In this paper, an investigation on the low-velocity impact (LVI) response of a shear deformable beam laminated by carbon nanotube reinforced composite (CNTRC) layers is performed. The composite beam is “auxetic” due to the negative out-of-plane Poisson’s ratio (NPR) through special symmetric stacking sequences of layers that are designed based on the Classical Laminate Theory. To study the effect of the out-of-plane NPR on the LVI response of the composite beam, a newly defined Hertz model is developed. The motion equations of Kármán type for the CNTRC laminate beam are derived in the framework of the Reddy beam theory and solved by means of a two-step perturbation approach while the dynamic equation of the impactor is built on Newton’s Law. Since temperature-dependent material properties of both carbon nanotube (CNT) and matrix are employed, the thermal influence on the LVI behavior is also investigated. Moreover, a piece-wise method is employed herein to investigate the effect of functionally graded (FG) patterns of the CNT reinforcements on the impact response. Numerical results elucidating the effects of temperature, FG distribution, and CNT volume fraction on the out-of-plane Poisson’s ratio and impact response of the beam are obtained by using a Range–Kutta method and discussed in details.

本文对碳纳米管增强复合材料（CNTRC）层层压的可剪切变形梁的低速冲击（LVI）响应进行了研究。通过基于经典层压理论设计的特殊对称对称层堆叠序列，由于负平面外泊松比（NPR），复合光束是“膨胀的”。为了研究面外NPR对复合梁的LVI响应的影响，开发了新定义的Hertz模型。CNTRC层合梁的Kármán型运动方程是在Reddy梁理论的框架内得出的，并通过两步扰动方法求解，而冲击器的动力学方程是基于牛顿定律建立的。由于采用了碳纳米管（CNT）和基质的温度相关材料特性，还研究了热对LVI行为的影响。此外，本文采用分段方法来研究CNT增强物的功能梯度（FG）图案对冲击响应的影响。通过使用Range-Kutta方法获得了阐明温度，FG分布和CNT体积分数对平面外泊松比和光束冲击响应的影响的数值结果，并进行了详细讨论。