Small Vibrations of Nonlinear Dynamic Systems Containing Non-Rigid Bodies Excited by Stationary Stochastic Processes

From a vibrational point of view, real vehicles form dynamic systems containing non-rigid bodies and nonlinear two-force elements, often excited by stationary random processes. Their theoretical investigation in a broader frequency range is practically possible in the frequency domain only. In the treatment of nonlinearities second-order stochastical linearization methods can be used advantageously. The amount of necessary computations can be vastly reduced by using known receptance matrices of all bodies in the system in its equations of motion after Fourier transformation. The article describes the receptance properties of non-rigid bodies, their use for the determination of the dynamic system's transfer functions and the determination of the output processes' spectral density matrix under stationary random external excitation using stochastical second-order linearization of the nonlinearities.