Estimations of non-linearities in structural vibrations of string musical instruments

TL;DR

This paper introduces a signal-model approach using cascade of Hammerstein models to estimate weak non-linearities in the vibrations of string instrument structures, offering an alternative to direct measurement.

Contribution

It presents a novel method for characterizing non-linearities in string instruments through a cascade of Hammerstein models, enabling estimation from acoustic excitation measurements.

Findings

Non-linearities vary across different string instruments.

The method effectively separates linear and non-linear contributions.

Experimental results on piano, guitars, and violin demonstrate the approach's applicability.

Abstract

Under the excitation of strings, the wooden structure of string instruments is generally assumed to undergo linear vibrations. As an alternative to the direct measurement of the distortion rate at several vibration levels and frequencies, we characterise weak non-linearities by a signal-model approach based on cascade of Hammerstein models. In this approach, in a chain of two non-linear systems, two measurements are sufficient to estimate the non-linear contribution of the second (sub-)system which cannot be directly linearly driven, as a function of the exciting frequency. The experiment consists in exciting the instrument acoustically. The linear and non-linear contributions to the response of (a) the loudspeaker coupled to the room, (b) the instrument can be separated. Some methodological issues will be discussed. Findings pertaining to several instruments - one piano, two guitars, one violin - will be presented.