  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.
