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含电学边界的压电层合梁的非线性弯曲波

赵希宁 杨晓东 张伟

赵希宁, 杨晓东, 张伟. 含电学边界的压电层合梁的非线性弯曲波[J]. 力学学报, 2021, 53(4): 1124-1137. doi: 10.6052/0459-1879-20-409
引用本文: 赵希宁, 杨晓东, 张伟. 含电学边界的压电层合梁的非线性弯曲波[J]. 力学学报, 2021, 53(4): 1124-1137. doi: 10.6052/0459-1879-20-409
Zhao Xining, Yang Xiaodong, Zhang Wei. NONLIEAR BENDING WAVES OF A PIEZOELECTRIC LAMINATED BEAM WITH ELECTRICAL BOUNDARY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1124-1137. doi: 10.6052/0459-1879-20-409
Citation: Zhao Xining, Yang Xiaodong, Zhang Wei. NONLIEAR BENDING WAVES OF A PIEZOELECTRIC LAMINATED BEAM WITH ELECTRICAL BOUNDARY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1124-1137. doi: 10.6052/0459-1879-20-409

含电学边界的压电层合梁的非线性弯曲波

doi: 10.6052/0459-1879-20-409
基金项目: 1)国家自然科学基金(11972050);国家自然科学基金(11672007)
详细信息
    作者简介:

    2)杨晓东, 教授, 主要研究方向: 非线性动力学. E-mail: jxdyang@163.com

    通讯作者:

    杨晓东

  • 中图分类号: O326

NONLIEAR BENDING WAVES OF A PIEZOELECTRIC LAMINATED BEAM WITH ELECTRICAL BOUNDARY

  • 摘要: 非线性科学己成为近代科学发展的一个重要标志, 特别是非线性动力学和非线性波的研究对于解决自然科学各领域中遇到的复杂现象和问题有着极其重要的意义. 本文研究了含电学边界条件的压电层合梁的非线性弯曲波传播特性.首先, 考虑几何非线性效应和压电耦合效应, 利用哈密顿原理建立了一维无限长矩形压电层合梁弯曲波的非线性方程.其次, 采用Jacobi椭圆函数展开法对非线性弯曲波方程进行求解, 得到了非线性弯曲波动方程在近似情况下对应的冲击波解和孤波解.最后, 利用约化摄动法得到了非线性薛定谔方程, 进一步得到了亮孤子和暗孤子解.基于两种方法具体研究了外加电压、压电层厚度等参数对冲击波和孤立波以及亮孤子和暗孤子特性的影响. 研究结果表明, 在波速较小时, 外加电压对冲击波的影响较大, 波速较大时, 外加电压对孤立波影响减弱.通过调整作用在压电层合梁上的电压发现了存在亮孤子和暗孤子, 分析结果表明随着外加电压值的增大, 亮孤子和暗孤子的振幅都增大.

     

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出版历程
  • 收稿日期:  2020-12-01
  • 刊出日期:  2021-04-10

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