An energy measure for mode localization

Abstract

The vibration characteristics of periodic structures are highly sensitive to its mass distribution, stiffness distribution and geometrical properties. Parametric uncertainties in structures that arise due to material defects, structural damage or variations in material properties can break the symmetry of periodic structures. This often leads to mode localization, where the deformation in a mode is concentrated in a small region of the structure. Localization can be directly detected by visually inspecting animated mode shapes given by finite element software. Although a visual approach is physically intuitive, for complex geometries the identification of mode localization can be subjective and may not be obvious. Hence this paper presents a reliable method to measure the degree of mode localization based on the distribution of energy within the modes of the finite element model. The properties of this measure are demonstrated by examples. Such a measure will be of great value in optimization studies where it can be included directly in objective functions or constraints.