Wrinkling of transversely loaded spinning membranes

Delapierre, Mélanie; Chakraborty, Debadi; Sader, John E.; Pellegrino, Sergio

doi:10.1016/j.ijsolstr.2018.01.031

Cited by 19 publications

(15 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There has also been considerable attention focused on the analysis of spinning elastic disks and membranes, in particular focusing on the natural frequencies of transverse oscillations which arise, and the corresponding mode shapes of these eigenmodes (Lamb and Southwell, 1921;Adams, 1987;Delapierre et al, 2018). One application of spinning membranes is the deployment of ultralight solar structures on satellites as the rotation causes the surface of the membrane to remain flat, increasing the propulsive action for solar sailing amongst other applications.…”

Section: Introductionmentioning

confidence: 99%

The boundary layer flow induced above the torsional motion of a disk

Turner

Weidman

2019

Physics of Fluids

View full text Add to dashboard Cite

The boundary layer flow above a disk in torsional motion with azimuthal velocity proportional to r m is investigated for all values of m ≥ 1; here r is the radial coordinate measured from the center of the disk. The resulting flow is a fully three-dimensional exact solution to the steady, axisymmetric boundary layer equations in the form of similarity solutions. We compute wall shear stresses in the radial and azimuthal directions as a function of the torsional exponent m, as well as the flow induced in the far field. The large m asymptotics of the problem are computed and compared with numerical solutions. The induced radial velocity profiles have a 'wall-jet' structure and it is found that both the radial and azimuthal velocity components become confined close to the surface of the disk as m increases.

show abstract

Section: Introductionmentioning

confidence: 99%

The boundary layer flow induced above the torsional motion of a disk

Turner

Weidman

2019

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…In particular, as the rafts continue to rotate faster, inertial forces increase the effective raft tension, reducing the amplitude of transverse vibration. This rotationally induced reduction in out-of-plane motion has been observed previously only in the limit of membranes that are extremely thin relative to their radius, such that the bending stiffness is negligibly small [51][52][53]. In this regime, the deflections of a spinning membrane result in compressive circumferential stresses, which can then lead to buckling around the membrane edge.…”

Section: Rotationally Activated Out-of-plane Bendingmentioning

confidence: 55%

Mechanical properties of acoustically levitated granular rafts

Lim¹,

VanSaders²,

Souslov³

et al. 2021

Preprint

View full text Add to dashboard Cite

We investigate a model system for inertial many-particle clustering, in which sub-millimeter objects are acoustically levitated in air. Driven by scattered sound, levitated grains self-assemble into a monolayer of particles, forming mesoscopic granular rafts with both an acoustic binding energy and a bending rigidity. Detuning the acoustic trap can give rise to stochastic forces and torques that impart angular momentum to levitated objects, activating soft modes in the rotating elastic membrane. As the angular momentum of a quasi-two-dimensional granular raft is increased, the raft deforms from a disk to an ellipse, eventually pinching off into multiple separate rafts, in a mechanism that resembles the break-up of a liquid drop. We extract the raft effective surface tension and bulk modulus, and show that acoustic forces give rise to elastic moduli that scale with the raft size. We also show that the raft size controls the microstructural basis of plastic deformation, resulting in a transition from fracture to ductile failure.

show abstract

“…One possible attractive extension of this study would be to include other external forces, like centrifugal ones, as these forces are relevant in the deployment and stability of spacecraft structures [10]. These forces introduce another dimensionless parameter [14,10] (Inset) original data of [10] the α → 0 limit and Ω = Ω(1 − α) 2 in the α → 1 limit.…”

Section: Discussion and Perspectivesmentioning

confidence: 99%

“…The resulting stretching energy can be relaxed by developing out-of-planes undulations at the expense of some bending energy that is energetically favorable since the sheet thickness is small. Following [13,14,10], two dimensionless parameters control this instability. First, a dimensionless measure of gravity G is defined as :…”

Section: System Descriptionmentioning

confidence: 99%

See 1 more Smart Citation

Disk wrinkling under gravity

Boëdec¹,

Deschamps²

2020

Preprint

View full text Add to dashboard Cite

We study the deflection by gravity of a circular elastic disk deposited on a rigid support. The axisymmetric deflection induces a compressive orthoradial stresses which leads to a wrinkling instability above a critical threshold of the dimensionless gravity force. We study this instability by a combination of experiments, numerical simulations and analytical tools, with a particular focus on the role of geometry. We show that aspect ratio is a crucial parameter that controls both the threshold of instability and the most unstable mode. The influence of this parameter on the threshold can be catched by introducing a new nondimensionalization of the transverse load.

show abstract

Wrinkling of transversely loaded spinning membranes

Cited by 19 publications

References 28 publications

The boundary layer flow induced above the torsional motion of a disk

The boundary layer flow induced above the torsional motion of a disk

Mechanical properties of acoustically levitated granular rafts

Disk wrinkling under gravity

Contact Info

Product

Resources

About