Band Gaps for Elastic Wave Propagation in a Periodic Composite Beam Structure Incorporating Microstructure and Surface Energy Effects
Abstract
Here, a new model for determining band gaps for elastic wave propagation in a periodic composite beam structure is developed using a nonclassical Bernoulli–Euler beam model that incorporates the microstructure, surface energy and rotational inertia effects. The Bloch theorem and transfer matrix method for periodic structures are employed in the formulation. The new model reduces to the classical elasticitybased model when both the microstructure and surface energy effects are not considered. The band gaps predicted by the new model depend on the microstructure and surface elasticity of each constituent material, the unit cell size, the rotational inertia, and the volume fraction. To quantitatively illustrate the effects of these factors, a parametric study is conducted. The numerical results reveal that the band gap predicted by the current nonclassical model is always larger than that predicted by the classical model when the beam thickness is very small, but the difference is diminishing as the thickness becomes large. Also, it is found that the first frequency for producing the band gap and the band gap size decrease with the increase of the unit cell length according to both the current and classical models. In addition, it is observed that the effect of themore »
 Authors:

 Southern Methodist University, Dallas, TX (United States). Department of Mechanical Engineering
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States). Solid Mechanics Department
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1411617
 Report Number(s):
 SAND201712947J
Journal ID: ISSN 02638223; PII: S0263822317318597
 Grant/Contract Number:
 AC0494AL85000
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Composite Structures
 Additional Journal Information:
 Journal Volume: 189; Journal ID: ISSN 02638223
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; Band gaps; Wave propagation; Couple stress; Surface elasticity; Rotational inertia; Bloch theorem; Transfer matrix method; BernoulliEuler beam; Size effect
Citation Formats
Zhang, G. Y., Gao, X. L., Bishop, J. E., and Fang, H. E. Band Gaps for Elastic Wave Propagation in a Periodic Composite Beam Structure Incorporating Microstructure and Surface Energy Effects. United States: N. p., 2017.
Web. doi:10.1016/j.compstruct.2017.11.040.
Zhang, G. Y., Gao, X. L., Bishop, J. E., & Fang, H. E. Band Gaps for Elastic Wave Propagation in a Periodic Composite Beam Structure Incorporating Microstructure and Surface Energy Effects. United States. doi:10.1016/j.compstruct.2017.11.040.
Zhang, G. Y., Gao, X. L., Bishop, J. E., and Fang, H. E. Mon .
"Band Gaps for Elastic Wave Propagation in a Periodic Composite Beam Structure Incorporating Microstructure and Surface Energy Effects". United States. doi:10.1016/j.compstruct.2017.11.040. https://www.osti.gov/servlets/purl/1411617.
@article{osti_1411617,
title = {Band Gaps for Elastic Wave Propagation in a Periodic Composite Beam Structure Incorporating Microstructure and Surface Energy Effects},
author = {Zhang, G. Y. and Gao, X. L. and Bishop, J. E. and Fang, H. E.},
abstractNote = {Here, a new model for determining band gaps for elastic wave propagation in a periodic composite beam structure is developed using a nonclassical Bernoulli–Euler beam model that incorporates the microstructure, surface energy and rotational inertia effects. The Bloch theorem and transfer matrix method for periodic structures are employed in the formulation. The new model reduces to the classical elasticitybased model when both the microstructure and surface energy effects are not considered. The band gaps predicted by the new model depend on the microstructure and surface elasticity of each constituent material, the unit cell size, the rotational inertia, and the volume fraction. To quantitatively illustrate the effects of these factors, a parametric study is conducted. The numerical results reveal that the band gap predicted by the current nonclassical model is always larger than that predicted by the classical model when the beam thickness is very small, but the difference is diminishing as the thickness becomes large. Also, it is found that the first frequency for producing the band gap and the band gap size decrease with the increase of the unit cell length according to both the current and classical models. In addition, it is observed that the effect of the rotational inertia is larger when the exciting frequency is higher and the unit cell length is smaller. Furthermore, it is seen that the volume fraction has a significant effect on the band gap size, and large band gaps can be obtained by tailoring the volume fraction and material parameters.},
doi = {10.1016/j.compstruct.2017.11.040},
journal = {Composite Structures},
number = ,
volume = 189,
place = {United States},
year = {2017},
month = {11}
}
Web of Science