Purpose <p>This study aims to analyze the nonlinear vibration behavior of n-order bifurcated beams with variable cross-sections made of DP980 steel. The primary research objective is to develop a robust theoretical model that can elucidate the synergistic effects of key geometric parameters—including bifurcation order, bifurcation angle, and taper geometry—on the structural dynamic response.</p> Methods <p>A semi-analytical model was developed based on traveling wave theory. The core methodology involves establishing a coupled vibration system that integrates axial, bending, and torsional deformations. Specifically, a perturbed traveling wave approach was proposed to solve the transverse vibration of variable-cross-section Timoshenko beams, and this solution was embedded within a transfer matrix formulation. The overall spatial dynamics were systematically encoded using a state-space representation.</p> Results <p>The investigation yielded three key findings: (1) An increase in bifurcation order introduces distinct low-frequency harmonic peaks while promoting modal decoupling in the mid-frequency range. (2) The taper ratio exerts an exponential influence on low-order modal frequencies, yet its effect on high-order modes is linear. (3) The beam intersection position and angle cooperatively modulate modal properties; offsetting the intersection point was found to enhance local modes and shift global resonance peaks.</p> Conclusion <p>The proposed semi-analytical model offers a comprehensive theoretical foundation and an effective parametric design strategy for vibration and noise control in complex, multiscale fractal beam structures, providing critical insights for optimizing their dynamic performance.</p>