# 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 non-classical 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 elasticity-based 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 non-classical 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. (SNL-NM), Albuquerque, NM (United States). Solid Mechanics Department

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1411617

- Report Number(s):
- SAND-2017-12947J

Journal ID: ISSN 0263-8223; PII: S0263822317318597

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Composite Structures

- Additional Journal Information:
- Journal Volume: 189; Journal ID: ISSN 0263-8223

- 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; Bernoulli-Euler 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.
```

```
@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 non-classical 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 elasticity-based 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 non-classical 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 = {Mon Nov 20 00:00:00 EST 2017},

month = {Mon Nov 20 00:00:00 EST 2017}

}