FULL STOCHASTIC RESPONSE, PSEUDO EXCITATION METHOD AND PSEUDO EQUIVALENT DETERMINISTIC EXCITATION: TWO SIMPLE SYSTEMS

The computational costs associated to the analysis of a stochastic response of a linear system can become unacceptable high, even using a full modal representation. Here, a new approach is proposed by invoking a pseudo equivalent deterministic excitation (PEDE). This is based on the given spectral load representation. The load used in a deterministic loop is derived from the column of the spectral load matrix. The method allows a good representation without using the eigenvalues and eigenvectors of the spectral load matrix; in fact the pseudo excitation method, (PEM), is just based on these, and the PEM is an exact representation being based on the modal decomposition of the spectral excitation. The two methods, PEM and PEDE, are then compared with a full stochastic response for two simple systems: a chain of five oscillators (mass and stiffness) and a plate. Both the system are considered excited by a spectral load representing the classical form due to Corcos for the wall pressure distribution due to a turbulent boundary layer: a random and convective excitation. A dimensionless representation of the frequency axis is also used; on this scale, the results demonstrated that in the first frequency ranges the PEDE is a very useful approximation.