VerticalRandom Response Analysis ofLocomotives Based on AugmentedM atrix

Augmentedmass, damping, stiffnessmatrix ofsystem was setup to derive verticaldynamic differential equations for locomotive components and obtain output responses of suspensions. To avoid cross-spectrum density of each inputwhen calculating spectrum density of system outpu,t multi-input excitation in six wheelsetwere converted to single-input excitations by making use of the time-delay between the input excitations inwheelsets, making the system a linear system with single-input-multi- outpu.t Frequency response functions of the converted system were obtained according to superposition principle of linear systems and spectrum analysis of frequency responsematrix. The relations between spectrum densities ofsystem outputresponses and frequencywere obtained by assuming input functions to be ergodic and stable stochastic processes.