Mechanical and optical investigation of dynamic behavior of violins at modal frequencies.

Two main aims of our investigation are to show differences in natural vibrations between two violins that differ in the thickness of the back plate and to determine whether they are linear systems. Two experiments were performed on the top and back plates. The first experiment was a mechanical modal analysis in a version with a fixed response point. In the second experiment optical measurements of the plate's velocities in modal frequencies obtained from the first experiment were performed by use of laser Doppler vibrometry. The second experiment was a simplified modal analysis experiment with a fixed excitation point. Changes in the thickness of the back plate caused changes in certain modal frequencies of both plates. However, no important differences in mode shapes were found in both experiments. Thus, violins can be treated as linear systems but with great care.