In this work, both magnetic and vibration amplitude dependent properties of magnetorheological elastomer (MRE) grid composite sandwich plates (MREGCSPs) are investigated. Initially, to prove such a nonlinearly dependent phenomenon, a series of characterization tests are performed on the MREGCSP specimens with different magnetic field intensities and base vibrational amplitudes. Then, using the Jones-Nelson nonlinear material theory, the strain energy density function method, the complex modulus approach, and the Biot-Savart law, the nonlinear material assumption of MRE is defined. A theoretical model consisting of an MRE grid core and two fiber-reinforced polymer (FRP) skins is also proposed to obtain the solutions for the nonlinear frequency, damping, and vibration response parameters, which is based on the modified first-order shear deformation theory, the energy principle, the eigenvalue increment method, the Newmark- beta approach, etc. Finally, a detailed comparison of magnetic and vibrational amplitude dependent natural frequencies, loss factors, and vibration responses is performed to confirm the effectiveness and superiority of the current model over a linear model. This provides a solid basis to reveal the nonlinear dynamic mechanism of the studied smart structure subjected to complex excitation loads. Also, some practical suggestions are summarized for improving its active vibration control capability.

在这项工作中，研究了磁流变弹性体 (MRE) 网格复合夹层板 (MREGCSP) 的磁性和振幅相关特性。最初，为了证明这种非线性相关现象，对具有不同磁场强度和基础振动幅度的 MREGCSP 样本进行了一系列表征测试。然后，利用Jones-Nelson非线性材料理论、应变能密度函数法、复模量法和Biot-Savart定律，定义了MRE的非线性材料假设。还提出了一个由 MRE 网格芯和两个纤维增强聚合物 (FRP) 表皮组成的理论模型，以获得非线性频率、阻尼和振动响应参数的解，它基于修正的一阶剪切变形理论、能量原理、特征值增量法、Newmark-beta 方法等。最后，详细比较了磁和振动振幅相关的固有频率、损耗因子和振动响应执行以确认当前模型相对于线性模型的有效性和优越性。这为揭示所研究的智能结构在复杂激励载荷作用下的非线性动力学机制提供了坚实的基础。同时，总结了一些提高其主动振动控制能力的实用建议。执行振动响应以确认当前模型相对于线性模型的有效性和优越性。这为揭示所研究的智能结构在复杂激励载荷作用下的非线性动力学机制提供了坚实的基础。同时，总结了一些提高其主动振动控制能力的实用建议。执行振动响应以确认当前模型相对于线性模型的有效性和优越性。这为揭示所研究的智能结构在复杂激励载荷作用下的非线性动力学机制提供了坚实的基础。同时，总结了一些提高其主动振动控制能力的实用建议。