基于分数阶模型的牡蛎壳动力学特性研究

袁良柱 陆建华 苗春贺 王鹏飞 徐松林

袁良柱, 陆建华, 苗春贺, 王鹏飞, 徐松林. 基于分数阶模型的牡蛎壳动力学特性研究[J]. 爆炸与冲击, 2023, 43(1): 011101. doi: 10.11883/bzycj-2022-0318
引用本文: 袁良柱, 陆建华, 苗春贺, 王鹏飞, 徐松林. 基于分数阶模型的牡蛎壳动力学特性研究[J]. 爆炸与冲击, 2023, 43(1): 011101. doi: 10.11883/bzycj-2022-0318
YUAN Liangzhu, LU Jianhua, MIAO Chunhe, WANG Pengfei, XU Songlin. Dynamic properties of oyster shells based on a fractional-order model[J]. Explosion And Shock Waves, 2023, 43(1): 011101. doi: 10.11883/bzycj-2022-0318
Citation: YUAN Liangzhu, LU Jianhua, MIAO Chunhe, WANG Pengfei, XU Songlin. Dynamic properties of oyster shells based on a fractional-order model[J]. Explosion And Shock Waves, 2023, 43(1): 011101. doi: 10.11883/bzycj-2022-0318

基于分数阶模型的牡蛎壳动力学特性研究

doi: 10.11883/bzycj-2022-0318
基金项目: 国家自然科学基金(11672286, 11872361);中央高校基本科研业务费专项资金(WK2480000008);中石油与中科院重大战略合作项目(2015A-4812);高压物理与地震科技联合实验室室开放基金(2019HPPES01)
详细信息
    作者简介:

    袁良柱(1998- ),男,博士研究生,ylzustcedu@mail.ustc.edu.cn

    通讯作者:

    徐松林(1971- ),男,博士,研究员,博士生导师,slxu99@ustc.edu.cn

  • 中图分类号: O347

Dynamic properties of oyster shells based on a fractional-order model

  • 摘要: 贝壳、牡蛎等天然材料因其轻质高强的力学特性在材料设计等领域受到了广泛的关注,但由于材料本身结构的复杂性,对其力学行为的研究十分困难。近年来,分数阶模型在研究材料的力学特性上取得了成功,相比传统模型,分数阶模型可以更好地表征复杂介质的应力或应变与时间的关系。因此,本文从波传播理论出发,以分数阶模型作为材料本构,得到了复杂介质的波传播控制方程。通过Laplace变换得到了控制方程的解析解,并通过Laplace数值逆变换分析了波的衰减对分数阶模型中参量的敏感性,讨论了不同于材料弹性、黏性的材料“惯性”特性。接着,基于解析解和多种实验测试信号,给出了得到分数阶模型参数的拟合式子。以牡蛎材料作为研究对象,利用CO2脉冲激光器进行小试样的冲击加载、应用两点激光干涉测速系统(laser interferometer velocimetry system, VISAR)对表面粒子的速度进行测量,得到了4种密度下不同厚度的牡蛎壳试样的粒子速度时程曲线,再结合上述理论方法分析得到了牡蛎壳试样的Abel模型和分数阶Maxwell模型的参数,模型参数反映了牡蛎壳试样的细微观结构特征。结果发现:牡蛎壳试样的密度越大,即在细微观上具有砖泥结构的珍珠层的占比越高,速度衰减越大,试样的黏性越大;这是由于CO2激光脉冲器发射的激光波长与牡蛎壳试样珍珠层的砖泥结构间的缝隙尺寸相近,使得激光在冲击牡蛎壳试样中的珍珠层时发生较大的散射。
  • 图  1  牡蛎壳材料、圆形实验试样、试样纵剖面电镜照片与局部放大

    Figure  1.  Oyster shell material, circular sample, longitudinal section electron microscopy (SEM) and local magnification

    图  2  CO2脉冲加载与激光干涉测速系统(VISAR)

    Figure  2.  CO2 pulse loading and laser interferometer velocimetry system (VISAR)

    图  3  几种分数阶本构模型

    Figure  3.  Several fractional differential constitutive models

    图  4  单个半脉宽正弦函数

    Figure  4.  Single half pulse width sine function

    图  5  正弦波在Abel黏壶模型介质的衰减

    Figure  5.  Attenuation of a single half pulse width sine wave in Abel model media

    图  6  α分别为1.0和2.0时的波传播特性

    Figure  6.  The property of wave propagation when the order α is 1.0 and 2.0 , respectively

    图  7  参数αηE对幅值衰减的影响

    Figure  7.  Influence of parameters α, η and E on amplitude attenuation

    图  8  各个密度下不同厚度牡蛎试样的速度信号及拟合曲线

    Figure  8.  Velocity signals and fitting curves of oyster samples with different thicknesses and densities

    图  9  牡蛎试样分数阶模型的拟合曲线及参数与牡蛎试样密度的关系

    Figure  9.  The fitting curve of the fractional model of the oyster sample and relationship between parameters and oyster sample density

    表  1  牡蛎壳试样分数阶模型的拟合参数

    Table  1.   Fitting parameters of the fractional model of the oyster sample

    材料本构密度/(g·cm−3)αE/GPaη/(Pa·sα)
    Abel模型0.50.631-9.09×104
    0.70.811-5.65×103
    0.71.025-192.12
    1.21.181-17.84
    1.41.297-2.19
    分数阶Maxwell模型0.50.690 2.216.71×104
    0.70.851 7.343.55×103
    0.70.8977.671.45×103
    1.21.03312.88170.01
    1.41.22415.406.76
    下载: 导出CSV

    表  2  固定分数阶阶数情况下,牡蛎壳试样分数阶Maxwell模型的拟合参数

    Table  2.   Fitting parameters of fractional Maxwell model for oyster shell samples in the case of fixed fractional order

    材料本构密度/(g·cm−3)αE/GPaη/(Pa·sα)
    分数阶Maxwell模型0.50.942.441518.00
    0.77.67929.35
    0.77.82751.88
    1.213.15687.85
    1.416.46471.30
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-07-21
  • 修回日期:  2022-10-11
  • 网络出版日期:  2022-11-21
  • 刊出日期:  2023-01-05

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