The Influence of Geometry on Linear Damping

Internal damping of vibration modes of bodies such as plates and shells generally depsnds on mode shape, boundary conditions and geometry. This dependence is explored systematically using linear continuum mechanics, exploiting the differences between different complex moduli which are frequently ignored, particularly in isotropic materials. Detailed results are given for isotropic plates, of constant and slightly varying thickness, under various boundary conditions. One prediction of the theory is tested experimentally, and good agreement is obtained. Effects of the kind described appear to be of great importance in the construction of musical instruments of the violin family, and they deserve attention in any situation where Q's of vibration modes are required to be accurately known.