The active-passive damping of the functionally graded piezoelectric layers-magnetorheological elastomer (FGPE-MRE) sandwich structures may fail due to the compressibility of the core. This work provides a unified modeling method for the failure characteristics of the active-passive damping in the FGPE-MRE sandwich structure. The unbounded condition and normal magnetic field are considered to approximate the practical applications of the active-passive damping. To clarify the failure mechanism of the active-passive damping, a novel compressible core method is proposed. To illustrate the effect of the normal magnetic field, the strain-stress relation with in-plane Lorenz force is developed by employing the Maxwell's equation. Moreover, to realize the unbounded condition of the FGPE-MRE sandwich structure, the classical boundary condition of sandwich structures is modified. To avoid the failure of the active-passive damping, the traditional feedback control law is improved by constructing a fractional negative feedback equation. Finally, numerical investigations are conducted to show the failure characteristics of the active-passive damping and the effectiveness of the proposed control law.

由于核心的可压缩性，功能梯度压电层-磁流变弹性体 (FGPE-MRE) 夹层结构的主动-被动阻尼可能会失效。这项工作为 FGPE-MRE 夹层结构中主动-被动阻尼的失效特性提供了统一的建模方法。无界条件和法向磁场被认为近似于主动-被动阻尼的实际应用。为了阐明主动-被动阻尼的失效机制，提出了一种新的可压缩核心方法。为了说明法向磁场的影响，使用麦克斯韦方程建立了应变-应力与面内洛伦兹力的关系。此外，为了实现 FGPE-MRE 夹层结构的无界条件，修改了夹层结构的经典边界条件。为避免主被动阻尼失效，通过构造分数负反馈方程对传统的反馈控制律进行改进。最后，通过数值研究显示了主动-被动阻尼的失效特性和所提出的控制律的有效性。