| 对边简支负泊松比蜂窝夹层板的弯曲自由振动 |
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| 引用本文： | 邸馗,茅献彪.对边简支负泊松比蜂窝夹层板的弯曲自由振动[J].复合材料学报,2016,33(4):910-920. |
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| 作者姓名： | 邸馗 茅献彪 |
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| 作者单位： | 1.中国矿业大学 深部岩土力学与地下工程国家重点实验室, 徐州 221116; |
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| 基金项目： | 教育部博士点基金(20120095110013) |
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| 摘 要： | 负泊松比蜂窝夹层板作为一种特殊的复合材料结构,目前对其动态行为尚缺乏认识。应用Reddy剪切板理论分析了对边简支负泊松比蜂窝夹层板的弯曲振动。将内凹六边形胞元的蜂窝芯层等效为一正交异性层,芯层的等效弹性参数由修正后的Gibson公式得出。由具体算例可知经典叠层板理论和一阶剪切板理论不适合用于蜂窝夹层板的振动分析。应用Reddy剪切板理论研究了蜂窝夹层板板厚比、芯层板厚及胞元角度对弯曲振动频率的影响,并绘出相应的曲线图。结果表明:对于对边简支负泊松比蜂窝夹层板,当板厚比小于某一值时,固有频率参数随板厚比的增加而增加;但当板厚比大于该值时,固有频率参数随板厚比的增加呈现复杂的变化形式。本文得到的结果为蜂窝夹层板的设计和实际应用提供了理论依据和数值参考。
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| 关 键 词： | 负泊松比 蜂窝夹层板 固有频率 弯曲振动 Reddy剪切板理论 |
| 收稿时间： | 2015-05-25 |
Free flexural vibration of honeycomb sandwich plate with negative Poisson's ratio simply supported on opposite edges |
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| DI Kui;MAO Xianbiao.Free flexural vibration of honeycomb sandwich plate with negative Poisson's ratio simply supported on opposite edges[J].Acta Materiae Compositae Sinica,2016,33(4):910-920. |
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| Authors: | DI Kui;MAO Xianbiao |
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| Affiliation: | 1.State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221116, China;2.School of Mechanics and Civil Engineering, China University of Mining & Technology, Xuzhou 221116, China |
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| Abstract: | Honeycomb sandwich plate with negative Poisson's ratio is a special composite structure, whose dynamic behavior has not yet been studied. We applied Reddy's shear plate theory to do a free flexural vibration analysis of honeycomb sandwich plate with negative Poisson's ratio simply supported on opposite edges. Honeycomb core that consists of concave hexagon cellular element can be taken as an orthotropic layer. Equivalent elastic parameters of core were derived from the revised Gibson formula. From concrete example, we conclude that the classical sandwich plate theory and one order shear plate theory were not applicable to the vibration analysis of honeycomb sandwich plate. With Reddy's shear plate theory, we studied the influence of plate thickness of honeycomb sandwich plate, core plate, and angle of cellular element on flexural vibration frequency. Besides the above, a related curve chart was drawn. Results show that for honeycomb sandwich plate with negative Poisson's ratio simply supported on opposite edges, the natural frequency parameter increases with the ratio of plate thickness if ratio of plate thickness is less than a certain value. However, if the ratio of plate thickness was more than this value, the increase of natural frequency parameter behaves a complex variation with the increase of ratio of plate thickness. The conclusion derived from this paper provides a theoretical ground and numerical reference for the design and practical application of honeycomb sandwich plate. |
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| Keywords: | negative Poisson' s ratio honeycomb sandwich plate natural frequency flexural vibration Reddy's shear plate theory |
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