利用模态截断技术分析多点连接主次结构耦合系统的地震反应

Seismic Analysis of the Primary-secondary Coupling Structural System with Multi-connections by Using Modal Truncation Technique

建立了多点连接主次结构耦合系统的数学模型,并利用模态截断技术求出各自的模态响应传递函数和位移响应,以主次结构系统的位移功率谱密度函数在整个频率域内的积分得到位移响应的均方根值并与精确解进行比较.算例表明,即使在只取主次结构前几阶模态的情况下,该方法仍具有很高的精度;将次结构视为MTMD(复合调频质量阻尼器)系统来控制主结构的位移均方响应,分析了主次结构的质量比、次结构的刚度质量比和模态阻尼比等因素对控制效果的影响,算例表明,次结构的刚度质量比是影响控制效果的关键因素.

The mathematical model of the primary-secondary coupling structural system with multi-connections is proposed. By using modal truncation technique, the frequency-domain modal transfer function and displacement response of the primary and secondary structures are obtained respectively. The root mean square of displacement responses are calculated by integrating the power spectral density functions in frequency domain. The results of an numerical example show that the accuracy of the approach is pretty good with comparison to the precise results, even only the first few modes of the two structural systems have been used. Meanwhile, the secondary structural system may be used as an MTMD system （Multiple Tuned Mass Damper） to control the root mean square of displacement responses of the primary structural system. And the control effectiveness are also discussed, including the mass ratio of the primary and secondary structural systems, the stiffness-mass ratio of the secondary structural system and the mode damping ratio. Numerical example shows that the stiffness-mass ratio of the secondary structural system is the key factor that affects the control effectiveness.