A constitutive model for the analysis of second harmonic Lamb waves in unidirectional composites
A constitutive model for the analysis of second harmonic Lamb waves in unidirectional composites
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DOI：
10.1016/j.ijsolstr.2017.11.019
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发表时间：
2017-11
影响因子：
3.6
通讯作者：
N. Rauter;R. Lammering
中科院分区：
文献类型：
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作者：
N. Rauter;R. Lammering
近年来在结构健康监测（SHM）方面的研究表明，导波尤其是非线性兰姆波是监测薄壁结构中材料劣化的一种合适手段。在相应的波传播数值模拟中，通常采用Murnaghan的非线性弹性理论，该理论对横向各向同性材料需要14个材料参数。提出了一种新的非线性超弹性横向各向同性材料模型，增强了现有的线性应变能势，将材料的独立参数减少到6个。为了验证所提出的材料模型在模拟复合材料结构中的非线性波传播和高次谐波模态产生方面的适用性，本文对基波到高次谐波模态的功率通量的存在性进行了分析和数值研究。分析的考虑表明，这种功率流像Murnaghan的理论一样存在。为了进行数值验证，使用了低频范围内的0 - 0模式对。因此，二次谐波模式的振幅随传播距离的增加而振荡。这一行为与理论预测非常吻合。进一步表明，即使是振荡行为，二次谐波模式的振幅也可以通过相当长的传播距离上的线性曲线拟合来近似，因此显示出准累积行为。因此，所引入的材料模型是替代Murnaghan理论来模拟复合材料结构中二次谐波Lamb波产生的有利方法。
In recent research on Structural Health Monitoring (SHM) guided waves, especially nonlinear Lamb waves, turned out to be a suitable means for monitoring material deterioration in thin-walled structures. In the corresponding numerical simulations on wave propagation the nonlinear elastic theory by Murnaghan is often implemented, which requires 14 material parameters for transversely isotropic materials. Enhancing an existing linear strain energy potential, a new nonlinear hyperelastic transversely isotropic material model is introduced which reduces the number of independent material parameters to six. In order to verify the applicability of the presented material model with respect to the simulation of nonlinear wave propagation in composite structures, and the generation of higher harmonic wave modes, the existence of a power flux from the fundamental to the higher harmonic mode is investigated analytically and numerically. Analytical considerations show that this power flux exists like in Murnaghan’s theory. For the numerical validation theS0–S0mode pair in the low frequency range is used. Therefore, the amplitude of the second harmonic wave mode is oscillating with increasing propagation distance. This behavior is in excellent agreement with the theoretical prediction. It is shown further, that even for an oscillating behavior the amplitude of the second harmonic mode can be approximated by a linear curve fit over a considerably propagation distance and hence shows a quasi cumulative behavior. Therefore, the introduced material model is an advantageous alternative to Murnaghan’s theory to simulate the second harmonic Lamb wave generation due to in composite structures.