This paper focuses on the primary development of novel analytical and numerical studies for the smart plate structure due to the effects of point mass locations, dynamic motions, and network segmentations. Instead of the alternative capabilities in active and passive control systems, the technical application of the present work can also be found in the energy harvesting system. The simplified theoretical studies have shown the simultaneous derivations with full variational parameters. In particular, these parameters consist of the mechanical and electromechanical systems, the mixed series–parallel electrode segment connection, and the harvesting circuit. The mechanical system parameters include elasticity with stress-strain relation, internal damping stress, air damping, and dynamics of the integrated physical system. The electromechanical system parameters include electrical displacement, electrical stress and electric-polarity field of the piezoelectricity. For the analytical approach, the governing equations of motion based on the Gram-Schmidt iterative process have been derived using the extended Hamiltonian principle and Ritz method-based weak form system. For validation, the electromechanical finite element equations reduced from the extended Lagrange’s equations have been developed using electromechanical discretisation and coupling transformation techniques. As a result, the two theoretical models have shown distinct frequency response equations for the dynamic solutions of the integrated physical system. In parametric studies, the two theoretical models of the smart plates with variable geometrical aspect ratio and different locations of point mass are discussed, giving good agreement. The strain mode analysis is utilised to identify the shape patterns at the region of the smart plate due to the change of strains. As a result, it can affect the electric power productions at the frequency domain. At certain cases, the appearance of asymmetric strain mode shapes may occur, resulting in the electric power reductions. To alleviate such condition, the activation of arbitrary electrode segments using the network connection can be implemented. Moreover, the smart structural model with different point mass locations is also subjected to the base excitation and the dynamic force. The proposed technique can adaptively and accumulatively generate the optimal power outputs and shift the resonance frequencies. All results of the parametric studies quantitatively show the dynamic system behaviours.

由于点质量位置，动态运动和网络分段的影响，本文重点研究了智能板结构的新颖分析和数值研究的初步发展。代替主动和被动控制系统中的替代功能，本工作的技术应用也可以在能量收集系统中找到。简化的理论研究表明具有完整变分参数的同时导数。尤其是，这些参数包括机械和机电系统，混合的串联－并联电极段连接以及采集电路。机械系统参数包括具有应力-应变关系的弹性，内部阻尼应力，空气阻尼以及集成物理系统的动力学。机电系统参数包括压电的电位移，电应力和极性场。对于分析方法，使用扩展的哈密顿原理和基于Ritz方法的弱形式系统，导出了基于Gram-Schmidt迭代过程的运动控制方程。为了进行验证，已经使用机电离散化和耦合变换技术开发了从扩展的拉格朗日方程简化的机电有限元方程。结果，这两个理论模型为集成物理系统的动态解决方案显示了截然不同的频率响应方程。在参数研究中，讨论了具有可变几何长宽比和点质量不同位置的智能板的两种理论模型，具有很好的一致性。利用应变模式分析来识别由于应变变化而在智能板区域上的形状图案。结果，它会影响频域的电力生产。在某些情况下，可能会出现不对称应变模式形状，从而导致电功率降低。为了减轻这种情况，可以实现使用网络连接来激活任意电极段。此外，具有不同点质量位置的智能结构模型也要经受基础激励和动力。所提出的技术可以自适应地和累积地产生最佳功率输出并改变谐振频率。参数研究的所有结果都定量显示了动态系统的行为。