The stochastic response of a linear system through equivalent deterministic forces

The response of a stochastic system in a discrete coordinate set, as in the finite element approach, can be associated to a high computational cost even when using a full modal representation. A stochastic representation of the load is needed when, for instance, the case of wall pressure fluctuations induced by turbulent boundary layer (TBL) is considered. A linear 1D system, under the stochastic dynamic load simulating TBL excitation, has been studied here aiming at enhancing a numerical procedure that, under some approximations, allows a reduction of the computational cost. The proposed numerical procedure is founded on the pseudo-excitation method (PEM) that can be considered an exact representation since it is based on a modal decomposition of the cross-spectral density matrix of the excitation. Although effective for some applications, PEM requires the extraction of the eigensolutions of the load matrix at each frequency step. To overcome this computational bottleneck, a new method called frequency Modulated Pseudo Equivalent Deterministic Excitation (PEDEM), is here proposed. The method introduces some equivalent deterministic forces on the basis of the analysis of the eigensolutions of the dynamic load matrix for increasing excitation frequency. Specifically, it is possible to identify different regions for the response defined by introducing a suitable dimensionless excitation frequency. Characteristic values for region bounds and the structural response are in this work investigated and compared with a reference solution obtained with the full stochastic response. Even if the method is here applied over a simple chain of rods, the results seem to be very promising for future applications to more realistic problems.