Harmonic waves in one-, two- and three-dimensional composites: Bounds for eigenfrequencies

Harmonic waves in one-, two- and three-dimensional elastic composites with periodic structure are considered. Based on a new quotient recently proposed by Nemat-Nasser, lower and upper bounds for the eigenfrequencies are developed. For illustration waves propagating normal to the layers in layered composites, and normal to the fibers in fiber-reinforced composites, are considered. These examples show that the new quotient is very effective and yields very accurate results for the considered class of problems. While these results are of interest in their own right, they can be used to check the effectiveness of various approximate theories which recently have been proposed by various authors.