Band gap transmission in periodic bistable mechanical systems

Frazier, Michael J.; Kochmann, Dennis M.

doi:10.1016/j.jsv.2016.10.041

Cited by 79 publications

(33 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In equations (15) and (16), K is the Jacobi's incomplete elliptic integral of the first kind, am is the Jacobi's amplitude function, sn is the Jacobi's sine amplitude function,…”

Section: )mentioning

confidence: 99%

“…Following the new paradigm of exploiting (instead of avoiding) instabilities in the structural design for advanced applications [17,29], in the last years many researchers have investigated the snap mechanisms towards the realization of bistable or multistable devices [2,9,10,11,12,13,30,32], metamaterials [15,25,28], locomotion [24,33,34,35], and energy harvesting [16,18]. Because the typical approach adopted in these investigations is to focus on specific evolutive mechanical problems and specific structural properties, the evaluation of the whole set of critical snap conditions is missed from a general perspective.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Snapping of elastic strips with controlled ends

Cazzolli

Corso

2019

International Journal of Solids and Structures

View full text Add to dashboard Cite

Snapping mechanisms are investigated for an elastic strip with ends imposed to move and rotate in time. Attacking the problem analytically via Euler's elastica and the second variation of the total potential energy, the number of stable equilibrium configurations is disclosed by varying the kinematics of the strip ends. This result leads to the definition of a 'universal snap surface', collecting the sets of critical boundary conditions for which the system snaps. The elastic energy release at snapping is also investigated, providing useful insights for the optimization of impulsive motion. The theoretical predictions are finally validated through comparisons with experimental results and finite element simulations, both fully confirming the reliability of the introduced universal surface. The presented analysis may find applications in a wide range of technological fields, as for instance energy harvesting and jumping robots.

show abstract

“…In equations (15) and (16), K is the Jacobi's incomplete elliptic integral of the first kind, am is the Jacobi's amplitude function, sn is the Jacobi's sine amplitude function,…”

Section: )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Snapping of elastic strips with controlled ends

Cazzolli

Corso

2019

International Journal of Solids and Structures

View full text Add to dashboard Cite

show abstract

“…Over decades, those have motivated numerous theoretical studies to characterize the motion of domain walls and phase boundaries particularly in 1D periodic physical, chemical, or biological systems, see, e.g., Refs. [117] and [278][279][280][281][282][283][284][285]. A related phenomenon is the transition wavelike propagation of signals in chains made of rigid elements with zero-energy modes [286].…”

Section: -16 / Vol 69 September 2017mentioning

confidence: 99%

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Kochmann

Bertoldi

2017

Applied Mechanics Reviews

Self Cite

181

View full text Add to dashboard Cite

Instabilities in solids and structures are ubiquitous across all length and time scales, and engineering design principles have commonly aimed at preventing instability. However, over the past two decades, engineering mechanics has undergone a paradigm shift, away from avoiding instability and toward taking advantage thereof. At the core of all instabilities-both at the microstructural scale in materials and at the macroscopic, structural level-lies a nonconvex potential energy landscape which is responsible, e.g., for phase transitions and domain switching, localization, pattern formation, or structural buckling and snapping. Deliberately driving a system close to, into, and beyond the unstable regime has been exploited to create new materials systems with superior, interesting, or extreme physical properties. Here, we review the state-of-the-art in utilizing mechanical instabilities in solids and structures at the microstructural level in order to control macroscopic (meta)material performance. After a brief theoretical review, we discuss examples of utilizing material instabilities (from phase transitions and ferroelectric switching to extreme composites) as well as examples of exploiting structural instabilities in acoustic and mechanical metamaterials.

show abstract

“…In addition to the modes k 1 , k 3 and 3k 1 introduced in equation (30), the first-order modes k 3 -2k 1 and 4k 1 -k 3 , and the third-order modes 2k 3 -3k 1 and 6k 1 -k 3 appear in equation (31). If k 3 =3k 1 , these modes will be reduced to k 1 and k 3 .…”

Section: Fc Solutionmentioning

confidence: 99%

“…In addition, multistate behavior of a wave in the bandgap is observed in NAMs [29]. Bistable periodic structures [31][32][33] also lead to interesting phenomena such as bandgap transmission.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation in a nonlinear acoustic metamaterial beam considering third harmonic generation

Fang

Wen

et al. 2018

New J. Phys.

View full text Add to dashboard Cite

Nonlinear acoustic metamaterials (NAMs) provide new ways to control elastic waves. In this work, flexural wave propagation in an infinite NAM beam consisting of periodic Duffing resonators is reported by considering the third harmonic generation. Different analytical methods are proposed for the homogenized medium. By combining analytical and numerical approaches, we unveiled extensive physical properties of NAMs, including the nonlinear resonance, the effective density, the nonlinear locally resonant (NLR) bandgap, passbands, and the propagation and coupling of the fundamental and third harmonics. These characteristics are highly interrelated and they feature an identical nearfield bifurcation frequency, which facilitates the prediction of functionalities. Moreover, we found that the NLR bandgap characterizes a distance-amplitude-dependent behavior that leads to a selfadaptive bandwidth in the far field. Our work will promote future studies, constructions and applications of NAMs with novel properties.

show abstract

Band gap transmission in periodic bistable mechanical systems

Cited by 79 publications

References 44 publications

Snapping of elastic strips with controlled ends

Snapping of elastic strips with controlled ends

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Wave propagation in a nonlinear acoustic metamaterial beam considering third harmonic generation

Contact Info

Product

Resources

About