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Locally resonant elastodynamic metasurfaces for suppressing surface waves have gained popularity in recent years, especially because of their potential in low-frequency applications such as seismic barriers. Their design strategy typically involves tailoring geometrical features of local resonators to attain a desired frequency bandgap through extensive dispersion analyses. In this paper, a systematic design methodology is presented to conceive these local resonators using topology optimization, where frequency bandgaps develop by matching multiple antiresonances with predefined target frequencies. The design approach modifies an individual resonator's response to unidirectional harmonic excitations in the in-plane and out-of-plane directions, mimicking the elliptical motion of surface waves. Once an arrangement of optimized resonators composes a locally resonant metasurface, frequency bandgaps appear around the designed antiresonance frequencies. Numerical investigations analyze three case studies, showing that longitudinal-like and flexural-like antiresonances lead to nonoverlapping bandgaps unless both antiresonance modes are combined to generate a single and wider bandgap. Experimental data demonstrate good agreement with the numerical results, validating the proposed design methodology as an effective tool to realize locally resonant metasurfaces by matching multiple antiresonances such that bandgaps generated as a result of in-plane and out-of-plane surface wave motion combine into wider bandgaps. 

Abstract In this article, we present a design methodology for resonant structures exhibiting particular dynamic responses by combining an eigenfrequency matching approach and a harmonic analysis-informed eigenmode identification strategy. This systematic design methodology, based on topology optimization, introduces a novel computationally efficient approach for 3D dynamic problems requiring antiresonances at specific target frequencies subject to specific harmonic loads. The optimization’s objective function minimizes the error between target antiresonance frequencies and the actual structure’s antiresonance eigenfrequencies, while the harmonic analysis-informed identification strategy compares harmonic displacement responses against eigenvectors using a modal assurance criterion, therefore ensuring an accurate recognition and selection of appropriate antiresonance eigenmodes used during the optimization process. At the same time, this method effectively prevents well-known problems in topology optimization of eigenfrequencies such as localized eigenmodes in low-density regions, eigenmodes switching order, and repeated eigenfrequencies. Additionally, our proposed localized eigenmode identification approach completely removes the spurious eigenmodes from the optimization problem by analyzing the eigenvectors’ response in low-density regions compared to high-density regions. The topology optimization problem is formulated with a density-based parametrization and solved with a gradient-based sequential linear programming method, including material interpolation models and topological filters. Two case studies demonstrate that the proposed design methodology successfully generates antiresonances at the desired target frequency subject to different harmonic loads, design domain dimensions, mesh discretization, or material properties. 

Abstract Magnetoactive elastomers (MAEs) are capable of large deformation, shape programming, and moderately large actuation forces when driven by an external magnetic field. These capabilities enable applications such as soft grippers, biomedical devices, and actuators. To facilitate complex shape deformation and enhanced range of motion, a unimorph can be designed with varying geometries, behave spatially varying multi-material properties, and be actuated with a non-uniform external magnetic field. To predict actuation performance under these complex conditions, an analytical model of a segmented MAE unimorph is developed based on beam theory with large deformation. The effect of the spatially-varying magnetic field is approximated using a segment-wise effective torque. The model accommodates spatially varying concentrations of magnetic particles and differentiates between the actuation mechanisms of hard and soft magnetic particles by accommodating different assumptions concerning the magnitude and direction of induced magnetization under a magnetic field. To validate the accuracy of the model predictions, four case studies are considered with various magnetic particles and matrix materials. Actuation performance is measured experimentally to validate the model for the case studies. The results show good agreement between experimental measurements and model predictions. A further parametric study is conducted to investigate the effects of the magnetic properties of particles and external magnetic fields on the free deflection. In addition, complex shape programming of the unimorph actuator is demonstrated by locally altering the geometric and material properties. 

Control of guided waves has applications across length scales ranging from surface acoustic wave devices to seismic barriers. Resonant elastodynamic metasurfaces present attractive means of guided wave control by generating frequency stop-bandgaps using local resonators. This work addresses the systematic design of these resonators using a density-based topology optimization formulated as an eigenfrequency matching problem that tailors antiresonance eigenfrequencies. The effectiveness of our systematic design methodology is presented in a case study, where topologically optimized resonators are shown to prevent the propagation of the S0 wave mode in an aluminum plate. 

Abstract We demonstrate the design of resonating structures using a density-based topology optimization approach, which requires the eigenfrequencies to match a set of target values. To develop a solution, several optimization modules are implemented, including material interpolation models, penalization schemes, filters, analytical sensitivities, and a solver. Moreover, common challenges in topology optimization for dynamic systems and their solutions are discussed. In this study, the objective function is to minimize the error between the target and actual eigenfrequency values. The finite element method is used to compute the eigenfrequencies at each iteration. To solve the optimization problem, we use the sequential linear programming algorithm with move limits, enhanced by a filtering technique. Finally, we present a resonator design as a case study and analyze the design process with different optimization parameters. 

Abstract Silicon is regarded as one of the most promising anode materials for lithium-ion batteries. Its high theoretical capacity (4000 mAh/g) has the potential to meet the demands of high-energy density applications, such as electric air and ground vehicles. The volume expansion of Si during lithiation is over 300%, indicating its promise as a large strain electrochemical actuator. A Si-anode battery is multifunctional, storing electrical energy and actuating through volume change by lithium-ion insertion. To utilize the property of large volume expansion, we design, fabricate, and test two types of Si anode cantilevers with bi-directional actuation: (a) bimorph actuator and (b) insulated double unimorph actuator. A transparent battery chamber is fabricated, provided with NCM cathodes, and filled with electrolyte. The relationship between state of charge and electrode deformation is measured using current integration and high-resolution photogrammetry, respectively. The electrochemical performance, including voltage versus capacity and Coulombic efficiency versus cycle number, is measured for several charge/discharge cycles. Both configurations exhibit deflections in two directions and can store energy. In case (a), the largest deflection is roughly 35% of the cantilever length. Twisting and unexpected bending deflections are observed in this case, possibly due to back-side lithiation, non-uniform coating thickness, and uneven lithium distribution. In case (b), the single silicon active coating layer can deflect 12 passive layers. 

Abstract Silicon anodes have been demonstrated to provide significant actuation in addition to energy storage in lithium-ion batteries (LIBs). This work studies the optimization of 1D unimorph and bimorph actuators to achieve a target shape upon actuation. A 1D shape matching with design optimization is used to estimate the varied charge distribution along the length for a LIB actuator and thereby the effect of distance between electrodes in charging. A genetic algorithm (GA) is used with actuation strain distribution as the design variable. The objective of the optimization is to shape-match by minimizing the shape error between a target shape and actuated shape, both defined by several points along the length. The approach is experimentally validated by shape matching a notched unimorph target shape. A shape error of 1.5% is obtained. An optimized unimorph converges to an objective function of less than 0.029% of the length at full state of charge (SOC) for a 5-segment beam. A second shape matching case study using a bimorph is investigated to showcase the tailorability of LIB actuators. The optimal bimorph achieves an objective function of less than 0.23% of the length for a design variable set of top and bottom actuation strain of an 8-segment beam. The actuated shape nearly matches the target shape by simultaneously activating top and bottom active layers to achieve the same differential actuation strain (the difference between top and bottom active layer actuation strain). The results show that a bimorph actuator can achieve a given shape while also storing significantly more charge than is necessary to maintain a given complex shape. This demonstrates a strength of energy storage based actuators: excess energy can be stored within the actuator and can be expended without affecting the work done or the shape maintained by the actuator.