连续梁在周期荷载下的动力稳定性简化分析方法

对于一般任意支撑的连续梁结构动力稳定性问题，已有的计算方法求解过程都很复杂，给工程设计带来极大的不便．本文提出了一个简化的分析方法，利用现有的商业软件，只需求得连续梁的自然频率及静力屈曲（失稳）荷载，就可容易得到结构的动力失稳区域，当考虑结构阻尼对不稳定区域的影响时，可将阻尼矩阵表达为Rayleigh阻尼的形式．研究结果表明：采用本文计算方法与已有的理论计算方法得到的连续梁主参数共振的不稳定边界非常吻合，而本文计算方法更为简单，计算结果可靠，计算精度高，可满足工程设计的需要．

Simplified Analysis Method for Dynamic Stability of Continuous Beams under Periodic Load

For the dynamic stability problem of a continuous beam with arbitrary supports, it is very complicated to solve these dynamic problems using the existing calculation methods, which brings great inconvenience to the engineering design. A simplified analysis method is proposed in this paper. By using the existing commercial software to obtain the natural frequency and static buckling (instability) load of the continuous beams, the dynamic instability regions of the continuous beams will be easily calculated. When the effect of structural damping on unstable domain is considered, the damping matrix can be expressed as a Rayleigh damping. The present investigation shows that the instability boundaries of principal parametric resonances by present calculation method agree well with those by existing theoretical methods. The proposed approach of this paper is simpler, with reliable results and high calculation precision. The present method can meet the needs of the engineering design.