Elasticity and Geometry

Audoly, Basile; Pomeau, Yves

doi:10.1142/9789812792778_0001

Cited by 195 publications

(395 citation statements)

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“…The dynamics of elastic waves propagating in a thin plate is described by the Föppl-von Kármán (FvK) equa-tion for the displacement ζ and the momentum p via the Airy stress potential χ [1,2]. Under the periodic boundary condition, the FvK equation is written as…”

Section: Formulation a Governing Equation And Numerical Schemementioning

confidence: 99%

“…Corresponding to the linear and nonlinear terms in dp k /dt, the transfer of the kinetic energy T Kk consists of the quadratic and quartic parts, T (2) Kk and T (4) Kk , i.e., T Kk =dK k /dt = T (2) Kk + T (4) Kk . From Eqs.…”

Section: B Energy Budgetmentioning

confidence: 99%

“…Although the kinetic energy is represented as a quadratic function of the complex amplitude, its transfer has both quadratic part T (2) Kk and quartic part T (4) Kk . While the transfer of the bending energy T V b k is a quadratic function of the complex amplitude, that of the stretching energy T Vsk is a quartic function.…”

Section: B Energy Budgetmentioning

confidence: 99%

“…In Refs. [1,2], the energy is decomposed into kinetic, bending and stretching energies to derive the governing equation of the elastic waves.…”

Section: Introductionmentioning

confidence: 99%

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Single-wave-number representation of nonlinear energy spectrum in elastic-wave turbulence of the Föppl–von Kármán equation: Energy decomposition analysis and energy budget

Yokoyama

Takaoka

2014

Phys. Rev. E

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A single-wavenumber representation of nonlinear energy spectrum, i.e., stretching energy spectrum is found in elastic-wave turbulence governed by the Föppl-von Kármán (FvK) equation. The representation enables energy decomposition analysis in the wavenumber space, and analytical expressions of detailed energy budget in the nonlinear interactions are obtained for the first time in wave turbulence systems. We numerically solved the FvK equation and observed the following facts. Kinetic and bending energies are comparable with each other at large wavenumbers as the weak turbulence theory suggests. On the other hand, the stretching energy is larger than the bending energy at small wavenumbers, i.e., the nonlinearity is relatively strong. The strong correlation between a mode a k and its companion mode a −k is observed at the small wavenumbers. Energy transfer shows that the energy is input into the wave field through stretching-energy transfer at the small wavenumbers, and dissipated through the quartic part of kinetic-energy transfer at the large wavenumbers. A total-energy flux consistent with the energy conservation is calculated directly by using the analytical expression of the total-energy transfer, and the forward energy cascade is observed clearly.

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Section: Formulation a Governing Equation And Numerical Schemementioning

confidence: 99%

Section: B Energy Budgetmentioning

confidence: 99%

Section: B Energy Budgetmentioning

confidence: 99%

“…In Refs. [1,2], the energy is decomposed into kinetic, bending and stretching energies to derive the governing equation of the elastic waves.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Single-wave-number representation of nonlinear energy spectrum in elastic-wave turbulence of the Föppl–von Kármán equation: Energy decomposition analysis and energy budget

Yokoyama

Takaoka

2014

Phys. Rev. E

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“…These expressions more clearly show the energy balance among the kinetic, bending, and stretching energies than those in Eq. (18). For example, a similar expression corresponding to the detailed energy balance, Eq.…”

Section: B Energy Transfers In Real Spacementioning

confidence: 99%

Integrated analysis of energy transfers in elastic-wave turbulence

Yokoyama

Takaoka

2017

Phys. Rev. E

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In elastic-wave turbulence, strong turbulence appears in small wave numbers while weak turbulence does in large wave numbers. Energy transfers in the coexistence of these turbulent states are numerically investigated in both of the Fourier space and the real space. An analytical expression of a detailed energy balance reveals from which mode to which mode energy is transferred in the triad interaction. Stretching energy excited by external force is transferred nonlocally and intermittently to large wave numbers as the kinetic energy in the strong turbulence. In the weak turbulence, the resonant interactions according to the weak turbulence theory produces cascading net energy transfer to large wave numbers. Because the system's nonlinearity shows strong temporal intermittency, the energy transfers are investigated at active and moderate phases separately. The nonlocal interactions in the Fourier space are characterized by the intermittent bundles of fibrous structures in the real space.

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Leveraging the Snap Buckling of Bistable Magnetic Shells to Design a Refreshable Braille Dot

Abbasi,

Chen,

Aymon

et al. 2023

Adv Materials Technologies

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A design concept is proposed for the building block, a dot, of programmable braille readers utilizing bistable shell buckling, magnetic actuation, and pneumatic loading. The design process is guided by Finite Element simulations, which are initially validated through precision experiments conducted on a scaled‐up, single‐shell model system. Then, the simulations are leveraged to systematically explore the design space, adhering to the standardized geometric and physical specifications of braille systems. The findings demonstrate the feasibility of selecting design parameters that satisfy both geometric requirements and blocking forces under moderate magnetic fields, facilitated by pneumatic loading to switch between the two stable states. While the study is focused on experimentally validated numerical simulations, it is also identify several manufacturing challenges that need to be resolved for future physical implementations .

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Elasticity and Geometry

Cited by 195 publications

References 0 publications

Single-wave-number representation of nonlinear energy spectrum in elastic-wave turbulence of the Föppl–von Kármán equation: Energy decomposition analysis and energy budget

Single-wave-number representation of nonlinear energy spectrum in elastic-wave turbulence of the Föppl–von Kármán equation: Energy decomposition analysis and energy budget

Integrated analysis of energy transfers in elastic-wave turbulence

Leveraging the Snap Buckling of Bistable Magnetic Shells to Design a Refreshable Braille Dot

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