Based on the advantages of thin-walled tubes and lattice structures in energy absorption and improved crashworthiness, a hybrid structure of lattice-reinforced thin-walled tubes with different cross-sectional cell numbers and gradient densities was constructed, and a high crashworthiness absorber with adjustable energy absorption was proposed. The experimental and finite element characterization of the impact resistance of uniform density and gradient density hybrid tubes with different lattice arrangements to withstand axial compression was carried out to investigate the interaction mechanism between the lattice packing and the metal shell, and the energy absorption of the hybrid structure was increased by 43.40% relative to the sum of its individual components. The effect of transverse cell number configuration and gradient configuration on the impact resistance of the hybrid structure was investigated, and the results showed that the hybrid structure showed higher energy absorption than the empty tube, and the best specific energy absorption was increased by 83.02%; the transverse cell number configuration had a greater effect on the specific energy absorption of the hybrid structure with uniform density, and the maximum specific energy absorption of the hybrid structure with different configurations was increased by 48.21%. The gradient density configuration had a significant effect on the peak crushing force of the gradient structure. In addition, the effects of wall thickness, density and gradient configuration on energy absorption were quantitatively analyzed. This study provides a new idea to optimize the impact resistance of lattice-structure-filled thin-walled square tube hybrid structures under compressive loading through a combination of experiments and numerical simulations.

To address the insufficient convergence robustness, strong dependence on the initial guess, and computational-efficiency bottlenecks of the incremental harmonic balance (IHB) method for strongly nonlinear systems, this paper develops an adaptive framework that integrates a trust-region strategy with a hybrid Hessian matrix. The framework reformulates the harmonic-balance iteration as a constrained nonlinear least-squares optimization problem, constructs a symmetric hybrid Hessian matrix by blending the Gauss–Newton and Newton directions, and uses a trust-region algorithm to adaptively regulate the step size, thereby jointly optimizing the iterative path and convergence behavior. Numerical results show that the proposed method significantly enhances convergence robustness, reduces sensitivity to initial guesses, and improves computational efficiency while maintaining high accuracy. It also captures both stable and unstable periodic solutions in strongly nonlinear systems.