Geometric Dispersion of Acoustic Waves by a Fibrous Composite

Abstract

This study was initiated to examine the transmission of acoustic waves through a fibrous composite whose only dispersive mechanism was geometric. The elastic-elastic composite chosen for study was composed of tungsten wires embedded in an aluminum matrix. This unidirectional com posite was manufactured in two constituent ratios, 2.2 and 22.1 percent by volume of tungsten. The dispersive characteristics of these composites were determined for harmonic waves propagating normal to the axes of the fibers by using standard water-bath techniques with wide-band transducers. The dispersion data obtained demonstrate that fibrous composites be have as wave filters which selectively transmit or reflect periodic waves. Further, this wave filtering is shown to be a boundary layer phenomenon which can and must be eliminated from dispersion data if it is to be meaningful.

A Mixture Model for Unidirectionally Fiber-Reinforced Composites

“…An example of these phenomena for dynamic environments is wave dispersion, and understanding of which is important both from the standpoints of direct response prediction and indirect analyses associated with such topics as nondestructive testing. For fibrous composites, wave dispersion has been amply demonstrated via ultrasonic techniques by such investigators as Tauchert and Guzelse (1972), and Sutherland and Lingle (1972).…”

“…To facilitate this task, the asymptotic procedure with multiple scales noted previously is combined with a variational technique (Murakami, 1985). Following development of the basic equations, the dispersion of time-harmonic waves is studied and the results are compared with experimental data for boron/epoxy (Tauchert and Guzelse, 1972) and tungusten/aluminum (Sutherland and Lingle, 1972) composites. The good correlation obtained with experimental data indicates that the proposed mixture model furnishes a basic tool by which -Qdynamic responses of elastic composites can be investigated.…”

Classical vibrational modes in phononic lattices: theory and experiment

“…Pass and stop bands were found in 1D layered composites consisting of steel and copper foils [177]; in 2D fibrous composites made up of tungsten wires in aluminum [178], boron fibers in epoxy [179] or piezoelectric PZT rods in different polymers [94]; in 3D composites consisting of glass spheres (1 mm diameter, cubic array with period 2.54 mm) in epoxy and steel balls (0.55 mm diameter, tetragonal array with unit cell 1.32 Â 1.32 Â 2.63 mm 3 ) acrylic glass [180]. The application of these composites as wave filters was already proposed by Sutherland and Lingle [178]. Kinra and Ker [180] point out that "an important property of the periodic heterogenous materials is the phenomenon of pass bands and stop bands".…”

“…Strong geometric dispersion effects were found in one-dimensional (1D) layered composites consisting of periodically arranged boron fibers and carbon cloth for ultrasound waves propagating parallel to the laminates [176]. Pass and stop bands were found in 1D layered composites consisting of steel and copper foils [177]; in 2D fibrous composites made up of tungsten wires in aluminum [178], boron fibers in epoxy [179] or piezoelectric PZT rods in different polymers [94]; in 3D composites consisting of glass spheres (1 mm diameter, cubic array with period 2.54 mm) in epoxy and steel balls (0.55 mm diameter, tetragonal array with unit cell 1.32 Â 1.32 Â 2.63 mm 3 ) acrylic glass [180]. The application of these composites as wave filters was already proposed by Sutherland and Lingle [178].…”

Waves in periodic dissipative laminate metamaterial generated by plate impact

“…The acoustic behavior of laminate materials exhibits dispersive properties induced by their periodic structure [1][2][3]. The formation of a steady shock wave can take much longer time than in homogeneous materials.…”