利用模态截断技术计算主次结构耦合系统的楼层反应谱

THE ANALYSIS OF FLOOR RESPONSE SPECTRUM IN EQUIPMENT-STRUCTURE INTERACTION FORM BY USING MODAL TRUNCATION TECHNIQUE

基于主结构固定基础模态的正交性,从主次结构各自的动力特性出发,利用模态截断技术直接推导出频率传递函数和次结构加速度均方根响应,并进一步得到楼层的加速度均方根反应谱。推导过程考虑了主次结构间调谐、耦合、非经典阻尼等因素的影响,避免了求解主次结构由于各自刚度和质量的巨大差异而导致的动力病态方程及主次结构由于阻尼不同而导致的复特征值解耦问题,成功实现了主次结构的实模态解耦分析。算例讨论了次结构固有频率和模态截断对其加速度功率谱密度函数和楼层加速度均方根反应谱的影响,结果表明,只需截取较低的几阶模态就能得到相当精确的反应谱值,从而大大减少了计算工作量。

The dynamic responses and their corresponding spectral responses of a combined system composed of a secondary equipment and a primary structure are investigated in frequency domain.This is based on the orthogonality condition of the fixed-base mode shapes of the structure.The transfer function and the response of rootmean-square acceleration of the equipment are derived directly from the dynamic properties of the structure and the equipment,considering the influencing factors such as tuning,interaction and non-classical damping.Furthermore,the floor response spectrum of root-mean-square acceleration is obtained subsequently.The analysis of uncoupling is successful while the complex eigenvalue problem and the ill-conditioned equation of motion are avoided.Numerical examples demonstrate the influence of the equipment natural frequency on the power spectral density function of acceleration,and the influence of both the equipment natural frequency and the modal truncation on the floor spectral response.And it is concluded that the responses estimation of good accuracy can be obtained only by a few modes of lower order.Therefore,the computer cost can be saved and the calculation efficiency is improved.