Root Mean Square Response of Transducer Systems to Spectral Density Inputs

Complex engineering systems are often subjected to significant vibration noise. In this analysis, we investigate the general problem of the response of linear transducers to vibration noise inputs which can be characterized by power spectral density functions whose profiles can be partitioned into discrete frequency intervals.

A generalized mathematical development is presented for evaluating the subsequent RMS (root-mean-square) response of the system to a known input noise-vibration power spectral density function. We specifically consider examples of two transducer systems which can be characterized by a linear system transfer function. One is that of an accelerometer and the other is that of a linear differential transformer core rod.