Noise analysis of geometrically complex mechanical structures using the analogy between electrical circuits and mechanical systems
Yaralioglu, G. G.
Review of Scientific Instruments
A I P Publishing LLC
2379 - 2383
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Random ﬂuctuations of displacement or velocity in mechanical systems can be calculated by using the analogy between electrical circuits and mechanical systems. The ﬂuctuation-dissipation theorem expresses the relation between the generalized mechanical admittance and the noise in velocity. Similarly, correlation of mechanical noise can be calculated by using the generalized Nyquist theorem which states that the current noise correlation between two ports in an electrical circuit is dictated by the real part of the transadmittance. In this article, we will present the determination of the mechanical transadmittance and we will use the mechanical transadmittance to calculate the noise correlation on geometrically complex structures where it is not possible to approximate the noise by using the simple harmonic oscillator model. We will apply our method to atomic force microscope cantilevers by means of ﬁnite element method tools. The application of the noise correlation calculation method to rectangular cantilever beams shows some interesting results. We found that on the resonance frequencies, the correlation coefﬁcient takes values 1 (full correlation) and 21 (anti-correlation) along the cantilever axis depending on the mode shapes of the structure.