The modal density of anisotropic structural components

Abstract

The modal density of a structural component is a key parameter in high-frequency vibration prediction techniques such as statistical energy analysis (SEA). A study of the literature reveals that the standard method of computing the modal density of a two-dimensional component, such as a plate or shell, is restricted to orthotropic components. This method (which is usually referred to as Courant’s method) is extended here to a generally anisotropic component by considering initially the case of periodic (or Born–von Kármán) boundary conditions. It is then shown that the resulting modal density is independent of the nature of the actual boundary conditions which act on the component. On a related issue, doubts have been expressed in the literature as to whether the results yielded by Courant’s method are applicable to general boundary conditions if the component exhibits degeneracy of the dynamic edge effect; the present analysis demonstrates that the method is in fact valid in such cases. The developed technique is applied to the bending vibrations of an anisotropic plate, and good agreement is found with empirical results for the modal density derived from natural frequency computations.