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Based on a robust numerical method for calculation of band structure for  stress-waves in heterogeneous media, a layered composite was designed and  fabricated. It is shown that in the second pass band of this simple 2-phase  layered structure, the direction of the energy flow is opposite that of the  phase velocity. The ultrasonic stress-wave transmission through multiple  thicknesses of this structure was studied experimentally and various  quantities, such as band structure, phase velocity, group velocity, and a  representation of the velocity of energy propagation were measured and  compared with numerical predictions. The numerical calculations are based on  hybrid (mixed min-max) variational principles presented previously by  Nemat-Nasser and coworkers. In the cases where a closed form solution exists,  the numerical results of this method agree very accurately with the results  of the exact solution. Furthermore, the computational efficiency of the mixed  variational method renders it an excellent tool for design and analysis of  stress-wave propagation in heterogeneous media

Experimental verification of stress-wave bands and negative phase velocity in layered media