Flexural vibration band gaps in Euler-Bernoulli beams with locally resonant structures with two degrees of freedom

Yu, Dianlong; Liu, Yaozong; Zhao, Honggang; Wang, Gang; Qiu, Jing

doi:10.1103/physrevb.73.064301

Cited by 206 publications

(114 citation statements)

References 16 publications

Supporting

Mentioning

113

Contrasting

Order By: Relevance

“…Remarkably, in periodic triangular lattices, even with a single material and building block, local resonances can be exploited to generate bandgaps, providing a foundation for the design of a new class of systems to manipulate the propagation of elastic waves. Furthermore, our results also demonstrate that, in order to attenuate the propagation of elastic waves through localized resonances, it is not necessary to embed additional resonating components 23,24,[34][35][36][37][38][39][40][41][42] within the beam lattices. Such singlebuilding-block and single-material system with locally resonant bandgap has been previously realized in onedimensional setup only 43 .…”

mentioning

confidence: 92%

Locally resonant band gaps in periodic beam lattices by tuning connectivity

et al. 2015

View full text Add to dashboard Cite

mentioning

confidence: 92%

Locally resonant band gaps in periodic beam lattices by tuning connectivity

et al. 2015

View full text Add to dashboard Cite

“…[5,[7][8][9][10][11][12][13][14][15][16][17][18]. Elastodynamics of finite or infinite periodic 1D rod or beam structures has been studied in [6,[19][20][21]. Comparisons between Floquet theory ( [1]) based unit cell analysis of a band structure and the vibration response analysis of the corresponding finite periodic structure, are presented in [22] for one-dimensional diatomic chains of uncoupled spheres and in [14] for 1D rod structures, respectively.…”

Section: Introductionmentioning

confidence: 99%

On Optimum Design and Periodicity of Band-Gap Structures

Olhoff¹,

Niu²,

Cheng³

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

View full text Add to dashboard Cite

Abstract. A band-gap structure usually consists of a periodic distribution of elastic materials or segments, where the propagation of waves is impeded or This paper extends earlier optimum shape design results for transversely vibrating Bernoulli-Euler beams by determining new optimum band-gap beam structures for (i) different combinations of classical boundary conditions, (ii) much larger values of the orders n (n>1) and n-1 of adjacent upper and lower eigenfrequencies of maximized band-gaps, and (iii) different values of a minimum beam cross-sectional area constraint. In the present paper, instead of maximizing band-gaps between frequencies of propagating waves or forced vibrations excited by external time-harmonic loads, the closely relatedproblem of maximizing the gap between two adjacent eigenfrequencies ω n and ω n-1 of any given consecutive orders n (n>1) and n-1, is considered. This is justified by the fact that external time-harmonic dynamic loads cannot excite resonance with high vibration levels of standing waves, if the eigenfrequencies of the structure are moved outside the range of the external excitation frequencies by the optimization.Finally, the present study shows that if an infinite beam structure is constructed by repeated translation of an inner beam segment obtained by the aforementioned frequency gap optimization, then a band-gap of traveling waves in this infinite beam is found to correlate almost perfectly with the maximized frequency gap in the finite structure.

show abstract

“…In all these examples, the careful microscale periodic architecture of multiscale engineered material systems leads to an interesting or beneficial effective dynamic behavior on the macroscale. Besides pronounced acoustic band gaps [15,16], this design paradigm has resulted in negative effective dynamic stiffness [17] and mass density [18,19] and combinations of both [20]. Here negative stiffness and negative mass density refer to the effective dynamic properties: An elastic system containing only positive-stiffness elements can demonstrate negative effective dynamic quantities near resonance.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

2014

View full text Add to dashboard Cite

We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.

show abstract

Flexural vibration band gaps in Euler-Bernoulli beams with locally resonant structures with two degrees of freedom

Cited by 206 publications

References 16 publications

Locally resonant band gaps in periodic beam lattices by tuning connectivity

Locally resonant band gaps in periodic beam lattices by tuning connectivity

On Optimum Design and Periodicity of Band-Gap Structures

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

Contact Info

Product

Resources

About