VIBRATIONAL CHARACTERISTICS OF HONEYCOMB SANDWICH CANTILEVER PLATE WITH CURVED-WALL CORE
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摘要: 蜂窝结构作为一种多孔材料具有轻质、高强度、高刚度的优点, 兼具隔声降噪、隔热等优良性能, 被广泛应用于交通运输、航空航天等领域. 传统直壁蜂窝在受力后容易出现应力集中的问题, 这将导致蜂窝夹层产生裂纹破坏, 缩短夹层板的使用寿命. 针对此问题本文设计了一种以圆弧曲壁蜂窝作为芯层的蜂窝夹层板, 基于单位载荷法推导了蜂窝芯的等效参数, 建立曲壁蜂窝夹层板的动力学模型, 利用Chebyshev-Ritz方法求解悬臂边界下曲壁蜂窝夹层板的固有频率, 并用有限元方法进行对比验证, 发现前5阶固有频率的误差均在5%以内, 每阶固有频率对应的振型一致. 通过3D打印聚乳酸(PLA)制备了曲壁蜂窝夹层板, 使用万能试验机对PLA拉伸试件进行准静态拉伸测定了打印材料的杨氏模量, 搭建振动试验平台对制备的曲壁蜂窝夹层板进行正弦扫频试验、定频谐波驻留试验和冲击试验. 对比发现3D打印模型振动试验获得的前5阶固有频率与理论模型和有限元模型的计算结果三者一致, 试验发现曲壁蜂窝芯在特定频段内具有一定的抗冲击性能. 研究结果将为曲壁蜂窝在振动和隔振方面的应用提供理论支持.Abstract: As a kind of porous material, the honeycomb structure has the advantages of light weight, high strength, high stiffness, sound insulation, noise reduction, heat insulation and other excellent performance. Therefore, it is widely used in the field of transportation vehicles and aerospace etc. The traditional straight wall honeycomb is prone to stress concentration after loading, which will lead to crack failure and shorten the service life of the honeycombs. In order to solve this problem of honeycombs with straight walls, a honeycomb sandwich plate with circular arc core layer is designed in this paper. The equivalent parameters of honeycomb core are derived based on unit load method and the dynamic model of the curved-wall-core honeycomb sandwich plate is derived. The Chebyshev-Ritz method was used to solve the natural frequencies of honeycomb sandwich plate under cantilever boundaries, and the finite element method is used to compare. The errors of the first five natural frequencies are all within 5% from the two methods. The modes corresponding to each order of natural frequencies obtained from the finite element model are consistent with those obtained from the theoretical model. The curved honeycomb sandwich plate is prepared by 3D printing polylactic acid (PLA). The Young’s modulus of the printed PLA was measured by quasi-static tensile of the tensile specimen using a universal testing machine. The vibration test platform is built to do the sine sweep test, fixed frequency harmonic resides test and impact test. The comparison shows that the first five natural frequencies obtained from the vibration test of the 3D printing model verify the calculation results of the theoretical model and the finite element model. It is found that the curved-wall honeycomb core has a certain impact resistant performance in a specific frequency band. The obtained research results will provide theoretical support for the application of curved wall honeycombs in vibration and vibrational isolation.
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图 6 不同截断数下夹层板的第一阶固有频率
Figure 6. The first natural frequency of the sandwich plate with different truncation orders
图 11 蜂窝芯振动试验工况及测点位置
Figure 11. Conditions of honeycomb core vibration test and position of test points
图 12 曲壁蜂窝夹层板有限元模型
Figure 12. Finite element model of honeycomb sandwich plate with curved wall
图 15 曲壁蜂窝夹层板在定频驻波试验中的响应
Figure 15. Responses of honeycomb sandwich plate in constant frequencies standing wave test
图 16 曲壁蜂窝夹层板的前5阶固有频率
Figure 16. The first 5 order natural frequencies of curved- wall honeycomb sandwich plate
图 17 试验和有限元模型的扫频频响曲线对比
Figure 17. Comparison of sweep frequency curves between test and finite element model
图 18 曲壁蜂窝夹层板的前3阶振型对比
Figure 18. Comparison of the first three modes of honeycomb sandwich plate
图 20 夹层板在8g正弦波激励下的响应
Figure 20. Response of honeycomb sandwich plate excited by 8g sine wave
表 1 前5阶固有频率结果对比
Table 1. Comparison of the first 5 order natural frequencies results
Frequency/Hz Vibration order 1st 2nd 3rd 4th 5th Theory 35.81 135.93 218.60 229.05 426.38 FEM 36.13 129.24 215.82 238.53 406.53 error/% 0.89 4.93 1.04 4.14 4.65 Test 32.25 149 252.25 — 444.25 error/% 9.94 9.61 15.2 — 4.19 
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表 2 不同壁厚夹层板的固有频率
Table 2. Natural frequencies of sandwich plate with different wall thicknesses
Vibration order Thickness/mm 1.50 1.75 2.00 2.25 2.50 1st 36.759 36.371 35.812 34.684 33.548 2nd 141.789 138.584 135.934 133.138 131.985 3rd 222.159 219.070 218.607 215.359 207.203 4th 239.694 234.894 229.055 222.481 218.335 5th 446.995 435.837 426.387 419.884 412.145
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表 3 不同曲壁半径夹层板的固有频率
Table 3. Natural frequencies of sandwich plate with different curved radius
Vibration order Radius/mm 15.0 17.5 20.0 22.5 25.0 1st 33.984 34.370 35.812 36.188 36.593 2nd 132.039 134.094 135.934 137.163 138.517 3rd 213.256 214.318 218.607 219.249 220.964 4th 223.894 226.731 229.055 236.473 239.395 5th 415.498 421.252 426.387 431.476 435.495
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表 4 不同曲壁弧度夹层板的固有频率
Table 4. Natural frequencies of sandwich plate with different curvature radian
Vibration order Radian/(°) 30 45 60 75 90 1st 35.812 36.486 40.334 42.981 41.093 2nd 135.934 139.518 153.903 155.815 156.117 3rd 218.607 219.439 240.159 247.947 233.314 4th 229.055 233.445 248.511 253.024 240.821 5th 426.387 434.681 467.185 478.395 458.317
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