变形统一理论下应变梯度石墨烯片层增强金属泡沫微板的动力学建模与分析
DYNAMIC MODELING AND ANALYSIS OF STRAIN GRADIENT GRAPHENE PLATELET-REINFORCED METAL FOAM MICROPLATES VIA A DEFORMATION-BASED UNIFIED THEORY
-
摘要: 基于变形统一理论(Deformation-based unified theory, DUT)与修正应变梯度理论(Modified strain gradient theory, MSGT), 本文建立了石墨烯片层(Graphene platelet, GPLs)增强金属泡沫微板的动力学模型, 并研究其自由振动与波传播特性. DUT 采用具有明确物理意义的第四位移分量, 有效放松了板沿着厚度方向变形的约束. MSGT通过引入拉伸梯度张量、膨胀梯度张量及旋转梯度张量的对称部分, 能够更全面地刻画材料尺度效应. 采用改进的Halpin–Tsai方法确定GPL增强铝基骨架的等效参数, 并结合孔隙退化模型描述泡沫基体的孔隙效应; 通过与已有文献结果对比, 验证了理论模型的有效性. 系统分析了孔隙分布构型、GPL质量分数、孔隙率、几何参数及材料尺度参数的影响. 结果表明: 对称非均匀孔隙分布能更好保留表层材料的承载能力, 使微板在自由振动及中低波数范围内具有较高的固有频率、频散频率和相速度; 增加GPL质量分数可提高结构等效刚度, 进而增大固有频率、圆频率和相速度, 而孔隙率增大则使上述响应普遍降低. 材料尺度参数可提高固有频率, 且对高阶模态的强化作用更明显. 厚度比显著影响频散曲线的演化, 导致第一、第二阶波分支发生模态交换, 第四阶分支则呈现不同于低阶分支的传播特征. 基于皮尔逊相关系数的分支追踪方法可有效识别模态交换现象, 提升相速度和群速度结果的连续性与物理一致性. 研究结果有望为微纳尺度板状器件的动力学设计与性能优化提供理论参考.Abstract: This study presents a dynamic model for graphene platelet (GPLs)-reinforced metal foam microplates based on a deformation-based unified theory (DUT) and the modified strain gradient theory (MSGT) for investigating the structural free vibration and wave propagation characteristics. DUT employs a fourth-order displacement field with explicit physical meaning to alleviate thickness-direction constraints, while MSGT incorporates symmetric stretching/dilatation/rotation gradient tensors to characterize material size effects. Equivalent properties of the GPL-aluminum skeleton are determined via a modified Halpin–Tsai model, with foam matrix porosity described by a degradation model. Validation against literature confirms model accuracy. Parametric studies systematically examine porosity distribution patterns, GPL mass fraction, porosity level, geometric parameters (thickness ratio), and material length-scale parameters. Results demonstrate that symmetric non-uniform porosity preserves surface-layer load capacity and bending stiffness, thus elevating natural frequencies while enhancing dispersion frequencies and phase velocities at low-to-mid wavenumbers. Increased GPL mass fraction enhances structural stiffness, thereby increasing natural/angular frequencies and phase velocities, whereas higher porosity reduces stiffness and diminishes these responses. Material length-scale parameters amplify natural frequencies with heightened effects on higher-order modes. Crucially, thickness ratio governs dispersion branch evolution, inducing mode veering between first/second wave branches while the fourth branch exhibits distinct propagation characteristics. A Pearson correlation-based branch-tracking method effectively identifies mode veering, ensuring physical consistency in phase/group velocities. This study provides theoretical foundations for dynamic optimization of GPL-reinforced foam microplates in micro-/nano-devices.
下载: