A locally resonant meta-surface for preferential excitation of a guided mode in a hollow pipe can improve ultrasonic guided wave inspection of pipelines. The proposed meta-surface comprises a periodic arrangement of bonded prismatic rod-like resonators in the circumferential and axial directions of the pipe. We demonstrate the presence of bandgaps for the low-frequency axisymmetric longitudinal modes L(0,1) and L(0,2) and the torsional mode T(0,1). The generated bandgaps can be used to filter the higher harmonics associated with the system nonlinearity to improve nonlinear ultrasonic measurements on pipes. These bandgaps exist even for the non-axisymmetric flexural modes but with their hybridized dispersion curves exhibiting mode-coupling for higher circumferential orders. Moreover, a “partial” bandgap is obtained where preferential transmission of the L(0,2) mode over L(0,1) is possible. We discuss the potential advantages of this partial bandgap to improve pipeline inspections using the L(0,2) mode. Time-domain finite element analyses are used to validate the presence of these bandgaps under radial, circumferential, and axial excitation that mimics the excitation using a ring of piezoelectric transducers. Finally, we discuss the influence of resonator spacing, filling fraction, and the number of resonator rings on the bandgaps for an informed meta-surface design.
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This content will become publicly available on March 1, 2025
The Role of Frequency and Impedance Contrasts in Bandgap Closing and Formation Patterns of Axially-Vibrating Phononic Crystals
Bandgaps, or frequency ranges of forbidden wave propagation, are a hallmark of phononic crystals (PnCs). Unlike their lattice counterparts, PnCs taking the form of continuous structures exhibit an infinite number of bandgaps of varying location, bandwidth, and distribution along the frequency spectrum. While these bandgaps are commonly predicted from benchmark tools such as the Bloch-wave theory, the conditions that dictate the patterns associated with bandgap symmetry, attenuation, or even closing in multi-bandgap PnCs remain an enigma. In this work, we establish these patterns in one-dimensional rods undergoing longitudinal motion via a canonical transfer-matrix-based approach. In doing so, we connect the conditions governing bandgap formation and closing to their physical origins in the context of the Bragg condition (for infinite media) and natural resonances (for finite counterparts). The developed framework uniquely characterizes individual bandgaps within a larger dispersion spectrum regardless of their parity (i.e., odd versus even bandgaps) or location (low versus high-frequency), by exploiting dimensionless constants of the PnC unit cell which quantify the different contrasts between its constitutive layers. These developments are detailed for a bi-layered PnC and then generalized for a PnC of any number of layers by increasing the model complexity. We envision this mathematical development to be a future standard for the realization of hierarchically structured PnCs with prescribed and finely tailored bandgap profiles.
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- Award ID(s):
- 1847254
- NSF-PAR ID:
- 10473234
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- Journal of Applied Mechanics
- Volume:
- 91
- Issue:
- 3
- ISSN:
- 0021-8936
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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