Low velocity impact response of porous metal ceramic functionally graded rectangular plate
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摘要: 为研究多孔金属陶瓷功能梯度矩形板在低速冲击下的动力学响应,提出了一种基于赫兹弹性理论和一阶剪切变形板理论的数值分析模型,获得了低速冲击下多孔金属陶瓷功能梯度矩形板的响应解析解。根据Hamilton原理推导出功能梯度矩形板的运动方程,引入两自由度弹簧-质量(S-M)模型用于获得冲击过程中与时间相关的接触力,利用Duhamel原理和Navier法计算了多孔功能梯度矩形板的横向位移。所得结果与文献数据进行比对,验证了有效性。在此基础上,针对相关参数对功能梯度板抗冲击性能的影响进行了比对分析。结果表明:随着孔隙率、功能梯度指数和宽厚比的减小,最大横向位移减小,功能梯度矩形板的能量吸收和抗冲击性能增强。Abstract: In order to study the dynamic response of porous metal ceramic functionally graded rectangular plate under low velocity impact, a numerical analysis model based on Hertzian elastic theory and first-order shear deformation plate theory was presented, the analytical solution of response of porous cermet functionally graded rectangular plate under low velocity impact was obtained. According to Hamilton's principle, the equation of motion of functionally graded rectangular plate was derived, a spring-mass (S-M) model with two degrees of freedom was introduced to obtain the time-dependent contact forces during impact, using the Duhamel principle and Navier method to calculate the transverse displacement of porous functionally graded rectangular plate. The results obtained were compared with literature data to verify the validity. On this basis, the influence of related parameters on the impact resistance of functionally graded rectangular plate was compared and analyzed. The results show that with the decrease of porosity, functionally graded index and width to thickness ratio, the maximum transverse displacement of the functionally graded rectangular plate decreases, energy absorption and impact resistance are increased.
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表 1 多孔FGM矩形板各组分材料特性
Table 1. Material properties of components of porous FGM rectangular plate
Material Young's
modulus/GPaPoisson's
ratioDensity/
(kg·m−3)Al6061 67 0.33 2702 SiC 302 0.17 3100 表 2 含孔隙FGM板的无量纲频率验证
Table 2. Non-dimensional frequencies verification of porous FGM plate
$ \eta $ Method Porosity Non-dimensional frequency $ p = 0 $ $ p = 0.5 $ $ p = 1 $ 20 Present 0.2 0.0300 0.0245 0.0210 Razaei et al[27] 0.0300 0.0245 0.0210 10 Present 0.2 0.1170 0.0959 0.0823 Razaei et al[27] 0.1170 0.0961 0.0824 5 Present 0.2 0.4284 0.3542 0.3052 Razaei et al[27] 0.4313 0.3562 0.3068 Notes: $ \eta $—Width to thickness ratio; $ p $—Functionally graded index. 表 3 不同冲击速度下理想FGM板接触力验证
Table 3. Verification of contact force for ideal FGM plate with different impact velocities
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