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板中热弹波传播: 一种改进的勒让德多项式方法

王现辉 李方琳 刘宇建 陈会涛 禹建功

王现辉, 李方琳, 刘宇建, 陈会涛, 禹建功. 板中热弹波传播: 一种改进的勒让德多项式方法[J]. 力学学报, 2020, 52(5): 1277-1285. doi: 10.6052/0459-1879-20-124
引用本文: 王现辉, 李方琳, 刘宇建, 陈会涛, 禹建功. 板中热弹波传播: 一种改进的勒让德多项式方法[J]. 力学学报, 2020, 52(5): 1277-1285. doi: 10.6052/0459-1879-20-124
Wang Xianhui, Li Fanglin, Liu Yujian, Chen Huitao, Yu Jiangong. THERMOELASTIC WAVE PROPAGATION IN PLATES: AN IMPROVED LEGENDRE POLYNOMIAL APPROACH[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1277-1285. doi: 10.6052/0459-1879-20-124
Citation: Wang Xianhui, Li Fanglin, Liu Yujian, Chen Huitao, Yu Jiangong. THERMOELASTIC WAVE PROPAGATION IN PLATES: AN IMPROVED LEGENDRE POLYNOMIAL APPROACH[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1277-1285. doi: 10.6052/0459-1879-20-124

板中热弹波传播: 一种改进的勒让德多项式方法

doi: 10.6052/0459-1879-20-124
基金项目: 1)国家自然科学基金(U1804134);国家自然科学基金(51975189);河南省科技计划(192102210189);河南省科技计划(182102210314);河南省科技计划(182102310793)
详细信息
    通讯作者:

    禹建功

  • 中图分类号: O347.4

THERMOELASTIC WAVE PROPAGATION IN PLATES: AN IMPROVED LEGENDRE POLYNOMIAL APPROACH

  • 摘要: 近年来, 超声导波因其衰减小, 传播距离远和信号覆盖范围广, 成为无损检测领域快速发展的方向之一. 然而, 基于超声导波的高温在线检测和激光超声技术却发展缓慢, 其关键在于热弹耦合波动方程求解难度大、传播与衰减特性研究困难. 作为一种有效的求解方法, 勒让德正交多项式方法已广泛应用于导波传播问题, 但该方法在求解热弹导波传播时存在两个不足, 限制其进一步的发展和应用. 这两个缺陷是: (1)求解过程中大量积分的存在, 致使计算效率低下; (2)仅能处理等热边界条件的热弹导波传播. 针对两项不足之处, 提出一种改进的勒让德正交多项式方法, 以求解分数阶热弹板中的导波传播. 推导求解方法中积分的解析表达式, 以提高计算效率; 引入温度梯度展开式, 发展适合勒让德多项式级数的绝热边界条件处理方法. 与已有文献结果对比表明改进方法的正确性; 与已有方法的计算时间对比说明改进方法的高效性. 最后将改进的方法用于求解分数阶热弹板中的导波传播, 研究分数阶次对频散、衰减曲线和应力、位移、温度分布等的影响.

     

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出版历程
  • 收稿日期:  2020-01-17
  • 刊出日期:  2020-10-10

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