Exact and nonlocal solutions for vibration of multiply connected bar-chain system with direct and indirect neighbouring interactions

Zhang, H.; Challamel, Noël; Wang, Chen; Zhang, Y.P.

doi:10.1016/j.jsv.2018.11.037

Cited by 10 publications

(1 citation statement)

References 23 publications

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“…Challamel et al [31] studied the dynamic behaviors of generalized axial lattices with direct and indirect interactions by considering extra higher-order boundary conditions. Zhang et al [32] discussed the vibration of the multiply connected bar-chain system with direct and indirect interactions and emphasized the effects of long-range interactions on mechanical vibration. Ghavanloo and Fazelzadeh [33] investigated the effect of long-range interactions on the wave propagation in 1D acoustic metamaterials.…”

Section: Introductionmentioning

confidence: 99%

On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model

Wang

Liu

Soh

et al. 2022

Appl. Math. Mech.-Engl. Ed.

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We have proposed an “exact” strain gradient (SG) continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions. The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing. Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice, resulting in a novel SG model. For various kinds of diatomic lattices, the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone, manifesting the robustness of the present model. Based on this SG model, we have conducted the following discussions. (I) Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials, which is very helpful for the design of metamaterials. (II) The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted. Without doing so, the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy. The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone. (III) The effects of the nonlocal interactions are analyzed. The nonlocal interactions reduce the workable range of the well-known long-wave approximation, causing more local extrema in the dispersive diagrams. The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing, i.e., when the long-wave approximation is no longer valid. For the convenience of band gap designs, we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.

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Section: Introductionmentioning

confidence: 99%

On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model

Wang

Liu

Soh

et al. 2022

Appl. Math. Mech.-Engl. Ed.

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Optimal design of functionally graded lattice structures using Hencky bar-grid model and topology optimization

Zhang

Wang

Challamel

et al. 2022

Struct Multidisc Optim

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Presented herein is a novel design framework for obtaining the optimal design of functionally graded lattice (FGL) structures that involve using a physical discrete structural model called the Hencky bar-grid model (HBM) and topology optimization (TO). The continuous FGL structure is discretized by HBM comprising rigid bars, frictionless hinges, frictionless pulleys, elastic primary and secondary axial springs, and torsional springs. A penalty function is introduced to each of the HBM spring’s stiffnesses to model non-uniform material properties. The gradient-based TO method is applied to find the stiffest structure via minimizing the compliance or elastic strain energy by adjusting the HBM spring stiffnesses subjected to prescribed design constraints. The optimal design of FGL structures is constructed based on the optimal spring stiffnesses of the HBM. The proposed design framework is simple to implement and for obtaining optimal FGL structures as it involves a relatively small number of design variables such as the spring stiffnesses of each grid cell. As illustration of the HBM-TO method, some optimization problems of FGL structures are considered and their optimal solutions obtained. The solutions are shown to converge after a small number of iterations. A Python code is given in the Appendix for interested readers who wish to reproduce the results.

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Elasticity solutions for nano-plane structures under body forces using lattice elasticity, continualised nonlocal model and Eringen nonlocal model

Zhang

Challamel

Wang

2021

Continuum Mech. Thermodyn.

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Exact and nonlocal solutions for vibration of multiply connected bar-chain system with direct and indirect neighbouring interactions

Cited by 10 publications

References 23 publications

On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model

On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model

Optimal design of functionally graded lattice structures using Hencky bar-grid model and topology optimization

Elasticity solutions for nano-plane structures under body forces using lattice elasticity, continualised nonlocal model and Eringen nonlocal model

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