Auto-parametric resonance of a continuous-beam-bridge model under two-point periodic excitation: an experimental investigation and stability analysis

The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study. An auto-parametric resonance experiment of the test model is conducted to observe and measure the auto-parametric resonance of a continuous beam under a two-point excitation on columns. The parametric vibration equation is established for the test model using the finite-element method. The auto-parametric resonance stability of the structure is analyzed by using Newmark’s method and the energy-growth exponent method. The effects of the phase difference of the two-point excitation on the stability boundaries of auto-parametric resonance are studied for the test model. Compared with the experiment, the numerical instability predictions of auto-parametric resonance are consistent with the test phenomena, and the numerical stability boundaries of auto-parametric resonance agree with the experimental ones. For a continuous beam bridge, when the ratio of multipoint excitation frequency (applied to the columns) to natural frequency of the continuous girder is approximately equal to 2, the continuous beam may undergo a strong auto-parametric resonance. Combined with the present experiment and analysis, a hypothesis of Volgograd Bridge’s serpentine vibration is discussed.