We study the formation of frequency band gaps in single column woodpile phononic crystals composed of orthogonally stacked slender cylinders. We focus on investigating the effect of the cylinders local vibrations on the dispersion of elastic waves al
ong the stacking direction of the woodpile phononic crystals. We experimentally verify that their frequency band structures depend significantly on the bending resonant behavior of unit cells. We propose a simple theoretical model based on a discrete element method to associate the behavior of locally resonant cylindrical rods with the band gap formation mechanism in woodpile phononic crystals. The findings in this work imply that we can achieve versatile control of frequency band structures in phononic crystals by using woodpile architectures. The woodpile phononic crystals can form a new type of vibration filtering devices that offer an enhanced degree of freedom in manipulating stress wave propagation.
Osteoporosis is a well recognized problem affecting millions of individuals worldwide. Consequently, the need to effectively, efficiently, and affordably diagnose and identify those at risk is essential; moreover, site-specific assessment of bone qua
lity is necessary, not only in the process of risk assessment, but may also be desirable for other applications. The present study evaluated a new one-dimensional granular crystal sensor, composed of a tightly packed chain of beads under Hertzian contact interaction, representing the most suitable fundamental component for solitary wave generation and propagation. First, the sensitivity of the novel sensor was tested using densities of rigid polyurethane foam, representing clinical bone quality ranging from healthy, to severely osteoporotic. Once the relationship between the signal response and known densities was established, the sensor was used to measure several sites located in the proximal femur of ten human cadaveric specimens. The accuracy of the model was then further investigated, using measurements of bone quality from the same cadaveric specimens, independently, using DEXA. The results indicate not only that the novel technique is capable of detecting differences in bone quality, but that the ability to measure site-specific properties without exposure to radiation, has the potential to be further developed for clinical applications.
We study the interaction of highly nonlinear solitary waves in granular crystals, with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary and seconda
ry reflected waves. Experimental tests are performed to correlate the linear medium geometry, materials, and mass with the formation and propagation of the reflected waves. We compare the experimental results with theoretical analysis based on the long-wavelength approximation and with numerical predictions obtained from discrete particle models. Studying variations of the reflected waves velocity and amplitude, we describe how the propagation of primary and secondary reflected waves responds sensitively to the states of the adjacent linear media. Experimental results are found to be in agreement with the theoretical analysis and numerical simulation. This preliminary study establishes the foundation for utilizing reflected solitary waves as novel information carriers in nondestructive evaluation of elastic material systems.
