Analytical and experimental studies on out-of-plane dynamic instability of shallow circular arch based on parametric resonance

作者：Liu, Airong; Lu, Hanwen; Fu, Jiyang^*; Pi, Yong-Lin; Huang, Youqin; Li, Jing; Ma, Yuwei

来源：Nonlinear Dynamics, 2017, 87(1): 677-694.

DOI：10.1007/s11071-016-3068-7

• Out-of-plane dynamic instability
• Parametric resonance
• Periodic concentrated load
• Shallow circular arch
• Vibration excitation tests

Little research about the out-of-plane dynamic stability of arches under in-plane loading has been reported in the literature hitherto. This paper presents analytical and experimental investigations of the out-of-plane dynamic instability of elastic shallow circular arches under an in-plane central concentrated periodic load owing to parametric resonance. Differential equations of out-of-plane motion of shallow arches are established using the Hamilton principle by accounting for the effects of geometric nonlinearity, additional concentrated weights and damping. The analytical solutions of the critical excitation frequencies of the concentrated periodic load for out-of-plane dynamic instability of arches are obtained. The corresponding experimental investigations are also carried out to verify the analytical solutions. Agreements between the analytical and experimental results are very good. In addition, the effects of the central concentrated weight and the in-plane excitation amplitude on out-of-plane dynamic instability of arches are investigated. It is found that as the weight increases, the bandwidth of the critical in-plane excitation frequencies for out-of-plane dynamic instability of the arch decreases. It is also found that the bandwidth of critical frequencies increases with an increase in the excitation amplitude. Furthermore, the nonlinear inertial force is derived, which is essential in determining the out-of-plane parametric resonance. It is shown that the curve of the excitation frequency versus amplitude of out-of-plane vibration bends toward the low-frequency region and that the "traction" out-of-plane instability may occur owing to "amplitude" perturbation. To authors' knowledge, the analytical solutions and experimental investigations for out-of-plane dynamic instability of arches owing to parametric resonance presented in the paper are first time reported in the literature. The new findings in the paper can provide an in-depth understanding of out-of-plane dynamic instability behavior of arches under a periodic load.

• 出版日期2017-1
• 单位广州大学