Geo-Congress 2020
Flexural Wave Attenuation in a Multi-Frequency Locally Resonant Phononic Crystals Beam Resting on Elastic Foundations
Publication: Geo-Congress 2020: Geotechnical Earthquake Engineering and Special Topics (GSP 318)
ABSTRACT
Phononic crystals (PCs) beam has band gaps’ characterization and the potential to inhibit flexural wave vibrations, and it can be used for vibration isolation in beam-foundation systems. To realize the broadband gaps, a multi-frequency locally resonant (LR) PCs model, in which two types of spring-oscillator are periodically attached to an Euler beam, is introduced into the beam-foundation systems. Based on the motion equations of flexural wave in beam, the complex band structures of beam-foundation systems are derived by transfer matrix method (TMM) and Bloch’s theorem. The derivation is verified by the frequency response function (FRF) of the system, which is conducted with finite element method (FEM). Then, the band gap characteristics in the beam-foundation systems are investigated theoretically. Furthermore, the effects of oscillator and foundation parameters on the band gaps are analyzed in detail. Results indicate that multi-band gaps exist in the novel LR PCs beam-foundation system and the multi-frequency LR PCs beam can effectively enlarge the range of flexural band gaps.
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ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China (grant numbers 51578147, 51278099). The authors thank the valuable comments from the reviewers.
REFERENCES
Gao, M., and Shi, Z.F. (2019) “A wave guided barrier to isolate antiplane elastic waves.” J. Sound. Vib., 443, 155-166.
Han, L., Zhang, Y., Li, X.M., Jiang, L.H., and Chen, D. (2015) “Flexural vibration reduction of hinged periodic beam-foundation systems.” Soil. Dyn. Earthq. Eng., 79, 1-4.
Kushwaha, M.S., Halevi, P., and Dobrzynski, L. (1993) “Acoustic band structure of periodic elastic composites.” Phys. Rev. Lett., 1993(71), 2022-2025.
Liu, X.N., Shi, Z.F., Mo, Y.L. (2016) “Effect of initial stress on periodic Timoshenko beams resting on an elastic foundation.” J. Vib. Control, 23(18), 3041-3054.
Liu, Z.Y., Zhang, X.X., Mao, Y.W., Zhu, Y.Y., Yang, Z.Y., Chan, C.T., and Sheng, P. (2000) “Locally resonant sonic materials.” Science, 289(5485), 1734-1736.
Liu, Z.Y., Chan, C.T., Sheng, P., Goertzen, A.L., and Page, J.H. (2000) “Elastic wave scattering by periodic structures of spherical objects: Theory and experiment.” Phys. Rev. B, 62(4), 2446-2457.
Mead, D.J. (1970) “Free Wave Propagation in Periodically Supported, Infinite Beams.” J. Sound. Vib., 11(2), 181-197.
Mead, D.J. (1986) “A New Method of Analyzing Wave Propagation in Periodic Structures: Applications to Periodic Timoshenko Beams and Stiffened Plates.” J. Sound. Vib., 104(1), 9-27.
Pu, X.B., and Shi, Z.F. (2018) “Surface-wave attenuation by periodic pile barriers in layered soils.” Constr. Build. Mater., 180, 177-187.
Sato, M., Kanie, S., and Mikami, T. (2007) “Structural modeling of beams on elastic foundations with elasticity couplings.” Mech. Res. Commun., 34(5-6), 451-459.
Shi, Z.F., Cheng, Z.B., and Xiang, H.J. (2014) “Seismic isolation foundations with effective attenuation zones.” Soil. Dyn. Earthq. Eng., 57, 143-151.
Sigalas, M.M., and Economou, E.N. (1992) “Elastic and acousticwave band structure.” J. Sound. Vib., 1992(158), 377-382.
Xiang, H.J., and Shi, Z.F. (2011) “Vibration attenuation in periodic composite Timoshenko beams on Pasternak foundation.” Struct. Eng. Mech., 40(3), 373-392.
Xiao, Y., Wen, J.H., Yu, D.L. and Wen, X.S. (2013) “Flexural wave propagation in beams with periodically attached vibration absorbers: Band-gap behavior and band formation mechanisms.” J. Sound. Vib., 332(4), 867-893.
Yu, D.L., Wen, J.H., Shen, H.J., Xiao, Y., and Wen, X.S. (2012) “Propagation of flexural wave in periodic beam on elastic foundations.” Phys. Lett. A, 376(4), 626-630.
Zhang, Y., Ni, Z.Q., Jiang, L.H., Han, L., and Kang, X.W. (2015) “Study of the bending vibration characteristic of phononic crystals beam-foundation structures by Timoshenko beam theory.” Int. J. Mod. Phys. B, 29(20), 1550136.
Information & Authors
Information
Published In
Geo-Congress 2020: Geotechnical Earthquake Engineering and Special Topics (GSP 318)
Pages: 60 - 68
Editors: James P. Hambleton, Ph.D., Northwestern University, Roman Makhnenko, Ph.D., University of Illinois at Urbana-Champaign, and Aaron S. Budge, Ph.D., Minnesota State University, Mankato
ISBN (Online): 978-0-7844-8281-0
Copyright
© 2020 American Society of Civil Engineers.
History
Published online: Feb 21, 2020
Published in print: Feb 21, 2020
ASCE Technical Topics:
- Beams
- Continuum mechanics
- Dynamics (solid mechanics)
- Elastic analysis
- Elastic foundations
- Engineering fundamentals
- Engineering mechanics
- Finite element method
- Flexural strength
- Fluid mechanics
- Foundations
- Geotechnical engineering
- Hydrologic engineering
- Material mechanics
- Material properties
- Materials engineering
- Methodology (by type)
- Motion (dynamics)
- Numerical methods
- Oscillations
- Resonance
- Solid mechanics
- Strength of materials
- Structural analysis
- Structural engineering
- Structural members
- Structural systems
- Water and water resources
- Wave attenuation
- Waves (fluid mechanics)
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