Nonlinear oscillations of a dual-joint system involving simultaneous 1:1 and 1:2 internal resonances

Bolted flange joints are typical connections form used in engineering structures. However, nonlinear factors such as discontinuity of the structure and mechanical contact of the connecting interface significantly affect and complicate the responses of the connection system. In this paper, the near-resonant response of a dual-joint system driven by harmonic excitation is investigated. Considering the effect of the nonlinear connection stiffness on the response of the dual-joint system, a lump mass model is established by transforming the contact nonlinearity into piecewise-smooth springs. The model captures the interaction of three modes (two bending modes and a longitudinal mode) with eigenfrequencies ω1, ω2, and ω3 such that 2ω1≈ω3 and ω2≈ω3, displaying 1:1, 1:2, and 1:2:2 internal resonances under specific excitation conditions. Harmonic Balance Method combined with Asymptotic Numerical Method (HBM–ANM method) is utilized to trace the branch of periodic solutions. Instability limits are derived numerically to show a more direct bifurcation scenario, determining the existence and stability of periodic solutions of the system. Four classes of periodic solutions are found for the longitudinal mode of the system driven at its resonance. In addition, three classes of periodic solutions are observed for the second-order bending mode driven at its resonance. Remarkable coupling oscillations are detected induced by the internal resonances such that ignoring internal resonances in the system will lead to notably different dynamic behavior and possibly misleading results.