Kirigami-based Elastic Metamaterials with Anisotropic Mass Density for Subwavelength Flexural Wave Control

A novel design of an elastic metamaterial with anisotropic mass density is proposed to manipulate flexural waves at a subwavelength scale. The three-dimensional metamaterial is inspired by kirigami, which can be easily manufactured by cutting and folding a thin metallic plate. By attaching the resonant kirigami structures periodically on the top of a host plate, a metamaterial plate can be constructed without any perforation that degrades the strength of the pristine plate. An analytical model is developed to understand the working mechanism of the proposed elastic metamaterial and the dispersion curves are calculated by using an extended plane wave expansion method. As a result, we verify an anisotropic effective mass density stemming from the coupling between the local resonance of the kirigami cells and the global flexural wave propagations in the host plate. Finally, numerical simulations on the directional flexural wave propagation in a two-dimensional array of kirigami metamaterial as well as super-resolution imaging through an elastic hyperlens are conducted to demonstrate the subwavelength-scale flexural wave control abilities. The proposed kirigami-based metamaterial has the advantages of no-perforation design and subwavelength flexural wave manipulation capability, which can be highly useful for engineering applications including non-destructive evaluations and structural health monitoring.Comment: 7 figure

Nonlinear dynamics of flexural wave turbulence

The Kolmogorov-Zakharov spectrum predicted by the Weak Turbulence Theory remains elusive for wave turbulence of flexural waves at the surface of an thin elastic plate. We report a direct measurement of the nonlinear timescale $T_{NL}$ related to energy transfer between waves. This time scale is extracted from the space-time measurement of the deformation of the plate by studying the temporal dynamics of wavelet coefficients of the turbulent field. The central hypothesis of the theory is the time scale separation between dissipative time scale, nonlinear time scale and the period of the wave ($T_d>>T_{NL}>>T$). We observe that this scale separation is valid in our system. The discrete modes due to the finite size effects are responsible for the disagreement between observations and theory. A crossover from continuous weak turbulence and discrete turbulence is observed when the nonlinear time scale is of the same order of magnitude as the frequency separation of the discrete modes. The Kolmogorov-Zakharov energy cascade is then strongly altered and is frozen before reaching the dissipative regime expected in the theory.Comment: accepted for publication in Physical Review

Non-destructive testing of composite plates by holographic vibrometry

We report on a wide-field optical monitoring method for revealing local delaminations in sandwich-type composite plates at video-rate by holographic vibrometry. Non-contact measurements of low frequency flexural waves is performed with time-averaged heterodyne holography. It enables narrowband imaging of local out-of-plane nanometric vibration amplitudes under sinusoidal excitation, and reveals delamination defects, which cause local resonances of flexural waves. The size of the defect can be estimated from the first resonance frequency of the flexural wave and the mechanical parameters of the observed layer of the composite plate

Scattering theory and cancellation of gravity-flexural waves of floating plates

We combine theories of scattering for linearized water waves and flexural waves in thin plates to characterize and achieve control of water wave scattering using floating plates. This requires manipulating a sixth-order partial differential equation with appropriate boundary conditions of the velocity potential. Making use of multipole expansions, we reduce the scattering problem to a linear algebraic system. The response of a floating plate in the quasistatic limit simplifies, considering a distinct behavior for water and flexural waves. Unlike similar studies in electromagnetics and acoustics, scattering of gravity-flexural waves is dominated by the zeroth-order multipole term and this results in non-vanishing scattering cross-section also in the zero-frequency limit. Potential applications lie in floating structures manipulating ocean waves.Comment: 19 pages, 4 figure

Studies on the influence on flexural wall deformations on the development of the flow boundary layer

Flexural wave-like deformations can be used to excite boundary layer waves which in turn lead to the onset of turbulence in the boundary layer. The investigations were performed with flow velocities between 5 m/s and 40 m/s. With four different flexural wave transmissions a frequency range from 0.2 kc/s to 1.5 kc/s and a phase velocity range from 3.5 m/s to 12 m/s was covered. The excitation of boundary layer waves becomes most effective if the phase velocity of the flexural wave coincides with the phase velocity region of unstable boundary layer waves