## 留言板

 引用本文: 徐晓建, 邓子辰. 多层简化应变梯度Timoshenko梁的变分原理分析[J]. 应用数学和力学, 2016, 37(3): 235-244.
XU Xiao-jian, DENG Zi-chen. The Variational Principle for Multi-Layer Timoshenko Beam Systems Based on the Simplified[J]. Applied Mathematics and Mechanics, 2016, 37(3): 235-244. doi: 10.3879/j.issn.1000-0887.2016.03.002
 Citation: XU Xiao-jian, DENG Zi-chen. The Variational Principle for Multi-Layer Timoshenko Beam Systems Based on the Simplified[J]. Applied Mathematics and Mechanics, 2016, 37(3): 235-244.

## 多层简化应变梯度Timoshenko梁的变分原理分析

##### doi: 10.3879/j.issn.1000-0887.2016.03.002

###### 作者简介:徐晓建(1986—), 男，讲师, 博士(E-mail: xuxiaojian@mail.nwpu.edu.cn);邓子辰(1964—)，男，教授，博士,博士生导师(通讯作者. E-mail: dweifan@nwpu.edu.cn).
• 中图分类号: TB383; O342

## The Variational Principle for Multi-Layer Timoshenko Beam Systems Based on the Simplified

Funds: The National Natural Science Foundation of China(11372252;11502202)
• 摘要: 材料特征尺寸与其内禀尺寸相当时，材料表现出明显的尺寸效应.基于简化的应变梯度理论，通过半逆法，本文给出多层简化应变梯度Timoshenko梁的变分原理，通过最小总势能原理导出系统的边界条件并对其低阶和高阶边界条件进行讨论，随后给出简支梁系统屈曲载荷和振动频率的Rayleigh(瑞利)解.通过双层梁系统的振动分析算例得到内禀尺寸、长径比等因素对梁系统振动频率的影响.该文构造的Rayleigh解有望对其他数值方法，如有限元法、传递矩阵法等，提供一定的参考和对比.
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##### 出版历程
• 收稿日期:  2015-11-24
• 修回日期:  2015-12-29
• 刊出日期:  2016-03-15

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