Nonlinear resonance dynamics of timoshenko-based locust-leg-inspired tubes

This study investigates the nonlinear dynamics of a variable-section curved tube (VST) inspired by the locust leg. Existing models largely rely on Euler–Bernoulli beam theory, neglecting shear deformation and rotary inertia. To address these limitations, we develop a bionic Timoshenko beam model that fully captures the curvature and axial variation of the locust leg-like structure. Based on this model, the equations of motion under harmonic excitation are derived via Hamilton's principle. Subsequently, the Galerkin method is employed for discretization, and the method of multiple scales is utilized to analyze the effects of key parameters on the frequency-response curves and force-response curves of the system under principal parametric resonance and 1/2-order subharmonic resonance of the 1st mode, together with 1:2 internal resonance between the 1st and 2nd modes. The complete evolution process of the VST from periodic motion to period-doubling bifurcation and ultimately to chaos is examined. The global bifurcation behaviors are obtained via Melnikov analysis and verified using phase portraits, Poincaré maps, and wavelet transform time-frequency diagrams. Furthermore, the effects of physical parameter on the dynamic characteristics of the system's multistable attractors are investigated, thereby revealing the influence of parameters on the bifurcation response and chaotic motion of the system.