Najd Jamal, Zappino Enrico, Carrera Erasmo, Harizi Walid, Aboura Zoheir
Mul2 Group, Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
Centre de Recherche Royallieu, Roberval (Mechanics Energy and Electricity), Université de Technologie de Compiègne, CEDEX CS 60 319, 60 203 Compiègne, France.
Sensors (Basel). 2022 Aug 17;22(16):6168. doi: 10.3390/s22166168.
The present paper assessed the use of variable kinematic two-dimensional elements in the dynamic analysis of Lamb waves propagation in an isotropic plate with piezo-patches. The multi-field finite element model used in this work was based on the Carrera Unified Formulation which offers a versatile application enabling the model to apply the desired order theory. The used variable kinematic model allowed for the kinematic model to vary in space, thereby providing the possibility to implement a classical plate model in collaboration with a refined kinematic model in selected areas where higher order kinematics are needed. The propagation of the symmetric (S0) and the antisymmetric (A0) fundamental lamb waves in an isotropic strip was considered in both mechanical and piezo-elastic plate models. The convergence of the models was discussed for different kinematics approaches, under different mesh refinement, and under different time steps. The results were compared to the exact solution proposed in the literature in order to assess and further determine the effects of the different parameters used when dynamically modeling a Lamb wave propagating in such material. It was shown that the higher order kinematic models delivered a higher accuracy of the propagating wave evaluated using the corresponding Time Of Flight (TOF). Upon using the appropriate mesh refinement of 2000 elements and sufficient time steps of 4000 steps, the error between the TOF obtained analytically and numerically using a high order kinematics was found to be less than 1% for both types of fundamental Lamb waves S0 and A0. Node-dependent kinematics models were also exploited in wave propagation to decrease the computational cost and to study their effect on the accuracy of the obtained results. The obtained results show, in both the mechanical and the piezo-electric models, that a reduction in the computational cost of up to 50% can be easily attained using such models while maintaining an error inferior to 1%.
本文评估了可变运动学二维单元在含压电片的各向同性板中兰姆波传播动态分析中的应用。本工作中使用的多场有限元模型基于卡雷拉统一公式，该公式具有广泛的适用性，使模型能够应用所需阶次的理论。所使用的可变运动学模型允许运动学模型在空间中变化，从而提供了在需要高阶运动学的选定区域将经典板模型与精细运动学模型相结合的可能性。在机械和压电弹性板模型中均考虑了各向同性条带中对称（S0）和反对称（A0）基本兰姆波的传播。讨论了不同运动学方法、不同网格细化和不同时间步长下模型的收敛性。将结果与文献中提出的精确解进行比较，以评估并进一步确定在对此类材料中传播的兰姆波进行动态建模时所使用的不同参数的影响。结果表明，高阶运动学模型在使用相应飞行时间（TOF）评估传播波时具有更高的精度。对于两种基本兰姆波S0和A0，在使用2000个单元的适当网格细化和4000步的足够时间步长时，使用高阶运动学通过解析和数值方法获得的TOF之间的误差小于1%。还在波传播中利用了节点相关的运动学模型以降低计算成本并研究其对所得结果精度的影响。所得结果表明，在机械和压电模型中，使用此类模型可轻松实现高达50%的计算成本降低，同时保持误差低于1%。
