Incorporating actively implemented resonators within elastic piezoelectric metastructures presents a unique approach for vibration attenuation, enabling the creation of tuneable low-frequency bandgaps. Through feedback control, we enhance the compactness of these metastructures by integrating resonator dynamics internally. We study the influence of varying the cross-section of the base substrate and the arrangement of transducers on bandgap generation. This influence is captured by the changes in the electromechanical coupling and stiffness of the metastructure, which appear directly in the formulas for bandgap edge frequencies in ideal conditions. This relationship is illustrated with numerical examples for realistic metastructures with a finite number of transducers. Our focus is on metastructures with sensors and actuators, employing feedback control techniques for resonator implementation as an alternative to shunt circuits. When a bandgap is generated in a finite metastructure, its edge frequencies can be calculated in closed form using the assumption of an infinite number of transducers of infinitesimal length distributed along the structure.

The shape memory effect (SME) is a source of internal compressive stresses that modify the vibration behavior of shape memory alloy (SMA) embedded composite structures. Generally, long fibers are used due to their suitability for activating SMA using resistive heating. Longer SMA fibers embedded in composite structures have their limitations in design and manufacturing. Minimal research work has been done on tuning the vibration behavior of composite structures embedded with short SMA fibers. In this research paper, an analytical model for evaluating the natural frequencies of an SMA embedded composite beam has been proposed. Effects of various design parameters for long (continuous) and short (discontinuous) SMA fibers embedded in composites have been investigated. It was observed that short SMA fibers with a higher aspect ratio can tune their frequencies similarly to long SMA fiber composites and are more effective in thicker beams. Matrix material with negative coefficient thermal expansion is more suitable for embedding SMA for modifying natural frequency in active mode.

Wave propagation in periodic media is crucial for energy transmission, enabling control over energy direction and isolation. This involves breaking the inversion symmetry of a spring-mass chain by introducing mirrored copies of periodic combinations, creating a unique, irreversible structure with distinct dispersion properties. The customizability and linearity of the interface lattice present the main challenge in controlling the interface mode. Our study focuses on designing a controllable on-demand interface mode using shape memory alloy-based smart material actuation mechanism. We included shape memory alloy-type springs along with the conventional springs in the analysis. SMA has the unique ability to change its phase in response to a temperature change due to the phase transition between martensite and austenite crystal structures. As a result, the modulus of elasticity also varies resulting in a change in stiffness. Through this system, the voltage-dependent stiffness can be tuned. This, in turn, enables the existence of an interface mode to be adjusted to the desired frequency and amplitude. The proposed system also allows us to obtain a range of split bandgaps that are dependent on controlling parameters. It is observed that the variation in the actuation voltage is to be controlled for the interface mode tuning and adjust stiffness accordingly. A generalized theoretical scheme is developed for several types of spring combinations at the interface and its effects are compared. Such system can significantly change the wave propagation in periodic media, leading to advancements in energy transmission systems with enhanced efficiency and versatility. Thus, the obtained interface mode within the bandgap can be tuned by the applied voltage enabling future application in wave focusing, wave guiding, and energy harvesting.

This study uses the data-driven machine-learning technique called ridge regression to address an innovative method of designing hourglass lattice-structured metamaterials. Metamaterials are engineered materials with properties derived from their intricate structural arrangements, holding promise for various applications. The hourglass lattice arrangement is exciting because of its unique mechanical characteristics and possible advantages in stiffness m odulation. D esigning s uch c omplex s tructures o ften i nvolves m anual i terations a nd simulations, which can be time-consuming and limited in exploring the vast design space. In this paper, we suggest an innovative approach that uses data-driven machine learning to speed up and improve the design process. By training models on a dataset of metamaterial behaviors, we enable the prediction of optimal hourglass lattice configurations f or d esired m echanical p roperties. T his p rediction u ses a m achine l earning a lgorithm t o analyze the data obtained from existing design simulations. This predictive capacity empowers researchers and engineers to explore an extensive design space efficiently, thus uncovering optimal configurations that might remain undiscovered using traditional methods like manual adjustments and iteration or physical prototyping and testing, which are time-consuming and labor-intensive. Engineers iteratively refine d esigns b ased o n s imulation o r test results, limiting design space exploration and potentially missing optimal configurations. T he c ore innovation lies in the ability of these models to predict the mechanical properties and behaviors of hourglass lattice metamaterials based on their structural characteristics, such as radius of curvature and thickness. This methodology can potentially revolutionize metamaterial design by efficiently us ing da ta-driven ma chine-learning models.

Nature's morphology and optimal energetic solutions remain the key motivation for designing cellular-based lattice structures. Understanding the nonlinear dynamical behaviors that arise from different lattice topologies of such structures in the metastructure framework is crucial for their successful implementation in various novel designs and technologies related to vibration and shape control. This paper presents a study of the static and dynamic response of auxetic and honeycomb lattices with hourglass or dome-shaped metastructures. The potential tailoring of nonlinearity of such responses through various design parameters that play a vital role in shaping the dynamic properties of such structures is discussed here. The impact of cell design parameters on the resulting macroscopic behavior is assessed using both numerical simulations and experimental studies. The transition from softening to hardening nonlinear dynamic responses is reported with cell topologies ranging from the regular honeycomb to auxetic topologies that are widely used as fundamental cells of cellular materials design. The experimental study is based on the time responses measured to verify the numerical predictions. The experimental system consists of different 3D printed hourglass samples based on the auxetic and honeycomb lattices on which dynamic testing using a laser Doppler vibrometer is performed. The design strategies proposed in this paper can be integrated into a wide range of lattice-based materials for noise and vibration control applications and biomedical devices.

2-D lattice structures have gained considerable attention over the past few decades due to their high strength-to-weight ratio. Enormous studies have been conducted on various shapes of the 2D lattice structures. Different shapes of the 2-D lattices exhibit different Poisson’s ratio values. The Poisson’s ratio ranges from negative to positive values for conventional lattice structures such as honeycomb and auxetic honeycomb lattice structures. However, there exist such lattice structures that exhibit Zero Poisson’s Ratio (ZPR). In this article, we propose a novel hourglass structure (HG) that exhibits Zero Poisson’s Ratio (ZPR HG), studied dispersion behaviour, and compared with negative (Aux HG) and positive (Hcb HG) Poisson’s Ratios. The emergence of the band structure in the HG-ZPR has been studied analytically and compared with the conventional hourglass structures that exhibit positive/negative Poisson’s ratio. The dependency of the band structure on Poisson’s ratio has been investigated. A significant variation in the band structure has been observed as the microstructure of the hourglass structure varies. This study intends to provide the necessary physical insights showing the dependency of the band structure on Poisson’s ratio.

Low-frequency bandgaps are generally achieved by using locally resonant metamaterials at much higher wavelengths than the lattice constant. However, it remains a challenge to control wave propagation and vibration in these structures due to the limited number of conventional options available as periodic unit cell arrangements. This work investigates the band structure of flexural waves in a metamaterial sandwich beam with an hourglass lattice core using the transfer matrix method. The double dome-shaped hourglass unit cell is modelled with different non-dimensional geometric ratios. A sandwiched metamaterial beam model is then established using a periodic finite hourglass array, considered under the flexural wave propagation. The complete hourglass sandwiched system is further studied to obtain the bandgaps corresponding to the microstructure of the hourglass which is varied in the frequency domain. Subsequently, parametric analysis is performed using some specific non-dimensional geometric parameters that are found to be sensitive towards tailoring the mechanical properties of such unit cells. This study builds a foundation for modelling lightweight hourglass lattice sandwich beams with complex dome shape structures and presents guidelines for designing sandwich beams to control wave propagation.

Nonreciprocity and topologically protected wave propagation have significant implications on how energy and information are transmitted or guided within materials to control or mitigate its effects. The major challenge in tailoring interface mode arises from challenges related to the customizability and linearity of interface lattice, moreover, there is a scarce of experimental analysis reported in the literature. Our study has focused on obtaining topologically protected nontrivial interface modes at a specific frequency by breaking the inversion symmetry through novel hourglass metastructure both theoretically and experimentally. Detailed work on wave transmission, dispersion, and bandgap analysis are carried out considering topological metamaterials. New cellular configurations based on regular honeycomb and auxetic cells, and variations of their geometric parameters responsible for interface mode tuning are reported here. A generalized theoretical scheme for different combinations of the hourglass lattice is derived at the interface, and consequent energy harvesting and damping prospects are reported. Analytical modeling of topological metamaterial lattice along with numerical simulation, additive layer manufacturing (3D printing), and finally experimental validations are carried out to justify the behavior and reveal the underlying physics responsible for its unique behavior. Three types of configurations including hourglass lattice at the interface define a general framework for introducing lattice-based imperfections in the continuous elastic structure for potential engineering applications. The localized topological interface mode obtained within the bandgap can be tuned significantly with the help of latticed hourglass and may be utilized for the purpose of wave guiding, wave focusing, and energy harvesting within the isolation zone.

This study reports the presence of an interface mode in the one-dimensional topologically arranged mechanical metamaterials using mechanical dome shaped metastructures which can be exhibited by hourglass configurations. The paper proposes the method of obtaining a localized interface mode within the bandgap using the hourglass shaped resonating elements in the one dimensional topologically arranged chain. Implementing a wide range of different re-entrant angles on the patterns imprinted on dome shaped hourglass metastructure ranging from negative to positive re-entrant angle would lead to lattice dependent stiffness characteristics in the system. The primary unit cell considered in this system is diatomic unit cell having identical masses and alternating spring stiffness driven by the dome shaped hourglass metastructure. Moreover, the variation in the stiffness of hourglass metastructure is also dependent on the height to thickness ratio which is also explored in this study to restrict the stiffness of hourglass unit in the linear regime which is easily obtainable in small deformation range. The interface unit cell is placed in the one-dimensional chain in such a way that inversion symmetry is broken using the different classes of hourglass lattice metastructures within the unit cell. The frequency response function of the one dimensional topologically protected chain is analytically computed and the interface mode is observed locally within the bandgap. The possibility of wave propagation at specific frequencies within the bandgaps is strategically achieved by defining lattice-dependent stiffness parameters at the interface modes. The considered configurations define a framework for introducing lattice-based imperfections in the continuous elastic structures that makes it potential engineering relevance.

Background: The architected mechanical metastructures have garnered significant research attention for various engineering applications due to their remarkable mechanical properties and unique deformation behavior. The lattice-based micro-structured materials have shown enhanced mechanical properties and the ability to control wave propagation, making them ideal for multifunctional applications. Objective: We report the family of lattice-based hourglass metastructures within the optimal design scope and its geometrical parameter selection. The lattice-based energy absorption performance and their damping characteristics have been classified based on different constitutive lattices. Methods: Herein, the uniaxial compressive response and lattice-based energy absorption capacity of a novel hybrid configuration, hourglass-shaped, consists of auxetic and honeycomb-based lattice, are systematically investigated through theoretical, finite element simulation and experimental methods. The proposed hourglass-shaped unit cell is a combination of two oppositely oriented coaxial domes that give more flexibility to control dynamic response and enhance lattice functionality passively. An additive manufacturing route has fabricated a series of hourglass-shaped lattice metastructures with nylon-based material. Results: It was found from the experimental data that the Ideal energy absorption efficiency parameter (E _i) is highest for the case of the auxetic-based hourglass with the increment of 22% and 35% than the solid shell and honeycomb lattice-based metastructure, respectively. The specific energy absorption parameters data have also been evaluated and compared with the numerical computational results. Conclusion: The combination of numerical simulation, additive layer manufacturing (3D printing), and experimental testing are implemented to quantitatively determine the lattice-based energy absorption properties and justify their evaluation. This study suggests the utilization of novel hourglass lattice-based metastructure for multifunctional engineering applications.

A novel hourglass-shaped lattice metamaterial with broadband and multiband characteristics is studied here. Its unique shape helps to evolve customizable stiffness profiles, which makes it succeed in significantly magnifying the vibration attenuation capability. The general concept of a locally resonant phononic crystal is used to design the proposed metamaterial with a wide bandgap. The concept utilizes elastic wave resonances to form constructive or destructive interference, which creates ranges of frequencies at which waves are either allowed to propagate (pass bands) or blocked in one (stop bands) or multiple directions (complete band gaps (BGs)). The bandgap depends on the geometric configuration and material of the unit cell, stiffness properties of the periodic structure as well as host matrix of the resonating mass, which has been exploited in designing the metamaterial. The unit cell is designed with the hourglass lattice integrated with a cubic resonating mass at the center which helps to induce ultrawide bandgaps with effective mechanical properties. A detailed bandgap analysis has been performed for a spherical and parabolic hourglass-based matrix with various parametric combinations. After numerical simulation, additive layer manufacturing (3D printing) and experimental testing are carried out to evaluate the system and reveal the underlying physics responsible for their unique dynamic behavior.

This study reports numerical modeling of phononic-based crystals with the hourglass lattice periodically arranged in 2D space. The investigated resonant elements include dome shape metastructure as well as their various combinations, in particular, hourglass configurations. The mechanical wave band structure and transmission characteristics of such systems have been computed using finite element simulations performed in Comsol multiphysics. The general concept of a locally resonant phononic crystal is proposed. The concept utilizes elastic wave resonances to form constructive or destructive interference, which creates ranges of frequencies at which waves are either allowed to propagate (pass bands) or block in one (stop bands) or any direction (complete band gaps). The bandgap depends on the configuration of the periodic structure, the material of scattering unit, and that of a host matrix, which has been explored in this study. The unit cell consists of hourglass-shaped resonators repeated in two orthonormal directions, making it a 2D phononic meta material. The existence of a separate attenuation mechanism associated with the hourglass resonant elements that increase performance in the lower frequency regime has been identified. The results show formation of broadband gaps positioned significantly below the first Bragg frequency. The most optimal configuration is the crystal for low-frequency broadband attenuation, where each scattering unit is composed of multiple hourglass-based resonators. This system forms numerous gaps in the lower frequency regime, below Bragg bands, while maintaining a reduced crystal size viable for vibration isolation technology. The finding opens alternative perspectives for the construction of vibration mitigation in the low-frequency range, usually inaccessible by traditional means, including conventional phononic crystals.

In this work, the vibration transmissibility behavior of novel dome shaped auxetic structures with different cellular configurations are simulated using Abaqus 6.14 and subsequently studied experimentally. The dynamic behavior of domes and hourglass shape auxetic structures are studied within the frequency bandwidth of 5-500 Hz by using base excitation technique. The auxetic samples are subjected to broadband excitation at low dynamic strain, followed by sine sweep around the resonance of the system. The dynamic and modal behaviors are experimentally analyzed by using 3D Laser Doppler Vibrometer. The system is shown to develop specific wave propagation and attenuation bands, outline of which is important for developing strategies for damping/energy harvesting. Further, analysis has been carried out to analyze the mechanical wave propagation behavior when the system is subjected to broadband excitation frequency at low dynamic strains. Here, we have arranged a large periodic repeating units of hourglass shape auxetics with lumped mass inside it placed at the center. The equivalent spring-mass-damper mechanical circuit has been developed for the shake of simplifying our system. The Non-linear stiffness of hourglass structure depend upon constitutive cellular cells i.e. auxetic, regular honeycomb and plane, which is evident for getting broader bandgap formation than the linear one. The lumped mass is considered here as locally resonating metamaterial enabling low-frequency vibration attenuation. Furthermore, the analysis is being done for bandgap expressions depending upon the added mass ratio and target frequency. Further study is proposed for attenuation and transmission band analysis to steer the waves which roots the idea of vibration sink, in which we can damp the mechanical waves effectively at a specific location. The Auxetic meta-materials are envisaged to have a significant role in wave attenuation and wave steering, and can be used effectively for vibration control.

Continuous demand for the improvement of mechanical performance of engineering structures pushes the need for metastructures to fulfil multiple functions. Extensive work on lattice-based metastructure has shown their ability to manipulate wave propagation and producing bandgaps at specific frequency ranges. Enhanced customizability makes them ideal candidates for multifunctional applications. This paper explores a wide range of nonlinear mechanical behavior that can be generated out of the same lattice material by changing the building block into dome shaped structures which improves the functionality of material significantly. We propose a novel hourglass shaped lattice metastructure that takes advantage of the combination of two oppositely oriented coaxial domes, providing an opportunity for higher customizability and the ability to tailor its dynamic response. Six new classes of hourglass shaped lattice metastructures have been developed through combinations of solid shells, regular honeycomb lattices and auxetic lattices. Numerical simulation, analytical modelling, additive layer manufacturing (3D printing) and experimental testing are implemented to justify the evaluation of their mechanics and reveal the underlying physics responsible for their unusual nonlinear behaviour. We further obtained the lattice dependent frequency response and damping offered by the various classes of hourglass metastructures. This study paves the way for incorporating hourglass based oscillators to be used as building block of future mechanical metamaterials, leading to a new class of tunable metamaterial over a wide range of operating frequencies. The proposed class of metastructure will be useful in applications where lightweight and tunable properties with broadband vibration suppression and wave attenuation abilities are necessary.

The auxetic meta-material is a special class of macro-structure designed for exhibiting negative Poisson's ratio. The spatial repetition of the lattice affects the wave propagation and dynamic responses. In this study, a mathematical basis of Bloch analysis for auxetic media have been presented and shaded some important light on the application of the technique. For this design an analysis has been carried out to show how the periodic boundary condition changes with the connectivity, orientation and geometry of unit lattice. The corresponding eigen value problem is developed to obtain the propagation frequency which is the function of mass, stiffness matrix and the wave vector. Mapping of different forms which are associated with the nodal displacements of a unit cell to adjacent cell have been demonstrated and formulated mathematically and observed its effect on the reduced stiffness and mass matrices is studied. Modal analysis has been carried out using Abaqus 6.14 and the transverse nodal displacements obtained from the F.E analysis. The Bloch formulation for revolving-square type auxetic structure has been formulated and validated. Further, we have obtained the changes in auxetic behavior of the structure under different boundary conditions. The periodicity of a given lattice assists in determining the frequency bands within which the propagation of elastic waves is permitted. Further study is proposed for attenuation and transmission band analysis to steer the waves which roots the idea of vibration sink, in which we can damp the mechanical waves effectively at a specific location. The Auxetic meta-materials is envisaged to have a significant role in wave attenuation and wave steering, and can be used effectively for vibration control.