboard platform and the applied load is defined up to the quadratic term. A modified incremental harmonic balance (IHB) method is utilized for solving the system’s steady-state responses. The simulation results show that the root mean square errors (RMSEs) of the vertical displacement, roll, and pitch angles are 2.289&#xa0;mm, 0.022°, and 0.010° compared with those from commercial dynamics software RecurDyn. Moreover, for the tested steady-state sinusoidal cases and the adopted truncation setting, the computational efficiency for steady-state solution can be increased by a factor of 31.305 compared with the original IHB method. The results indicate that the proposed integrated approach can capture the nonlinear coupling effects within the investigated low-frequency vertical dynamics range while providing an improved accuracy-efficiency balance. The nonlinear-parameter analyses provide quantitative insights for chassis dynamics assessment within the investigated low-frequency range.</p>