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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。
Based on the orthogonality of the fixed basic modal of the main structure, based on the dynamic characteristics of the primary and secondary structures, the modal truncation technique is used to directly derive the root mean square root mean square response of the frequency transfer function and the substructure acceleration, and further obtain the mean square acceleration of the floor Root response spectrum. The derivation process takes into account the effects of tuning, coupling and non-classical damping among the primary and secondary structures, and avoids the dynamic pathological equations and primary and secondary structures due to the different damping due to the huge differences in their stiffness and mass. Complex eigenvalue decoupling problem, the successful realization of the primary and secondary structure real mode decoupling analysis. An example is given to discuss the effect of sub-structure natural frequency and modal truncation on its RMS power spectral density function and floor acceleration rms spectrum. The results show that only a few lower modes can be intercepted to obtain a fairly accurate response Spectral values, thus greatly reducing the computational workload.