Articulated multiple-plate structures (AMPSs) use elastic hinges to facilitate folding and deployment, yet encounter nonlinearities and multi-frequency excitations, which result in complicated multi-mode coupling and nonlinear dynamic behaviors. To further understand the mechanism of multi-mode coupling and the influence of multi-frequency excitation, this study investigates the 1:1 internal resonance of the AMPS induced by mode interchanging under two-harmonic excitation. The explicit mode functions are derived using the Rayleigh-Ritz method, in which the deformations of the plate are expressed by orthogonal characteristic polynomials, and the hinge constraints are described via Lagrange multipliers. The mode interchanging phenomenon between the bending and torsional modes is discovered by varying the hinge linear stiffness. Single-mode resonance and 1:1 internal resonance under primary and order-1/3 subharmonic resonance excitations are analyzed to investigate the nonlinear oscillations and stability characteristics of the coupling modes. The averaged equations governing the steady-state responses are derived using the method of multiple scales. Resonance analysis demonstrates that although the vertical base excitation only weakly stimulates the torsional mode, its resonance peaks, response amplitudes, and bifurcation behaviors are significantly influenced by the plate-rigid bending mode through 1:1 internal resonance. The system exhibits pronounced bi-stability and tri-stability, with subharmonic resonance introducing additional bifurcation points, localized resonance peaks, and jump phenomena. Larger hinge cubic stiffness and excitation amplitude, along with lower damping, significantly enhance the multi-mode coupling and the subharmonic resonance, thereby expanding the multi-stable regions. The internal detuning parameter notably affects the position and amplitude of the primary resonance peak as well as the subharmonic resonance regions of the torsional mode, while having minimal effect on the bending mode. This study elucidates the nonlinear resonance mechanisms of the AMPS under multi-frequency excitation, providing valuable insights for optimizing structural parameters, avoiding detrimental resonances, and preventing dynamic instabilities.
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