The out-of-plane dynamic stability of an arch under a vertical periodical base excitation is investigated by using both analytical and experimental methods. When the excitation frequency is near twice the out-of-plane natural frequency of the arch, an out-of-plane divergent vibration is induced, which will eventually leads to an out-of-plane dynamic parametric instability of the arch. Firstly, Hamiltonian principle is employed to derive the in-plane dynamic equations, and analytical solutions for the dynamic axial compressive force and bending moment in pre-stability state are obtained and verified by numerical simulations. Then the mode shape functions for the out-of-plane dynamic instability are analytically determined and the out-of-plane dynamic instability regions are obtained by Bolotin's method. Factors affecting the critical excitation frequencies of the out-of-plane dynamic instability regions, such as the arch's included angle, the slenderness ratio, and the logarithmic decrement, are thoroughly analyzed and verified via the method of multiple scales. Lastly, laboratory tests are carried out for the out-of-plane parametric resonance instability of fix-ended circular arches with various included angles and slenderness ratios. The critical excitation frequencies of dynamic instability regions of the tested arches are determined by increasing and decreasing the excitation frequency, and the experimental results agree with the theoretical counterparts very well. The main contributions of this work include: (1) obtaining an analytical solution of out-of-plane dynamic instability regions for the arch under a vertical harmonic base excitation; (2) applying a newly-designed experimental system to conduct the out-of-plane dynamic instability tests; (3) proposing a method of time domain analytical solution to determine the critical excitation frequencies of the out-of-plane dynamic instability region, and (4) discussing the dynamic instability mechanism for base-excited arches.

通过分析和实验方法研究了拱梁在垂直周期基础激励下的面外动态稳定性。当激励频率接近拱的平面外固有频率的两倍时，会引起平面外的发散振动，最终将导致拱的平面外动态参数不稳定性。首先，利用哈密顿原理推导了平面内的动力学方程，得到了在稳定前状态下的动态轴向压缩力和弯矩的解析解，并通过数值模拟对其进行了验证。然后，分析确定了平面外动态不稳定性的模形状函数，并通过Bolotin方法获得了平面外动态不稳定性区域。通过多尺度方法，彻底分析和验证了影响面外动态不稳定性区域的临界激励频率的因素，例如拱的夹角，细长比和对数递减。最后，针对具有各种夹角和细长比的固定端圆拱进行了平面外参数共振不稳定性的实验室测试。通过增加和减少激励频率来确定被测拱的动态失稳区域的临界激励频率，实验结果与理论对应非常吻合。这项工作的主要贡献包括：（1）获得在垂直谐波基础激励下拱的平面外动态失稳区域的解析解；（2）应用新设计的实验系统进行平面外动态不稳定性测试；（3）提出了一种时域解析解的方法来确定平面外动态失稳区域的临界激励频率，以及（4）讨论了基激励拱的动态失稳机制。