Controllable wave propagation in a weakly nonlinear monoatomic lattice chain with nonlocal interaction and active control

Wang, Jiao; Zhou, Weijian; Huang, Yang; Lyu, Chaofeng; Chen, Weiqiu; Zhu, Wei

doi:10.1007/s10483-018-2360-6

Cited by 21 publications

(3 citation statements)

References 34 publications

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“…There are some significant limitations pertinent to employing the nonlocal model including paradox outcomes for some special case models of boundary conditions and loading such as a concentrated load at free end, or a clamped-pinned (C-P) as well as C-C boundary condition models. Furthermore, the differential model, higher-order model, and integral form give various results in different ranges of loading or boundary conditions with various applications [252][253][254][255][369][370][371][372][373][374][375][376][377][378].…”

Section: Nonlocal Elasticity Of Eringenmentioning

confidence: 99%

A review of size-dependent continuum mechanics models for micro- and nano-structures

Roudbari

Jorshari

et al. 2022

Thin-Walled Structures

120

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Section: Nonlocal Elasticity Of Eringenmentioning

confidence: 99%

A review of size-dependent continuum mechanics models for micro- and nano-structures

Roudbari

Jorshari

et al. 2022

Thin-Walled Structures

120

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“…Perturbation methods were used in solving weakly nonlinear wave problems [19][20][21][22][23]. Vakakis et al [8,24] used a multi-scale perturbation method to study a nonlinear periodic system with external excitations.…”

Section: Introductionmentioning

confidence: 99%

Steady-State Wave Responses of One-Dimensional Multi-Degree-of-Freedom Lattices with Strong Nonlinearities by an Improved Incremental Harmonic Balance Method

Wang

Zhao

et al. 2022

Preprint

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The nonlinearity plays an important role in modulation of wave propagation characteristics, such as the adjustment of band structures by media nonlinearities. There was a modified incremental harmonic balance (IHB) method developed to hand single- and two-degree-of-freedom (2-DoF) wave propagation problems with nonlinearities. When the nonlinearity is strong, high-order basis functions are used to achieve accurate solutions, which requires complex formula derivation and high computational effort, especially for a general multi-DoF wave problem. To handle the issue, an improved IHB method is developed for solving multi-DoF wave problems with strong nonlinearities. In the method, construction of analytical Jacobian matrices of delay differential equations that are transformed from original wave problems is formulated for any DoFs and expansion orders, by which no manual derivation and numerical integration are needed. Thus, computational effort can be significantly reduced, and convergence analysis of solutions obtained from the IHB method with different expansion orders can be conducted to determine the minimum order of stable solutions, which has not been done for wave problems with strong nonlinearities. Moreover, the algorithm to solve nonlinear wave problems with given frequencies and unknown wave vectors is newly proposed in this work based on the improved IHB method, which is can be a more efficient approach if external excitations are given. In this work, one-dimensional diatomic lattices with Hertz contact law and cubic spring models are studied as examples, where dispersion curves and bandgap properties are generated. Results show that it is necessary to use high-order Fourier functions to obtain accurate steady-state wave responses when strong nonlinearities exist, which was not explicitly recognized in past works without convergence analysis for wave problems. Results also show that the convergence rate of the method with use of a fixed frequency is faster than that of a fixed wave vector.

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“…Pnevmatikos et al proposed the concept of second-neighbor interactions in the 1D mass-spring structure and calculated the soliton solutions [33]. Wang et al found that the nonlocal effect in a monoatomic lattice can change the direction and the speed of the transporting wave energy [34].…”

Section: Introductionmentioning

confidence: 99%

Abnormal wave propagation behaviors in two-dimensional mass–spring structures with nonlocal effect

Wang

Huang

Chen

et al. 2019

Mathematics and Mechanics of Solids

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This paper considers the propagation of elastic waves in periodic two-dimensional mass–spring structures with diagonal springs. The second-neighbor interactions in non-diagonal directions are included to account for the nonlocal effect. The influences of the spring stiffness in the diagonal directions and the nonlocal effect on the propagation characteristics of elastic waves are then scrutinized. Through the dispersion relation curve and the equi-frequency contours, it is seen that when the diagonal spring stiffness increases, the slope of the second curve in the [Formula: see text]–M direction will not always be positive, meaning that the negative group velocity occurs. Therefore, an incident wavevector with a chosen angle to the negative group velocity can lead to the negative refraction phenomenon in the two-dimensional mass–spring structure. Another interesting phenomenon called directional radiation of elastic waves can also be achieved by adjusting the nonlocal effect. Within a certain range, the stronger the nonlocal effect in a specific direction is, the more obviously the elastic waves propagate along this direction. In this paper, we theoretically analyze and numerically simulate the phenomena of negative refraction and directional wave propagation by choosing a proper set of parameters of the two-dimensional mass–spring structure.

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Controllable wave propagation in a weakly nonlinear monoatomic lattice chain with nonlocal interaction and active control

Cited by 21 publications

References 34 publications

A review of size-dependent continuum mechanics models for micro- and nano-structures

A review of size-dependent continuum mechanics models for micro- and nano-structures

Steady-State Wave Responses of One-Dimensional Multi-Degree-of-Freedom Lattices with Strong Nonlinearities by an Improved Incremental Harmonic Balance Method

Abnormal wave propagation behaviors in two-dimensional mass–spring structures with nonlocal effect

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