It should be noted that in addition to the geometry, constituent material also affects the strength and rigidity of the cylindrical shell, some factors that determine the transient response are its geometry and the constituent material. The capability of piezoelectric materials to adept their properties in reaction to environmental factors including electricity and loading is one of the major reasons for using in this work. Therefore, in this study, the transient response of a symmetric annular sandwich plate incorporating functionally graded core and piezoelectric layers under external harmonic force and electrical voltage is investigated. The properties of the core material vary along its thickness according to a power law model. The displacement field is represented by the third-order shear deformation theory. With the aid of Hamilton’s principle, the structural equations are obtained in terms of displacement components, then solved using the differential quadrature method. In addition, the time response is evaluated with respect to effective parameters including the internal radius, power law index, core thickness, and external voltage. According to the simulation results, the oscillation amplitude decreases as the internal radius of the plate increases over the desired time interval. Also, a higher index parameter is associated with a wider time response range. Moreover, the stability analysis of a piezoelectric system with H∞ performance is considered based on the theory of Markovian jump systems. To this end, a Markovian jump state-space model of the piezoelectric system obtained using system identification under the effect of external disturbance is presented. The H∞ stability index is selected based on a candidate Lyapunov function that leads to a set of linear matrix inequalities for each region. The uncontrolled and controlled transient responses of the coupled system under external disturbance are calculated and compared, indicating the satisfactory controller performance in the presence of external disturbance and jump in the sensor and system dynamics.

中文翻译：

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使用马尔可夫跳跃方法在参数不确定条件下使用压电层抑制 FGM 板的响应

需要注意的是，除了几何形状，组成材料也会影响圆柱壳的强度和刚度，决定瞬态响应的一些因素是它的几何形状和组成材料。压电材料能够适应环境因素（包括电和负载）的特性是在这项工作中使用的主要原因之一。因此，在本研究中，研究了包含功能梯度核心和压电层的对称环形夹层板在外部谐波力和电压下的瞬态响应。根据幂律模型，芯材的特性沿其厚度变化。位移场由三阶剪切变形理论表示。借助Hamilton原理，根据位移分量得到结构方程，然后用微分求积法求解。此外，还根据有效参数（包括内部半径、幂律指数、磁芯厚度和外部电压）对时间响应进行了评估。根据模拟结果，振荡幅度随着板的内半径在所需时间间隔内的增加而减小。此外，较高的指数参数与较宽的时间响应范围相关联。此外，压电系统的稳定性分析 时间响应是根据有效参数评估的，包括内半径、幂律指数、核心厚度和外部电压。根据模拟结果，振荡幅度随着板的内半径在所需时间间隔内的增加而减小。此外，较高的指数参数与较宽的时间响应范围相关联。此外，压电系统的稳定性分析 时间响应是根据有效参数评估的，包括内半径、幂律指数、核心厚度和外部电压。根据模拟结果，振荡幅度随着板的内半径在所需时间间隔内的增加而减小。此外，较高的指数参数与较宽的时间响应范围相关联。此外，压电系统的稳定性分析H∞基于马尔可夫跳跃系统的理论考虑性能。为此，提出了在外扰作用下通过系统辨识得到的压电系统的马尔可夫跳跃状态空间模型。这H∞稳定性指数是基于一个候选 Lyapunov 函数选择的，该函数导致每个区域的一组线性矩阵不等式。计算并比较了耦合系统在外扰作用下的非受控和受控暂态响应，表明在存在外扰和传感器和系统动力学跳跃的情况下控制器性能令人满意。