失谐连续双跨梁结构振动特性的理论和实验研究

Theoretical and experimental studies on the vibration characteristics of disordered two-span beams

基于Euler-Bernoulli梁理论建立了双跨梁结构的动力学模型,采用模态分析方法求解动力学方程,根据边界条件获得双跨梁的频率方程,由此求解出双跨梁的固有频率,以此为基础进一步得到结构各点的时间响应历程曲线。针对双跨梁的两跨长度不等长造成的结构尺寸失谐,分析了不同跨长比对结构振动特性的影响,将理论计算结果与有限元仿真和实验结果进行比较,得到了较好的吻合。研究结果对于工程领域中失谐双跨梁结构的动力学分析和设计具有一定的参考价值。

Based on the Euler-Bernoullibeam theory,the dynamical model of the disordered two-span beam is established.The dynamical equation is solved by using the modal superposition method,and the frequency equation of the two-span beam is obtained according to the boundary conditions.From the frequency equation,the natural frequencies of the two-span beam are solved,and the time-history response curves of the two-span beam are further obtained.Considering the structural size disorder resulted from the two different span lengths of the two-span beam,we analyzed the influences of the different span length ratios on the vibration characteristics of the structure.By comparing the results from theoretical calculation with those from the commercial software Ansys and experiments,good agreement is obtained.The research results of this paper can be of great important on the dynamical analysis and design of disordered two-span beams in practical engineering fields.