Journal of Sound and Vibration vol:332 issue:26 pages:7205-7225
An alternative to numerical quadrature is proposed to compute the power in-
jected into a vibrating structure over a certain frequency band. Instead of evalu-
ating the system response at several sampling frequencies within the considered
band, the integral is computed by estimating the residue at a few complex fre-
quencies, corresponding to the poles of the weighting function. This technique
provides considerable benefits in terms of computation time, since the integra-
tion is independent of the width of the frequency band.
Two application examples show the effectiveness of the approach. Firstly, the
use of a Butterworth filter instead of a rectangular weighting function is assessed.
Secondly, the accuracy of the approximation in case of hysteretic damping is
proven. Finally, the computational performance of the technique is compared
with classical numerical quadrature schemes.