随机相位简谐激励下稳态振动的合成响应

Synthetic Displacement of Steady-State Vibration under Random-Phase Harmonic Excitation

多层厂房中,厂房上部结构构件将直接承受转动机器产生的动力荷载.如何准确计算此类构件的位移响应被认为是多层厂房振动设计中亟待解决的关键性问题.借助概率论及振动学原理,经推导得到2个随机相位简谐振动合成振幅的分布函数的解析式及3个随机相位简谐振动合成振幅的分布函数的一元积分形式.对多个振动合成振幅分布特性的数值模拟结果进行分布拟合检验,结果证实,合成振幅的实际分布与正态分布之间存在显著差异.通过将振幅和随机相位进行分离并进行必要的线性变换,提出一种优于平方和开方法的合成振幅近似方法.借助位移互等定理,通过某多层织机厂房振动分析实例给出该方法在有限元建模计算中的应用步骤.

The superstructure members of multi-story factories directly sustain the dynamic loads of power machines. Accurate displacement calculation of such members is considered as a key problem that remains to be solved. Based on the theories of probability and vibration, the distribution function of synthetic displacement of two random-phase harmonic vibrations in the form of analytic expression, as well as the distribution function of three random-phase harmonic vibrations in the form of single variable integral was deduced. The distribution fitting tests of numerical simulation results show significant difference between the actual distribution of synthetic displacement and normal distribution. Moreover, with amplitude separated from random phase and linear transformation, a new approximation of synthetic displacement was established, which is superior to the square root sum of square method. On the basis of reciprocal-displacement theorem, an example of a multistory loom factory building was used to illustrate the approximation procedures in the finite element modeling and calculation.