The adverse effect of mechanical vibration is inevitable and can be observed in machine components either on the long- or short-term of machine life-span based on the severity of oscillation. This in turn motivates researchers to find solutions to the vibration and its harmful influences through developing and creating isolation structures. The isolation is of high importance in reducing and controlling the high-amplitude vibration. Over the years, porous materials have been explored for vibration damping and isolation. Due to the closed feature and the non-uniformity in the structure, the porous materials fail to predict the vibration energy absorption and the associated oscillation behavior, as well as other the mechanical properties. However, the advent of additive manufacturing technology opens more avenues for developing structures with a unique combination of open, uniform, and periodically distributed unit cells. These structures are called metamaterials, which are very useful in the real-life applications since they exhibit good competence for attenuating the oscillation waves and controlling the vibration behavior, along with offering good mechanical properties. This study provides a review of the fundamentals of vibration with an emphasis on the isolation structures, like the porous materials (PM) and mechanical metamaterials, specifically periodic cellular structures (PCS) or lattice cellular structure (LCS). An overview, modeling, mechanical properties, and vibration methods of each material are discussed. In this regard, thorough explanation for damping enhancement using metamaterials is provided. Besides, the paper presents separate sections to shed the light on single and 3D bandgap structures. This study also highlights the advantage of metamaterials over the porous ones, thereby showing the future of using the metamaterials as isolators. In addition, theoretical works and other aspects of metamaterials are illustrated. To this end, remarks are explained and farther studies are proposed for researchers as future investigations in the vibration field to cover the weaknesses and gaps left in the literature.

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Sandwich structures are widely used due to their light weight, high specific strength, and high specific energy absorption. Three-dimensional (3D) printing has recently been explored for creating the lattice cores of these sandwich structures. Experimental evaluation of the mechanical response of lattice cell structures (LCSs) is expensive in time and materials. As such, the finite element analysis (FEA) can be used to predict the mechanical behavior of LCSs with many different design variations more economically. Though there have been several reports on the use of FEA to develop models for predicting the post-yielding stages of 3D-printed LCSs, they are still insufficient to be a more general purpose due to the limitations associated with the lattice prediction behavior of specific features, certain geometries, and common materials along with showing sometimes poor prediction due to the computationally cheap elements out of which these models have been composed in most cases. This study focuses on the response of different LCSs at post-yielding stages based on the hexahedral elements to capture accurately the behaviors of 3D-printed polymeric lattices made of the Acrylonitrile Butadiene Styrene material. For this reason, three types of lattices such as body centered cubic, tetrahedron with horizontal struts, and pyramidal are considered. The FEA models are developed to capture the post-yielding compressive behavior of these different LCSs. These models are used to understand and provide detailed information of the failure mechanisms and relation between post-yielding deformations and the topologies of the lattice. All of these configurations were tested before experimentally during compression in the z-direction under quasi-static conditions and are compared here with the FEA results. The post-yielding behavior obtained from FEA matches reasonably well with the experimental observations, providing the validity of the FEA models.

The objective of this study is to develop generalized empirical closed‐form equations to predict the compressive mechanical properties and determine geometrical parameters. To achieve that, 117 models are built and analyzed using ABAQUS/CAE 2016 to provide two types of reliable data: one for lattice mechanical properties based on finite element method and the other for geometrical parameters using the measurements of ABAQUS diagnostic tool. All the models are created by modifying the basic feature of body‐centered cubic lattice structure based on a range of strut angles, a set of relative densities, and two design sets. Also, the influence of lattice cell tessellations and material distribution at strut intersections are considered within these models to provide accurate results. The first data set is fitted with the scaling laws, relating relative elastic modulus and stress with the relative density, to determine Gibson and Ashby's coefficients. The second type of data regarding lattice geometries is correlated with the relative density to estimate actual lattice volume, strut radius, aspect ratio, and overall lattice volume. By this way, these equations can be used to predict directly the lattice characteristics and geometrical parameters without the need for ABAQUS. The results show that the generalized empirical closed‐form equations can predict well both the lattice characteristics and geometries. In addition, the relative stresses and elastic modulus increase with increasing the strut angles since the main deformation mechanisms move toward stretch‐dominated rather than bending. Besides, Gibson and Ashby's coefficients along with the geometrical factors of aspect ratios are found to be approximately similar for both generations. This study contributes to developing efficient equations to provide the researchers with a preliminary insight about the best lattice design and its compatibility in a certain application before starting the fabrication process.

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