Exploring the dynamics of hourglass shaped lattice metastructures

The continuous demand for improved mechanical performance in engineering structures has driven the development of metastructures. Lattice-based metastructures, known for their ability to manipulate wave propagation and create bandgaps, offer enhanced customizability for multifunctional applications. This research introduces a novel hourglass-shaped lattice metastructure, formed by combining two oppositely oriented coaxial domes. This design significantly enhances the functionality of the material by enabling higher customizability and the ability to tailor its dynamic response. The exploration of metamaterials began with electromagnetic metamaterials exhibiting negative permittivity and permeability. This concept was extended to acoustic metamaterials, also known as phononic crystals, characterized by periodicity or translational symmetry. These metamaterials derive their mechanical properties from the geometry of their building blocks rather than the constituent materials. Unlike traditional phononic crystals with fixed bandgap behavior, metamaterials are tunable due to adjustable local structural resonances. The focus has shifted towards developing tunable metamaterials, which can adjust operating frequencies and find applications in acoustic imaging, cloaking, and infrastructure protection. Metastructures, inspired by metamaterials, offer excellent wave absorption and stiffness-to-weight ratios. Tailoring the geometric and elastic properties of metastructure building blocks can tune wave behavior. However, existing designs have limited tunability due to simple geometries. The need for a unit metastructure with more customizable properties led to the exploration of lattice-based architected metastructures, which exhibit enhanced static properties and wave propagation control, making them suitable for multifunctional applications. Dome-based lattice structures, despite their potential in tuning stiffness and Poisson's ratio, have been rarely explored. This research expands the design space of metastructures by integrating the advantages of lattice geometry with the tunability of the hourglass shape, a unique combination not previously reported.

The paper extensively reviews existing literature on metamaterials and metastructures, highlighting the evolution from electromagnetic and acoustic metamaterials to tunable metamaterials with adjustable operating frequencies. It discusses various approaches to designing metastructures, including lumped mass models, cycloidal resonators, and arrays of cylindrical resonators, emphasizing their limitations in tunability due to relatively simple geometries. The review underscores the potential of lattice-based architected metastructures for multifunctional applications due to their enhanced static properties and wave propagation control. It also points out the under-exploration of dome-based lattice structures in metastructure design, despite their demonstrated potential in tuning stiffness and Poisson's ratio. The paper positions its novel hourglass-shaped lattice metastructure as a significant advancement in addressing the limitations of existing designs and expanding the possibilities of tunable metamaterials.

This study proposes six new classes of hourglass-shaped lattice metastructures, combining solid shells, regular honeycomb lattices, and auxetic lattices. These structures are categorized into homogeneous (lattice symmetry between the two domes) and non-homogeneous (unsymmetrical lattices) classes. The research employs a multi-pronged approach involving analytical modeling, finite element analysis (FEA), additive layer manufacturing (3D printing), and experimental testing. The analytical model treats the hourglass metastructure as a combination of two coned-disk springs, enabling the study of load-deflection behavior under various topological parameters and lattice geometries. Finite element analysis (FEA) using Ansys 15.0 is performed to understand the modal behavior of the six different hourglass structures. Modal analysis, using a subspace-based algorithm, extracts the first ten eigenmodes for all samples. The sixth mode, observed along the axis of the hourglass structure, is found to be directly related to the fundamental axial mode. Additive layer manufacturing (3D printing) using an Ultimaker 3.0 printer fabricates the homogeneous and non-homogeneous hourglass samples. The material used is PCTPE (plasticized copolyamide thermoplastic elastomer), with properties characterized through tensile testing of a standard dog bone specimen. Experimental testing includes static loading-unloading tests using an Instron UTM-1195 to obtain load-deflection curves under quasi-static strain rates. Dynamic testing using a laser Doppler vibrometer (LDV) measures displacement transmissibility under base excitation with pseudo-random signals. The damping factor is calculated using the half-power bandwidth method. The dispersion analysis, based on a 1D diatomic system with a second-order lattice-based oscillator, mathematically investigates the dynamics of the hourglass and dome-shaped lattices. An equivalent 1D diatomic, locally resonant metamaterial is considered for the initial investigation. The dispersion curves for the hourglass-based metamaterial are obtained experimentally using LDV.

The study reveals several key findings: The analytical model accurately predicts the load-deflection behavior, showing good agreement with experimental results. The load-deflection characteristics exhibit nonlinearity, varying with geometric parameters and the h/t ratio (ratio of dome height to shell thickness). A 'wide zero-rate range' is observed for specific h/t ratios, indicating zero stiffness over a wide range of deflection. The lattice cell angle significantly influences the stiffness, with auxetic lattices exhibiting reduced snap-through buckling compared to honeycomb lattices. Experimental dynamic testing reveals lattice-dependent natural frequencies, with auxetic-based metastructures showing lower natural frequencies than honeycomb-based ones. Auxetic lattice-based metastructures demonstrate higher damping capabilities compared to honeycomb lattices. The FEA results closely match the experimental transmissibility data. The dispersion analysis shows that auxetic lattices are effective for low-frequency attenuation, while honeycomb lattices are better for higher frequencies. The study shows that non-linear effects are insignificant at lower strain values. The load-bearing capacity can be tuned by adjusting the lattice cell angle. By altering the height-to-thickness ratio and lattice cell angle, the hourglass metastructure's non-linear stiffness can be customized, achieving different stiffness profiles and natural frequencies. Auxetic lattices display superior damping capabilities compared to honeycomb structures, particularly in the homogeneous class. The sixth mode shape, along the longitudinal axis, is consistent between FEA and experiments. The study demonstrates the feasibility of developing tunable metamaterials using the hourglass-shaped lattice metastructure as a building block.

The findings address the research question by demonstrating the successful design, fabrication, and characterization of a novel hourglass-shaped lattice metastructure with tunable mechanical properties. The observed nonlinear stiffness and damping characteristics, dependent on lattice topology and geometry, are significant for applications requiring vibration isolation and wave attenuation. The ability to achieve a wide zero-rate range, where the equivalent stiffness is zero over a broad range of deflection, suggests potential use in nonlinear oscillators. The superior performance of auxetic lattices in terms of both damping and reduced snap-through buckling confirms their suitability for energy absorption applications. The agreement between analytical, numerical, and experimental results validates the approach and provides a solid foundation for future research. The study's findings have implications for the design of tunable metamaterials, offering a customizable platform for tailoring mechanical response to specific application needs. The concept of pre-stressing, coupled with piezoelectric materials, holds the potential to achieve remotely controlled bandgap tuning.

This paper successfully demonstrates the design, fabrication, and characterization of a novel hourglass-shaped lattice metastructure. Six distinct metastructures with varying lattice topologies are analyzed, revealing tunable nonlinear stiffness and damping properties. The findings highlight the superior performance of auxetic lattices compared to honeycomb lattices for energy absorption. The close agreement between experimental, analytical, and numerical results validates the proposed model and opens up exciting possibilities for designing tunable metamaterials for vibration isolation and wave attenuation applications. Future research should explore the integration of piezoelectric/magnetostrictive materials to enable electrical switching of band-gap behavior and further investigation into the influence of different dome shapes on macro-mechanical behavior.

The study focuses on a specific material (PCTPE) and a limited range of geometric parameters. The effects of other material properties and a wider range of geometric parameters need further exploration. The analytical model simplifies the complex behavior of the metastructure, which might limit the accuracy of predictions under specific conditions. The experimental setup and testing methods have inherent limitations that might slightly affect the accuracy and precision of the results. While the study demonstrates the potential of using the hourglass-shaped metastructure as a building block for tunable metamaterials, the actual implementation and optimization for specific applications remain areas for future research.