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谐变力作用功能梯度旋转圆板强非线性主共振

王永刚 胡宇达 徐浩然

王永刚, 胡宇达, 徐浩然. 谐变力作用功能梯度旋转圆板强非线性主共振[J]. 工程力学, 2022, 39(11): 31-41. doi: 10.6052/j.issn.1000-4750.2021.07.0498
引用本文: 王永刚, 胡宇达, 徐浩然. 谐变力作用功能梯度旋转圆板强非线性主共振[J]. 工程力学, 2022, 39(11): 31-41. doi: 10.6052/j.issn.1000-4750.2021.07.0498
WANG Yong-gang, HU Yu-da, XU Hao-ran. STRONG NONLINEAR PRIMARY RESONANCE OF ROTATING FUNCTIONALLY GRADED CIRCULAR PLATES UNDER HARMONIC FORCE[J]. Engineering Mechanics, 2022, 39(11): 31-41. doi: 10.6052/j.issn.1000-4750.2021.07.0498
Citation: WANG Yong-gang, HU Yu-da, XU Hao-ran. STRONG NONLINEAR PRIMARY RESONANCE OF ROTATING FUNCTIONALLY GRADED CIRCULAR PLATES UNDER HARMONIC FORCE[J]. Engineering Mechanics, 2022, 39(11): 31-41. doi: 10.6052/j.issn.1000-4750.2021.07.0498

谐变力作用功能梯度旋转圆板强非线性主共振

doi: 10.6052/j.issn.1000-4750.2021.07.0498
基金项目: 国家自然科学基金项目(12172321, 11472239);河北省自然科学基金项目(A2020203007)
详细信息
    作者简介:

    王永刚(1991−),男,山西人,硕士生,主要从事非线性动力学研究(E-mail: wangyonggang57@163.com)

    徐浩然(1990−),男,河北人,博士生,主要从事非线性动力学研究(E-mail: 18830379208@163.com)

    通讯作者:

    胡宇达(1968−),男,黑龙江人,教授,博士,博导,主要从事非线性动力学、电磁弹性力学研究(E-mail: huyuda03@163.com)

  • 中图分类号: O322;TB33

STRONG NONLINEAR PRIMARY RESONANCE OF ROTATING FUNCTIONALLY GRADED CIRCULAR PLATES UNDER HARMONIC FORCE

  • 摘要: 功能梯度材料作为一种新型材料,具有良好的力学性能,近年来被广泛关注和应用。该文针对金属-陶瓷功能梯度圆板,考虑周边夹支边界约束条件,选取多项式形式的振型函数,利用伽辽金法,推得旋转运动状态和热效应作用下系统的纵横耦合非线性振动方程,求得由旋转及密度差引起的静挠度项。用改进多尺度法求解方程,得到强非线性系统的频幅响应方程和解析解。通过算例,给出功能梯度圆板的幅频曲线、幅值-激励力曲线、幅值-温度曲线,分析了不同物理量对结构共振幅值的影响规律,并且比较了解析解和数值解,两者结果较为吻合。
  • 图  1  FGM圆板模型

    Figure  1.  Mechanical model of a FGM circular plate

    2  幅值-调谐值特征曲线

    2.  Curves of amplitude-tuning value

    3  幅值-陶瓷侧温度特性曲线

    3.  Curves of amplitudes - ceramic side temperature

    4  幅值-激励力特性曲线

    4.  Curves of amplitudes-excitation force

    5  分岔点曲线图

    5.  Bifurcation points curves

    图  6  多值解对比图(Ω=2000 r/min)

    Figure  6.  Comparison of multivalued solutions (Ω=2000 r/min)

    图  7  本文解析解与文献数值解验证图

    Figure  7.  Verification diagram between analytical solution in this paper and numerical solution in the reference

    表  1  两种材料的温度相关系数

    Table  1.   The coefficients of two materials related to temperature

    相关系数材料$P_{-1} $$P_{0} $$P_{1} $$P_{2} $$P_{3} $
    弹性模量系数$ \mathrm{Si}_{3} \mathrm{~N}_{4}$$ 0$$348.43 \times 10^{9} $$-3.07 \times 10^{-4} $$2.16 \times 10^{-7} $$-8.95 \times 10^{-11} $
    $\text { SUS304 } $$ 0$$ 201.04 \times 10^{9}$$ 3.08 \times 10^{-4}$$-6.53 \times 10^{-7} $$ 0$
    热膨胀系数$ \mathrm{Si}_{3} \mathrm{~N}_{4}$$ 0$$ 5.87 \times 10^{-6}$$ 9.10 \times 10^{-4}$$ 0$$ 0$
    $\text { SUS304 } $$ 0$$ 12.33 \times 10^{-6}$$8.09 \times 10^{-4} $$ 0$$ 0$
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-07-02
  • 录用日期:  2022-02-28
  • 修回日期:  2021-12-24
  • 网络出版日期:  2022-02-28
  • 刊出日期:  2022-11-01

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