Network segmentations of smart plate structure with attached mass and dynamic motions

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.