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Two-dimensional thin plates are widely used in many aerospace, automotive and marine applications. Vibration attenuation can be achieved in these structures by attaching piezoelectric elements on to the structure integrated with shunt damping circuits. This enables a compact vibration damping method without adding significant mass and volumetric occupancy, unlike the bulky mechanical dampers. Practical implementation of shunt damping technique requires accurate modeling of the host structure, the piezoelectric elements and the dynamics of the shunt circuit. Unlike other studies in the literature of piezoelectric shunt damping, this work utilizes a multi-modal equivalent circuit model (ECM) of a thin plate with multiple piezo-patches, to demonstrate the performance of shunt circuits. The equivalent system parameters are obtained from the modal analysis solution based on the Rayleigh-Ritz method. The ECM is coupled to the shunt circuits in SPICE software, where the shunt configuration consists of three branches of electrical resonators, each tuned to one vibration mode of the structure. Using the harmonic analysis in SPICE for a range of excitation frequencies, current output of each ECM branch is calculated for open-circuit and optimum shunt circuit conditions. The current of ECM branches are then converted to the displacement outputs in physical coordinates and validated by the finite-element simulations in ANSYS. It is shown that the vibration attenuation of a vibration mode can be successfully achieved when there is a reduction in the corresponding current amplitude of the ECM branch. This correlation can be utilized in the design of efficient linear/nonlinear shunt circuits.

Recently, topology optimization of structures with cracks becomes an important topic for avoiding manufacturing defects at the design stage. This paper presents a comprehensive comparative study of peridynamics-based topology optimization method (PD-TO) and classical finite element topology optimization approach (FEM-TO) for designing lightweight structures with/without cracks. Peridynamics (PD) is a robust and accurate non-local theory that can overcome various difficulties of classical continuum mechanics for dealing with crack modeling and its propagation analysis. To implement the PD-TO in this study, bond-based approach is coupled with optimality criteria method. This methodology is applicable to topology optimization of structures with any symmetric/asymmetric distribution of cracks under general boundary conditions. For comparison, optimality criteria approach is also employed in the FEM-TO process, and then topology optimization of four different structures with/without cracks are investigated. After that, strain energy and displacement results are compared between PD-TO and FEM-TO methods. For design domain without cracks, it is observed that PD and FEM algorithms provide very close optimum topologies with a negligibly small percent difference in the results. After this validation step, each case study is solved by integrating the cracks in the design domain as well. According to the simulation results, PD-TO always provides a lower strain energy than FEM-TO for optimum topology of cracked structures. In addition, the PD-TO methodology ensures a better design of stiffer supports in the areas of cracks as compared to FEM-TO. Furthermore, in the final case study, an intended crack with a symmetrically designed size and location is embedded in the design domain to minimize the strain energy of optimum topology through PD-TO analysis. It is demonstrated that hot-spot strain/stress regions of the pristine structure are the most effective areas to locate the designed cracks for effective redistribution of strain/stress during topology optimization.