低速冲击下负泊松比蝴蝶形蜂窝夹芯板的动力响应

Dynamic response of a sandwich panel cored by butterfly-shaped honeycombs with negative Poisson’s ratio to low-velocity impact

为了研究负泊松比蝴蝶形蜂窝夹芯板在低速冲击下的动力学响应,采用质量-弹簧模型获得了冲击器与蜂窝夹芯板之间的接触力,同时基于哈密顿原理和一阶剪切变形理论推导了负泊松比蝴蝶形蜂窝夹芯板的运动方程,采用Navier法和Duhamel积分对蜂窝板的振动位移进行了理论解析求解。在理论验证方面,蜂窝夹芯板前5阶固有频率的数值模拟结果与理论模型计算结果的最大相对误差为6.52%,蜂窝夹芯板中心最大横向位移的数值模拟结果与理论模型计算结果的最大相对误差为6.84%,理论模型求解的接触力与文献得到的接触力的最大相对误差为8%,验证了理论模型的有效性。结果表明,随着球形冲击器冲击速度的递增,蜂窝夹芯板的最大横向位移呈现递增的规律。而在相同冲击载荷下,蜂窝夹芯板的抗冲击特性随着胞元壁厚的增大而增强,随着胞元角度的增大而减弱;随着负泊松比蝴蝶形蜂窝夹芯板长宽比以及夹芯层与顶部蒙皮层的高度比的增大,蜂窝夹芯板的横向位移减小,冲击器与蜂窝夹芯板之间的接触力增大。当蜂窝夹芯板的宽长比从1∶1变化到1∶2时,蜂窝夹芯板最大横向位移减小6.1%;当顶部蒙皮层与蜂窝芯层的高度比从1∶6变化到1∶14时,蜂窝夹芯板的最大横向位移减小5.4%,这表明蜂窝夹芯板的抗冲击性能增强,吸能效果明显。

In order to study the dynamic response of a sandwich panel cored by butterfly-shaped honeycomb with negative Poisson’s ratio to low-velocity impact,a mass-spring(MS)model is applied to obtain the contact force between the spherical impactor and the honeycomb sandwich panel.Meanwhile,based on the Hamilton’s principle and the first-order shear deformation theory,the equation of motion for the butterfly-shaped honeycomb sandwich panel with negative Poisson’s ratio is derived.Besides,the Navier method and Duhamel’s integral are used to solve the vibration displacement of the honeycomb sandwich panel.To validate the theoretical model,the results are compared with the results of ABAQUS’numerical simulation or published literature.It is shown that the maximum relative error between the numerical modeling results of the first five order natural frequencies and the results of theoretical model calculated in this paper is 6.52%,the maximum relative error between the numerical modeling results of the honeycomb sandwich panel under low-velocity impact and the calculated results of the theoretical model in this paper is 6.84%,and the maximum relative error of the contact force between the theoretical model in this paper and the published studies is 8%,thus verifying the validity of the theoretical model.The results show that the maximum lateral displacement of the honeycomb sandwich panel increases with the increasing velocity of the spherical impactor.Under the same impact load,the impact resistance of the honeycomb sandwich panel increases with the increase of the wall thickness of the unit cell,and decreases with the increase of the unit cell angle.The impact resistance of the honeycomb sandwich panel increases by 3.7%when the thickness of the unit cell wall changes from 1 mm to 3 mm.The lateral displacement of the butterfly-shaped honeycomb sandwich panel decreases while the contact force between the impactor and the honeycomb sandwich panel increases with the increase of the length-width ratio and the height ratio.When the width-length ratio of the honeycomb sandwich panel changes from 1∶1 to 1∶2,the maximum lateral displacement of the honeycomb sandwich panel decreases by 6.1%,and when the height ratio of the top skin layer to the honeycomb core layer changes from 1∶6 to 1∶14,the maximum lateral displacement of the honeycomb sandwich panel decreases by 5.4%,which indicates that the impact resistance of the honeycomb sandwich panel is enhanced and the energy absorption effect is obvious.