Study on the bending properties of composite sandwich sheets embedded with magnetorheological elastomer smart grids
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摘要:
对基于磁流变弹性体智能格栅单元的复材三明治板的弯曲特性进行了分析和实验研究。基于一阶剪切变形理论、能量法、最小势能原理、正交多项式法，建立了该三明治板的弯曲特性分析模型，在确定了总应变能的基础上，推导了结构的控制方程，并成功求解了悬臂边界下该三明治板在线分布载荷作用下的弹性弯曲变形。在分别完成上、下面板和磁流变弹性体格栅功能芯层的制备后，基于所建立的弯曲特性测试平台，对试件在不同磁感应强度和磁场控制区域作用下的弯曲变形进行了测试。验证结果表明：理论模型的最大计算误差不超过8.2%，处在误差允许的范围内，可有效预测结构的弯曲特性。研究发现随着内部磁场强度和磁场控制区域数量的增大，可提升结构的抗弯性能约15%～21%。
Abstract:The bending properties of composite sandwich sheets embedded with magnetorheological elastomer smart grid units were theoretically and experimentally investigated. A model was proposed to predict the bending characteristics of such sandwich sheets using the first-order shear deformation theory, energy technique, minimal potential energy principle, and the orthogonal polynomial methodology. After the total strain energy was obtained, the governing equation of the structure was deduced. As a result, the elastic bending deformation of such a sheet under the cantilever boundary subjected to the linearly distributed load can be successfully solved. When the preparation work of the upper and lower panels and the magnetorheological elastomer grid functional core was completed, the structural bending deformation was tested at different magnetic induction amplitudes and magnetic field control regions, based on an established test platform of such a specimen. The verification results showed that the maximum calculation error of the theoretical model did not exceed 8.2%, which was within an allowable error range. Hence, this model is trustworthy to predict the bending characteristics of such composite sandwich structures. It was also found that with the increase of the internal magnetic field amplitude and the number of magnetic field control regions, the structural bending resistance can be further improved by about 15%—21%.
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Key words:
- magnetorheological elastomer /
- smart grid /
- bending property /
- composite material /
- sandwich sheet
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图 1 CSS-MSGs结构弯曲特性分析模型
Figure 1. Analysis model of bending characteristics of CSS-MSGs structure
图 4 CSS-MSGs结构弯曲特性测试平台
Figure 4. Bending characteristic test platform of the CSS-MSGs structure
图 5 不同磁感应强度作用下多个测点的弯曲变形峰值计算与测试结果对比
Figure 5. Comparison of calculation and test results of the peaks of bending deformation with several measurement points and different magnetic field intensities
图 6 不同磁场控制区域作用下多个测点的弯曲变形峰值计算与测试结果对比
Figure 6. Comparison of calculation and test results of the peaks of bending deformation with several measurement points and different magnetic field control regions
表 1 理论分析时的材料与尺寸参数
Table 1. Material and dimensional parameters in theoretical analysis
类型 参数和数值 铜线圈层 $ {a_{\text{c}}}{\text{ = 80 mm}} $, $ {b_{\text{c}}}{\text{ = 80 mm}} $, $ {h_{\text{c}}}{\text{ = 2 mm}} $,
$ {E_{\text{c}}} = {\text{120}} \times {\text{1}}{{\text{0}}^{\text{3}}}{\text{ MPa}} $, $ {G_{\text{c}}} = {\text{3}} \times {\text{1}}{{\text{0}}^{\text{3}}}{\text{ MPa}} $,
$ {\upsilon _{\text{c}}} = {\text{0}}{\text{.25}} $, $ {\rho _{\text{c}}} = {{7\;800 \;{\mathrm{kg}}/}}{{\text{m}}^{\text{3}}} $肋条 $ {a_{{\text{gb}}}}{\text{ = 278 mm}} $, $ {b_{{\text{gb}}}}{\text{ = 13 mm}} $, $ {h_{{\text{gf}}}}{\text{ = 1 mm}} $
$ {E_{{\text{gb}}}} = {\text{110}} \times {10^2}{\text{ MPa}} $, $ {G_{{\text{gb}}}} = {\text{2}}{\text{.5}} \times {10^{\text{2}}}{\text{ MPa}} $
$ {\upsilon _{{\text{gb}}}} = {\text{0}}{\text{.4}} $, $ {\rho _{{\text{gb}}}} = {{2\;500\;{\mathrm{kg}}/}}{{\text{m}}^{\text{3}}} $MRE层 $ {a_{\text{v}}}{\text{ = 80 mm}} $, $ {b_{\text{v}}}{\text{ = 80 mm}} $, $ {h_{\text{v}}}{\text{ = 5 mm}} $,
$ {E_{\text{v}}} = {\text{1}}2{\text{ MPa}} $, $ {G_{\text{v}}} = 6{\text{ MPa}} $,
$ {\upsilon _{\text{v}}} = {\text{0}}{\text{.47}} $, $ {\rho _{\text{v}}} = {{4\;000 \;{\mathrm{kg}}/}}{{\text{m}}^{\text{3}}} $压电层 $ {a_{\text{p}}}{\text{ = 80 mm}} $,$ {b_{\text{p}}}{\text{ = 80 mm}} $,$ {h_{\text{p}}}{\text{ = 1 mm}} $,
$ {E_{\text{p}}} = {\text{76}} \times {\text{1}}{{\text{0}}^{\text{3}}}{\text{ MPa}} $,$ {G_{\text{p}}} = 4{\text{ MPa}} $,
$ {\upsilon _{\text{p}}} = 0.{\text{32}} $, $ {\rho _{\text{p}}} = {{3\;500 \;{\mathrm{kg}}/}}{{\text{m}}^{\text{3}}} $矩形格栅框 $ {a_{{\text{gf}}}}{\text{ = 84 mm}} $,$ {b_{{\text{gf}}}}{\text{ = 84 mm}} $,$ {h_{{\text{gf}}}}{\text{ = 9 mm}} $
$ {E_{{\text{gf}}}} = {\text{1}}{\text{.1}} \times {10^4}{\text{ MPa}} $,$ {G_{{\text{gf}}}} = {\text{2}}{\text{.5}} \times {10^{\text{2}}}{\text{ MPa}} $
$ {\upsilon _{{\text{gf}}}} = {\text{0}}{\text{.4}} $, $ {\rho _{{\text{gf}}}} = 2\;500{\text{ kg/}}{{\text{m}}^{\text{3}}} $碳纤维/
树脂面板层$ {a_{\text{f}}}{\text{ = 278 mm}} $, $ {b_{\text{f}}}{\text{ = 181 mm}} $, $ {h_{\text{f}}}{\text{ = 1}}{\text{.4 mm}} $,
$ {E_{{\text{f1}}}}{\text{ = 150}} \times {\text{1}}{{\text{0}}^{\text{3}}}{\text{ MPa}} $, $ {E_{{\text{f2}}}} = {\text{8}} \times {\text{1}}{{\text{0}}^{\text{3}}}{\text{ MPa}} $,
$ {G_{{\text{f}}12}} = {G_{{\text{f}}13}} = {G_{{\text{f23}}}} = {\text{4}} \times {\text{1}}{{\text{0}}^{\text{3}}}{\text{ MPa}} $,
$ {\upsilon _{\text{f}}} = {\text{0}}{\text{.3}} $, $ {\rho _{\text{f}}} = {{1\;618\; {\mathrm{kg}}/}}{{\text{m}}^{\text{3}}} $
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