One-dimensional experimental verification of weak-form homogenization theory for heterogenous systems

Abstract

Metamaterials are synthetic composite materials that exhibit specific effective properties for long-wavelength stimuli. Modeling of these materials often relies upon homogenization methods to replace inhomogeneous systems with more simple to analyze homogenous systems. In this work, wediscuss a one-dimensional experimental verification of a weak-form homogenization method based on Hamilton’s principle for mechanical media. In the experiment, a heterogeneous structure is fabricated out of wood and placed within a four inch diameter section of PVC pipe. This heterogeneous structure is designed such that it restricts the cross-sectional area at regular intervals, yielding alternating sections of restriction/no-restrictionalong the pipe length. The source is a compression driver outputting weakly non-linear sinusoidal waveforms, located at one end of the PVC pipe, while the other end of the pipe is terminated with anechoic foam to negate end reflections. Data are gathered through implementation of the two-microphone method at multiple locations along the pipe length, which enables isolation of the forward traveling wave. Verification of the homogenization theory in the one-dimensional case is discussed, as well as the ability for the heterogeneous structure to reduce the shock formation distance.