Gg. Yaralioglu et A. Atalar, Noise analysis of geometrically complex mechanical structures using the analogy between electrical circuits and mechanical systems, REV SCI INS, 70(5), 1999, pp. 2379-2383
Random fluctuations of displacement or velocity in mechanical systems can b
e calculated by using the analogy between electrical circuits and mechanica
l systems. The fluctuation-dissipation theorem expresses the relation betwe
en the generalized mechanical admittance and the noise in velocity. Similar
ly, correlation of mechanical noise can be calculated by using the generali
zed Nyquist theorem which states that the current noise correlation between
two ports in an electrical circuit is dictated by the real part of the tra
nsadmittance. In this article, we will present the determination of the mec
hanical transadmittance and we will use the mechanical transadmittance to c
alculate the noise correlation on geometrically complex structures where it
is not possible to approximate the noise by using the simple harmonic osci
llator model. We will apply our method to atomic force microscope cantileve
rs by means of finite element method tools. The application of the noise co
rrelation calculation method to rectangular cantilever beams shows some int
eresting results. We found that on the resonance frequencies, the correlati
on coefficient takes values 1 (full correlation) and -1 (anti-correlation)
along the cantilever axis depending on the mode shapes of the structure. (C
) 1999 American Institute of Physics. [S0034-6748(99)04005-8].