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考虑记忆效应及尺寸效应窄长薄板的磁-热弹性耦合动态响应

马永斌 李东升

马永斌,李东升. 考虑记忆效应及尺寸效应窄长薄板的磁-热弹性耦合动态响应 [J]. 应用数学和力学,2022,43(8):888-900 doi: 10.21656/1000-0887.420200
引用本文: 马永斌,李东升. 考虑记忆效应及尺寸效应窄长薄板的磁-热弹性耦合动态响应 [J]. 应用数学和力学,2022,43(8):888-900 doi: 10.21656/1000-0887.420200
MA Yongbin, LI Dongsheng. Magneto-Thermoelastic Coupling Dynamic Responses of Narrow Long Thin Plates Under Memory Effects and Size Effects[J]. Applied Mathematics and Mechanics, 2022, 43(8): 888-900. doi: 10.21656/1000-0887.420200
Citation: MA Yongbin, LI Dongsheng. Magneto-Thermoelastic Coupling Dynamic Responses of Narrow Long Thin Plates Under Memory Effects and Size Effects[J]. Applied Mathematics and Mechanics, 2022, 43(8): 888-900. doi: 10.21656/1000-0887.420200

考虑记忆效应及尺寸效应窄长薄板的磁-热弹性耦合动态响应

doi: 10.21656/1000-0887.420200
基金项目: 国家自然科学基金(12062011;11972176)
详细信息
    作者简介:

    马永斌(1974—),男,副教授,博士,硕士生导师(通讯作者.  E-mail:1373794737@qq.com

  • 中图分类号: O343

Magneto-Thermoelastic Coupling Dynamic Responses of Narrow Long Thin Plates Under Memory Effects and Size Effects

  • 摘要:

    引入记忆依赖微分的双相滞后热弹性理论能较完善地描述非Fourier导热现象,然而迄今尚未发现该理论综合考虑微尺度效应和磁、热、弹等多场耦合效应对材料力学行为的影响。通过考虑记忆依赖效应和非局部效应修正了双相滞后广义热弹性理论,基于改进后的理论研究了受周期性变化热源作用时窄长薄板的磁-热弹性耦合问题。首先建立问题的控制方程;然后结合边界条件与初值条件,利用Laplace变换和反变换技术对该问题进行求解;最后分别考察了磁场、相位滞后、时间延迟因子、核函数、非局部效应、时间对各无量纲量的影响,为微尺度材料的动态响应提供了有力参考依据。

  • 图  1  板受磁场和热作用示意图

    Figure  1.  A plate in a magnetic field under thermal shock

    图  2  磁场取不同值时温度θ的变化情况

    Figure  2.  The variation of temperature θ for different values of the magnetic field

    图  4  磁场取不同值时应力σ的变化情况

    Figure  4.  The variation of stress σ for different values of the magnetic field

    图  3  磁场取不同值时位移u的变化情况

    Figure  3.  The variation of displacement u for different values of the magnetic field

    图  5  核函数取不同形式时温度θ的变化情况

    Figure  5.  The variation of temperature θ for different forms of the kernal function

    图  6  核函数取不同形式时位移u的变化情况

    Figure  6.  The variation of displacement u for different forms of the kernal function

    图  7  核函数取不同形式时应力σ的变化情况

    Figure  7.  The variation of stress σ for different forms of the kernal function

    图  8  $ {\tau _q} $$ {\tau _\theta } $$ \omega $取不同值时温度θ的变化情况

    Figure  8.  The variation of temperature θ for different values of $ {\tau _q} $, $ {\tau _\theta } $ and $ \omega $

    图  9  $ {\tau _q} $$ {\tau _\theta } $$ \omega $取不同值时位移u的变化情况

    Figure  9.  The variation of displacement u for different values of $ {\tau _q} $, $ {\tau _\theta } $ and $ \omega $

    图  10  $ {\tau _q} $$ {\tau _\theta } $$ \omega $取不同值时应力σ的变化情况

    Figure  10.  The variation of stress σ for different values of $ {\tau _q} $, $ {\tau _\theta } $ and $ \omega $

    图  11  $ {e_0}a $取不同值时温度θ的变化情况

    Figure  11.  The variation of temperature θ for different values of $ {e_0}a $

    图  12  $ {e_0}a $取不同值时位移u的变化情况

    Figure  12.  The variation of displacement u for different values of $ {e_0}a $

    图  13  $ {e_0}a $取不同值时应力σ的变化情况

    Figure  13.  The variation of stress σ for different values of $ {e_0}a $

    图  14  t取不同值时温度θ的变化情况

    Figure  14.  The variation of temperature θ for different values of t

    图  16  t取不同值时应力σ的变化情况

    Figure  16.  The variation of stress σ for different values of t

    图  15  t取不同值时位移u的变化情况

    Figure  15.  The variation of displacement u for different values of t

    图  17  P取不同值时应力σ的变化情况

    Figure  17.  The variation of stress σ for different values of P

    图  18  M取不同值时应力σ的变化情况

    Figure  18.  The variation of stress σ for different values of M

    表  1  相关参数

    Table  1.   Related parameters

    parametervalue
    thermal conductivity K/(N·K−1·s−1) 386
    specific heat at constant strain $ {C_E} $/($ {m^2} $/K) 383.1
    Lamé constant $ \mu $/(N/m2) 3.86 × 1010
    Lamé constant $ \lambda $/(N/m2) 7.76 × 1010
    density $ \rho $/(kg/m3) 8 954
    magnetic permeability in vacuum $ {\mu _0} $/( N·s2/C2) 1.256 × 10-6
    electric permittivity in vacuum $ {\varepsilon _0} $/( C2·N−1·m−2) 10−9/(36π)
    reference temperature $ {T_0} $/K 293
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出版历程
  • 收稿日期:  2021-07-13
  • 修回日期:  2022-07-15
  • 网络出版日期:  2022-07-06
  • 刊出日期:  2022-08-01

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