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.

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.

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.

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.

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 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.

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.