Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 51

When the input can only be defined by a cross spectral matrix [Sff], the same is true for the response Gm(ω).

(1.205)

with

and so

(1.206)

The system matrix H can be removed from the expected value operator

(1.207)

and finally

(1.208)

This expression determines the cross spectral response of a linear MIMO system excited by random load. Typical numerical system equations have millions of degrees of freedom. Therefore, in many cases the above equation cannot by used straightforwardly, because this would lead to triple multiplication of Hermitian-but-huge matrices. Thus, for random excitation we need different approaches for the response calculation. The conjugate version of Equation (1.208) is

(1.209)