Interactions beyond nearest neighbors in a periodic structure: Force analysis

Farzbod, Farhad; Scott‐Emuakpor, Onome

doi:10.1016/j.ijsolstr.2020.04.014

Cited by 12 publications

(11 citation statements)

References 31 publications

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“…Other types of micro-structures, such as layered media, or unit cells with solid inclusions in a solid matrix, are not the suitable modeling target for the proposed ROM (instead, one can use RBME 26 ). In addition, the proposed ROM approach is only applicable to systems with stiffness coupling between nearest neighbors, i.e., the long-range interaction 41 is not considered.…”

Section: Discussionmentioning

confidence: 99%

Reduced Order Modeling of Dynamic Mechanical Metamaterials for Analysis of Infinite and Finite Systems

Wang¹,

Amirkhizi²

2023

Preprint

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Dynamic mechanical metamaterials (MMs) are artificial media composed of periodic micro-structures, designed to manipulate wave propagation. Modeling and designing these materials can be computationally demanding due to the broad design space spanned by a range of geometric and material parameters. This work aims to develop a generalized reduced order modeling (ROM) approach for determining MM dynamics in low frequency ranges with accuracy and speed, using a limited number of parameters and small matrices. The MM unit cells are treated as assemblies of structural elements and discrete degrees of freedom, whose effective stiffness and inertia are determined by optimizing energy criteria based on continuum results derived from a small number of eigen-study simulations. This proposed approach offers a parameterized and discretized representation of MM systems, which leads to fast and accurate computation of eigen-study results for periodic arrays of repeating unit cells, as well as dynamic responses for finite-sized arrays. The high computational efficiency and physical accuracy of this method will help to streamline the modeling process and aid in design discovery and optimization, especially in combination with scientific machine learning and data-driven techniques.

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Section: Discussionmentioning

confidence: 99%

Reduced Order Modeling of Dynamic Mechanical Metamaterials for Analysis of Infinite and Finite Systems

Wang¹,

Amirkhizi²

2023

Preprint

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“…For example, the maximum number of wavevectors at each frequency in periodic materials depends on the various interacting layers (Farzbod, 2017). It was also shown (Farzbod, 2017;Farzbod and Scott-Emuakpor, 2020) that dispersion curves are affected topologically when interactions are not limited to the nearest neighbor. In the following, we show that by using electrostatic forces, it is possible to fabricate such structures.…”

Section: Introductionmentioning

confidence: 99%

Periodic structure with electrostatic forces: Interactions beyond the nearest neighbor

Sudesh

Gagan

Farzbod

2023

Journal of Vibration and Control

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Periodic structures are a type of metamaterial in which the physical properties depend not only on the details of the unit cell but also on how unit cells are arranged and interact with each other. In conventional engineering structures, each unit cell interacts with adjacent cells. Methods developed for vibrational and wave propagation analysis in periodic engineering structures consider only nearest-neighbor interactions. The dispersion curves of such systems, in which only adjacent cells interact, have been extensively studied. Metamaterial properties depend on the interactions of a unit cell with other cells. Further interactions, and specifically, interactions beyond the closest neighbors, imply a more complex band structure and wave behavior. In this paper, an example class of such structures, in which electrostatic forces are the driving force, has been investigated. In this paper, properties affecting these periodic structures, such as elastic forces, have been investigated. An attractive property of such structures is that the band structures of such metamaterials can be tuned by changing electric voltages.

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“…Recent investigations have focused on studying wave propagation in periodic structures, particularly metamaterials, wherein the physical responses of the system are shaped not only by nearestneighbor interactions but also by long-range hoppings. 14 These non-local effects can introduce roton-like dispersion behavior in periodic lattices with beyond-nearest neighbor interactions, [15][16][17][18][19] introducing the local maximums and minimums in dispersion curves within the first Brillouin zone. Apart from the roton-like dispersion, long-range hoppings in one-dimensional topological insulators can affect both bulk topological invariants and edgestates due to the existence of hidden symmetries.…”

Section: Introductionmentioning

confidence: 99%

Inerter-controlled topological interface states in locally resonant lattices with beyond-nearest neighbor coupling

Cajić,

Karličić,

Adhikari

2024

Journal of Applied Physics

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This paper explores the emergence of topological interface states in one-dimensional locally resonant lattices incorporating inerters in both nearest neighbor (NN) and beyond-nearest neighbor (BNN) coupling. The investigation focuses on the unique wave propagation characteristics of these lattices, particularly the presence and behavior of interface states. The non-trivial topological behavior due to broken inversion symmetry within the unit cell of the locally resonant lattice is comprehensively investigated in the presence of inerters in NN and BNN coupling. The emerging interface states in the supercell analysis exhibit specific spatial and frequency localization properties due to inerter-based BNN interactions. Additionally, the study demonstrates the ability of inerter elements with weak inertance to control the frequency of interface states while maintaining the fundamental topological properties of the lattice. The identified topological interface states in lattices with BNN coupling present an opportunity for designing diverse devices, such as waveguides, filters, sensors, and energy harvesting systems. Overall, this research enhances our comprehension of topological phenomena in inerter-based locally resonant lattices with BNN interactions and introduces possibilities for creating robust and versatile devices based on topologically protected edge/interface states.

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Interactions beyond nearest neighbors in a periodic structure: Force analysis

Cited by 12 publications

References 31 publications

Reduced Order Modeling of Dynamic Mechanical Metamaterials for Analysis of Infinite and Finite Systems

Reduced Order Modeling of Dynamic Mechanical Metamaterials for Analysis of Infinite and Finite Systems

Periodic structure with electrostatic forces: Interactions beyond the nearest neighbor

Inerter-controlled topological interface states in locally resonant lattices with beyond-nearest neighbor coupling

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