### 摘要

The theory of flexural waves in an elastic beam with periodic structure is developed in terms of Floquet waves. Special relationships have been determined among the fundamental solutions of the governing equation. Two lemmas about the properties of the fundamental solutions are proved. With the help of these relations and lemmas, the analysis and classification of the dynamic nature of the problem is greatly simplified. We show that the flexural wave propagation in a periodic beam can be interpreted as the superposition of two pairs of waves propagating in opposite directions, of which one pair behaves as an attenuated wave. The dispersion spectrum of the second pair of waves shows the band structure, consisting of stopping bands and passing bands. Exploiting the symmetry of the structure, the dispersion equation at the end points of Brillouin zones is uncoupled into two simpler equations. These uncoupled equations represent the dispersion spectrum of waves which are either symmetric, or antisymmetric.

原文 | English |
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頁（從 - 到） | S189-S196 |

期刊 | Journal of Applied Mechanics, Transactions ASME |

卷 | 59 |

發行號 | 2 |

DOIs | |

出版狀態 | Published - 1992 一月 1 |

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

## 指紋 深入研究「Flexural wave propagation in an elastic beam with periodic structure」主題。共同形成了獨特的指紋。

## 引用此

*Journal of Applied Mechanics, Transactions ASME*,

*59*(2), S189-S196. https://doi.org/10.1115/1.2899487