Structural random vibration analysis by using recursive formulas

This paper discusses the application of β-recursive formula to structural random vibration analysis. This recursive formula is able to calculate the accurate stationary mean and mean square responses of a linear or equivalent linearized nonlinear structure subjected to stationary excitations. To enhance the computational efficiency, the basic formulae for calculating structural mean and mean square responses which are obtained from β-recursive formula are transformed into other forms which directly use the band-shape and symmetric structural dynamic characteristic matrices in calculation. The detailed formulations are given according to different excitation environments, such as white noise excitations, time-domain correlated white noise excitations, independent filtered white noise excitations and spatially correlated filtered white noise excitations. Some numerical examples are given to show the applications of the recursive formula.