ACOUSTICAL AND OPTICAL BRANCHES OF WAVE PROPAGATION IN AN EPOXY MATRIX CONTAINING A RANDOM DISTRIBUTION OF LEAD INCLUSIONS.
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Lead/epoxy random particulate composites were studied. The phase velocity of longitudinal waves, less than C//1 greater than , was measured as a function of the frequency, OMEGA equals k//1a, and the volume faction of inclusions, similar C. Here, a is the radius of the spherical inclusions and k//1 equals 2 pi / lambda //1 is the wavenumber in the neat matrix. Contrary to the predictions of the majority of the existing analyses the wave propagation was found to be highly dispersive, particularly when OMEGA equals 0(1). The principal objective of this work is to demonstrate the existence of a new branch of wave propagation, the so-called optical branch. It is shown that at low frequencies the wave propagation occurs along the slower, classical acoustical branch; here the inclusions move in phase with the matrix. At high frequencies a new, faster optical branch is excited where the inclusions move out of phase with the excitation. The two branches are separated by a well-defined cut-off frequency. OMEGA //C, which corresponds to the rigid-body-translational resonance of the inclusions. Across OMEGA //C the phase velocity takes a large positive jump with OMEGA , the highest jump recorded was about 75%. At very high frequencies the wavespeed appears to reach a frequency-independent optical limit.
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