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基于非均匀梁模型的二维柔性机翼固有振动分析

黄可 张家应 王青云

黄可, 张家应, 王青云. 基于非均匀梁模型的二维柔性机翼固有振动分析. 力学学报, 2023, 55(2): 1-10 doi: 10.6052/0459-1879-22-551
引用本文: 黄可, 张家应, 王青云. 基于非均匀梁模型的二维柔性机翼固有振动分析. 力学学报, 2023, 55(2): 1-10 doi: 10.6052/0459-1879-22-551
Huang Ke, Zhang Jiaying, Wang Qingyun. Natural vibration analysis of two-dimensional flexible wing based on non-uniform beam model. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 1-10 doi: 10.6052/0459-1879-22-551
Citation: Huang Ke, Zhang Jiaying, Wang Qingyun. Natural vibration analysis of two-dimensional flexible wing based on non-uniform beam model. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 1-10 doi: 10.6052/0459-1879-22-551

基于非均匀梁模型的二维柔性机翼固有振动分析

doi: 10.6052/0459-1879-22-551
基金项目: 国家自然科学基金(12102017)和机械结构力学及控制国家重点实验室开放课题(MCMS-E-0522G02)资助项目
详细信息
    通讯作者:

    张家应, 副教授, 主要研究方向为动力学与控制, 变体飞行器设计. Email: jiaying.zhang@buaa.edu.cn

  • 中图分类号: O327

NATURAL VIBRATION ANALYSIS OF TWO-DIMENSIONAL FLEXIBLE WING BASED ON NON-UNIFORM BEAM MODEL

  • 摘要: 变体飞行器通过光滑连续的结构变形改变气动特性, 从而提高飞行器的飞行性能, 具有很大的应用前景. 由于这类新概念飞行器主要通过改变自身结构形状以获得最佳工作性能的需求, 因此具有变形大、质量轻等特点, 较容易发生结构振动响应. 本文研究了一种以柔性变后缘作为变体形式的二维柔性机翼等效建模方法, 基于非均匀梁模型假设, 建立了该柔性翼的动力学模型. 通过利用Frobenius方法得到解析解及固有频率, 并用有限元方法进行对比验证, 发现前4阶固有频率的误差均在1%以内, 每阶固有频率对应的振型一致. 通过3D打印工程塑料ABS和硅胶蒙皮材料制备了柔性机翼结构件, 并通过动态测量法和拉伸试验分别测定了打印材料和硅胶蒙皮材料的杨氏模量, 搭建振动响应实验平台对制备的柔性机翼试验件进行振动试验. 对比发现模型振动试验获得的基频与理论模型结果一致, 并与有限元方法误差在3%以内. 本文通过理论分析和实验验证, 建立了二维柔性机翼等效建模方法, 研究结果将为柔性变后缘结构动力学特性分析及其控制应用方面提供理论支持.

     

  • 图  1  基于波纹板结构的变体翼尖[10]

    Figure  1.  Conceptual design of morphing wingtip and layout of corrugated panels[10]

    图  2  后缘偏心梁驱动的变弯度机翼[13]

    Figure  2.  The morphing trailing edge drived by eccentric beam[13]

    图  3  鱼骨柔性翼结构示意图[15]

    Figure  3.  The structural schematic diagram of FishBAC[15]

    图  4  鱼骨柔性翼的等效力学模型

    Figure  4.  Schematic diagram of FishBAC structural model

    图  5  等截面悬臂梁的前四阶模态

    Figure  5.  The first four modes of cantilever beam with equal section

    图  6  柔性段原模型的有限元模型

    Figure  6.  Finite element model of the flexible section

    图  7  两种级数解法的计算结果

    Figure  7.  The calculation results of two series solutions

    图  8  FishBAC柔性段的模态

    Figure  8.  The modes of the FishBAC flexible section

    图  9  级数解与刚度拟合的阶数对频率的影响

    Figure  9.  Effect of order of series solution and stiffness fitting polynomial on frequency

    9  级数解与刚度拟合的阶数对频率的影响(续)

    9.  Effect of order of series solution and stiffness fitting polynomial on frequency (continued)

    图  10  ABS塑料动态法测杨氏模量实验实物图

    Figure  10.  Dynamic measurement test of Young's modulus of ABS plastic

    图  11  硅胶单向拉伸实验实物图

    Figure  11.  Uniaxial tensile tests of silicone rubber

    图  12  硅胶单向拉伸实验应变-应力曲线

    Figure  12.  Strain-stress curve of silicone rubber in uniaxial tensile test

    图  13  动态法测FishBAC固有频率实验实物图

    Figure  13.  Dynamic measurement test of the natural frequency of FishBAC flexible section

    图  14  动态法测量FishBAC固有频率的实验结果

    Figure  14.  Dynamic measurement test results of the natural frequency of FishBAC

    表  1  鱼骨柔性翼段模型参数

    Table  1.   Model parameters of the FishBAC morphing concept

    ParametersValue
    baseline airfoilNACA0012
    chord c/mm305
    span b/mm150
    start of morph xS/mm107
    end of morph xE/mm260
    number of stringer pairs n14
    stringer thickness tst/mm0.8
    skin thickness tsk/mm1.5
    spine thickness tbs/mm2
    stringer modulus Est/GPa2.14
    spine modulus Ebs/GPa2.14
    spine Poisson's ratio νbs0.4
    spine density ρbs/(kg·m−3)1010
    skin modulus Esk/MPa4.56
    skin Poisson's ratio νsk0.4
    skin density ρsk/(kg·m−3)1010
    下载: 导出CSV

    表  2  验证算例参数

    Table  2.   Parameters of verification example

    ParametersValue
    length l/mm152.5
    density ρ/(kg·m−3)2700
    width b/mm1
    thickness t/mm2
    Poisson's ratio ν0.4
    modulus of elasticity E/GPa2.14
    下载: 导出CSV

    表  3  等截面悬臂梁的频率(Hz)

    Table  3.   Frequency of cantilever beam with equal section (Hz)

    MethodsVibration order
    1234
    Euler beam solution12.367977.5085217.025425.283
    Euler exact solution12.367877.3732217.022425.280
    shear beam series solution12.365677.4313216.513423.434
    FEM (NASTRAN)12.366577.4470216.619423.817
    下载: 导出CSV

    表  4  FishBAC柔性段的频率(Hz)

    Table  4.   Frequency of the FishBAC (Hz)

    MethodsVibration order
    1234
    FEM (shell)22.7621118.163292.228
    FEM (beam)24.4647136.962368.522709.733
    Euler beam series solution24.5482138.507373.935725.166
    shear beam series solution24.5339138.151371.708717.439
    下载: 导出CSV

    表  5  材料特性实验结果

    Table  5.   Experimental results of material properties

    ParametersValue
    modulus of elasticity (ABS plastics) E1/GPa1.823
    modulus of elasticity (silicone rubber) E2/MPa2.919
    下载: 导出CSV

    表  6  FishBAC柔性段的固有频率(Hz)

    Table  6.   The natural frequency of FishBAC (Hz)

    MethodsFrequency
    dynamic measurement test19.4521
    FEM (shell element)18.5898
    Euler beam series solution19.9821
    shear beam series solution19.9654
    下载: 导出CSV
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  • 收稿日期:  2022-11-21
  • 录用日期:  2023-01-07
  • 网络出版日期:  2023-01-09

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