Noise analysis of geometrically complex mechanical structures using the analogy between electrical circuits and mechanical systems

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].