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

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.