Laser vibrometry for measurement of nonlinear distortions in the vibration of weakly nonlinear slowly time-varying systems

Abstract

Recently, a new signal analysis method was developed to detect small non-linear distortions in weakly non-linear systems using specially designed broadband excitation signals, i.e. odd random phase multisines. The method allows the detection and quantification of the system response, noise level and both odd and even degree nonlinear distortions over an extensive frequency range from one single short-term measurement. Here, this method is implemented in an opto-acoustical set-up to detect small non-linearities in the response of vibrating structures. Because of the highly linear response achievable with heterodyne vibrometry, it is possible to detect non-linearities in the system under test with extremely high sensitivity. Non-linear behaviour is very common in biomechanical systems, but their dynamics and thus response might change over time. This leads to measurement artifacts that cause an overestimation of the noise level. A correction algorithm can be applied to remove the effect of these time variations, so that heterodyne vibrometry also allows the detection and quantification of non-linearities in unstable biomechanical systems. In this paper the technique is demonstrated with a measurement of the non-linear distortions in the vibration of the gerbil middle ear, where the use of a non-contact optical detection method is essential to not disturb the tiny vibrating structures.