Directional Wave Propagation Research Articles

Aircraft icing detection via flow-induced ambient random noise: from theory to wind tunnel experiments

Aircraft icing is a serious threat to flight safety. This paper presents a passive approach to detect ice accreted on an airfoil using flow-induced random noise considering spatially-inhomogeneous transient excitations. Under the assumption of diffuse-field, by computing the cross-correlation of ambient vibration measured at two receivers and band-pass filtering it, the guided wave dispersion curve of the structure can be well-reconstructed, by which one can estimate the ice thickness by matching the reconstructed dispersion curve with its theoretical model. In practice, however, the diffuse-field assumption may not hold as spatially-inhomogeneous strong transient excitations exist. The associated directional wave propagation generates additional peaks in the cross-correlation and this contaminates the ice detection result. Therefore, this paper proposes a signal processing technique to identify and suppress the contributions from the transient source in the measurements, by which a reliable dispersion curve reconstruction and an accurate ice detection can be retrieved. The proposed method is shown to be efficient via a wind tunnel experiment. The passive ice detection method is specifically suitable for aircraft online monitoring because only passive sensors are needed which can be tiny, light, and mounted on the internal surface of fuselage skin without any influence on aircraft aerodynamics.

Generation of quasi-traveling waves in a finite rectangular membrane with two internal viscoelastic line supports

In this work we study the forced vibration of a finite rectangular membrane driven by arbitrarily distributed boundary motion on two adjacent edges and internally coupled with multiple viscoelastic line supports, as an extension of the analysis of coexisting vibrations and waves in one-dimensional elastic strings and ducts. Using the static solution for the membrane displacement in the absence of interior supports, the response of the nonclassically damped system is obtained through a normal-mode expansion. A traveling-wave index based on complex orthogonal decomposition is utilized to identify and optimize the traveling waves in the rectangular membrane. A vibration localization condition in a semi-infinite membrane is analytically derived, from which the complex boundary excitations and constraints in a finite membrane are specified to effectively realize pure traveling waves and confine the vibration to a restricted area. Then the membrane is edge-driven by a simpler time-periodic, spatially sinusoidal excitation for practical realization, with the line-support parameters optimized using the traveling-wave index function and a derivative-free optimization routine with lower-bound constraints. Analytical results show that quasi-traveling waves are produced for ranges of line-support parameters (location, stiffness and damping) following optimization using the traveling-wave index. The developed wave patterns are examined with a power-flow analysis and numerically verified through finite element analysis. Wave localization is demonstrated to be valid in a finite membrane with specific boundary conditions and multiple viscoelastic line supports. The proposed method shows the predictive ability of the orthogonally stiffened membrane configuration as the basic unit cell for the design of periodic structures with directional wave propagation as well as vibration localization dynamics.

Flexural wave manipulation in perforated metamaterial plates with acoustic black holes interconnected by piezoelectric studs

Aiming at achieving lower and broader bandgaps (BGs) and stronger collimation effect, this research proposes a novel perforated metamaterial plate with acoustic black holes (ABHs) interconnected by piezoelectric studs for flexural wave manipulation. Based on the differential quadrature element method together with the first-order shear deformation plate theory, the governing equations of the metamaterial plate are derived. The proposed model is validated by comparing with finite element simulation results. Finally, the wave propagation characteristics including the BGs, equi-frequency contours (EFCs), and group velocities are obtained. The results reveal that the introduction of the stud embedded with piezoelectric patches brings wider complete BGs and stronger collimation effect at lower frequencies. The boundary frequencies and bandwidth of BGs and the preferential direction of wave energy flow are tunable by adjusting geometry parameters of the unit cell. The balance between ABH and piezoelectric effects should be kept to enhance the collimation by generating the caustic lobes. Utilizing the BG and self-collimation mechanism, flexural wave propagation can be manipulated by creating point or line defects in the metamaterial plates. This research provides guidance on the design of metamaterial structure with ABHs and piezoelectric material to achieve broadband vibration absorption and directional wave propagation.

Study on the bandgap and directional wave propagation mechanism of novel auxiliary semicircle rings lattices

In this study, a novel auxiliary semicircle rings lattice is proposed, and the proposed structure consists of connecting ligaments and auxiliary semicircle rings on ligaments. The bandgap and wave propagation characteristics of the proposed structure are analyzed. The generation mechanism of bandgap is carefully studied according to the vibration shape of the structure. Based on the Bloch's theorem and the finite element method, the dynamic model of the structure is solved to explore the wave behavior in the lattice. Then, the effects of different semicircle directions, the number of semicircle rings and the size of semicircle rings on the bandgap width and position are analyzed. In particular, we calculated the group velocity to analyze the influence of the direction of the semicircle rings on the directional frequency related energy flow in the structure. We also simulated the directional wave behavior in a finite-size lattice. It was found that in the proposed structure, the elastic wave with a specific frequency propagated along a certain direction. This study provides an ideological guidance for the topology design of metamaterials with directional wave propagation.

Directional long-frequency phase wave propagation characteristics, anisotropy, and effective yield surfaces of architected spinodal constructs

This work explores the directional long-frequency phase wave propagation characteristics, anisotropy, and multiaxial loading yield surface property of spinodal architectures, for the first time. Here, the theoretical model is developed for directional long-frequency wave propagation in three-dimensional (3D) anisotropic spinodal architecture and spinodal-reinforced interpenetrating phase composites (IPCs), and then verified by 3D finite element method (FEM) with a good agreement found. Based on the directional wave propagation profile, the anisotropic magnitude of spinodal architectures is captured and analyzed. Wherein, the effect of varying relative density, propagation plane, and matrix phase architecture property on directional wave propagation properties of the spinodal structure, IPCs, and anisotropy is explored. Furthermore, numerical homogenization is presented to compute the yield strength of spinodal topology, and verified by experiment in terms of effective stiffness and yield stress with an agreement found. Two well-established constitutive laws including extended Hill’s model and D-F model are used to derive the macroscopic analytical function for multiaxial yield response of spinodal architectures. Our findings show that lower relative density leads to a lower phase wave velocity and a higher anisotropic magnitude of the spinodal topology. Interpenetrating soft phase materials in spinodal architecture can help reduce the wave velocity as well as the adversity wave energy generated by harmful sources such as impact, shock, sound, etc. The analytical functions based on considered constitutive laws exhibit an ability to fit the multiaxial yield stress data, but the function based on extended Hill’s model demonstrates a better fit compared with that based on D-F model.

Study on the band gap and directional wave propagation mechanism of novel single-phase metamaterials

In this paper, a new type of single-phase metamaterial is proposed. Based on the finite element method, the band gap characteristics of the structures with different branches are comprehensively analyzed, and the existence of the band gap is further verified by the frequency response transmission spectrum. Then, the propagation characteristics of elastic waves of different frequencies in different combinations of structures are investigated respectively. The results show that the proposed single-phase metamaterial structure has an excellent band gap range, and under the action of relatively low-frequency elastic waves, the wave propagation in the structure has a certain direction and regionality, while the elastic waves at higher frequencies are applied, the propagation direction of the wave tends to propagate in all directions. This paper provides a new idea for studying the structural design of metamaterials with specific wave propagation directions.

Elastic anisotropy and wave propagation properties of multifunctional hollow sphere foams

Obtaining multifunctionality from microstructures instead of constituents provides a new direction for developing multifunctional materials. Periodic hollow sphere foams (HSFs) offer one lightweight structural motif with open and closed cells, high energy absorption, low thermal conductivity, snap-through instability, and triple-negative material indices. Here, we investigate the direction-dependent mechanical property, instability, and elastic wave isolation behavior of HSFs. Explicit formulas, stereographic projections, and general scaling relationships are developed to quantify and visualize the anisotropic mechanical properties of HSFs. By investigating the directional wave propagation in HSFs, extremely wide phononic band gaps are identified in the HSFs. The derived formulas and the simulation-informed parametric maps allow the design of HSFs with desired static and dynamic anisotropic property profiles, including tailorable direction-dependent stiffness/shear modulus, negative Poisson’s ratio, and wave isolation properties. Building upon these results, multifunctional design concepts of HSFs are further set forth. This study not only reveals tailorable mechanical anisotropy and band gap in HSFs, but also develops a general approach to investigate the direction-dependent properties of periodic materials, enabling multifunctional applications where lightweight, direction-dependent property, wave attenuation, and programmability are required simultaneously.

Study on bandgap and directional wave propagation of a two-dimensional lattice with a nested core

This paper proposes a two-dimensional lattice structure with a nested core. The bandgap distribution and the anisotropy of the phase velocity and group velocity were studied based on Bloch’s theorem and the finite element method. The effects of the eccentric ratio (e) and the rotation angle () of the dual-phase structure on the bandgap distribution were investigated, and the anisotropy was studied via phase velocity and group velocity. The structure of e = 0.3 displayed the maximum total bandgap width. As increased, the total bandgap widths of structures of different e all obviously increased and the low-frequency bandgap properties were improved. The phase velocity and group velocity of e = 0 displayed strong anisotropy, and the anisotropy was adjusted by tuning . Furthermore, the group velocity of the eighth mode displayed high-directional wave propagation. For practical applications, a single-phase structure was proposed and analyzed. Through additive manufacturing technology, the single-phase structure was prepared and tested by a low amplitude test setup. The experimental results displayed good agreement with the numerical results, which demonstrated high directional propagation. This finding may pave the way for practical applications of the proposed lattice metamaterial in terms of wave filtering.

Study on the Band Gap and Directional Wave Propagation Mechanism of Novel Single-Phase Metamaterials

Study on the Band Gap and Directional Wave Propagation Mechanism of Novel Single-Phase Metamaterials

Nonreciprocal and directional wave propagation in a two-dimensional lattice with bilinear properties

A passive method of realizing nonreciprocal wave propagation in a two-dimensional (2D) lattice is proposed, using bilinear springs combined with the necessary spatial asymmetry to provide a stable and strong departure from reciprocity. The bilinear property is unique among nonlinear mechanisms in that it is independent of amplitude but sensitive to the sign of the wave motion; the 2D setup allows the flexibility of generating spatial asymmetry at both small and large scales. The starting point is a linear 2D monatomic spring–mass lattice with strong directionally dependent wave propagation. The source and receiver are aligned so that there is virtually no direct wave transmission between them. Adding a region of bilinearity combined with spatial asymmetry that is not in the direct path between the source and receiver causes signal transmission via nonreciprocal scattering. A variety of spatially asymmetric bilinear configurations are considered, ranging from compact modulations confined within the unit cell to extended ones over the whole section, to obtain different dynamic nonreciprocal effects. Simulations illustrate how the combination of bilinearity and spatial asymmetry ensures a passive amplitude-independent nonreciprocal 2D system for a variety of different excitations.

Wave propagation properties of rotationally symmetric lattices with curved beams.

In this study, we design a type of rotationally symmetric lattice with curved beams and investigate the wave propagation properties of the structure. The analytical model of the structure is established to obtain the mass and stiffness matrices first. Because the dimensions of the mass and stiffness matrices will become very large if the structure is meshed with a number of small elements, we introduce the symplectic solution method to overcome the above difficulties of solving the eigenvalue problem. The effects of geometrical parameters and slenderness ratios on the distributions of bandgaps and variations of group velocities are investigated. We also numerically investigate the dynamic wave dispersion behavior and the transient responses of displacement and transmission coefficients in lattices subjected to excitations. Excellent agreement is obtained between the results obtained by the symplectic solution method and numerical simulations. The special wave-attenuation property of this type of structure is demonstrated and validated through experimental testing. The measured transmission coefficients in lattices with different geometrical parameters and slenderness ratios are in good agreement with the numerical simulations. The work provides a method for calculating wave behaviors in lattices and obtains lower bandgaps and directional wave propagation.

Elastic Wave Propagation in Lattice Metamaterials with Koch Fractal

In this study, the wave propagation properties of lattice metamaterials with Koch fractal structures are investigated in terms of band structures and directional wave propagation. The analytical models of lattice metamaterials are established using the finite element method, and the dispersion relation is solved using the Bloch’s theorem. The band structures of the lattice metamaterials with different numbers of iterations are studied, and the group velocities at a selected frequency are calculated to analyze the directional wave propagation characteristics. Furthermore, dynamic responses of the finite structures are calculated using commercial finite element software to verify the band gaps and directional wave propagation behaviors in the lattice metamaterials. The results show that multiple and low band gaps are present in the lattice materials with various geometric parameters of the Koch fractal, and the position of the lowest band gap decreases as the number of iterations increases. The results indicate the potential applications of lattice metamaterials with Koch fractals for vibration isolation and multi-functional design.

Study on the mechanism of band gap and directional wave propagation of the auxetic chiral lattices

In this study, the wave propagation properties in terms of the band gap and directions of wave propagation of the auxetic chiral structure are analyzed. The mechanism of generation of the band gap are carefully investigated. The auxetic chiral structure are assembled with the repeat unit cells and the unit cell contains a number of rigidly connected beams. The dynamic model of the unit cell are established by the principle of finite element method. The wave behaviors of the lattices are calculated by solving the dynamic model with the help of the Bloch’s theorem. The band structure are obtained and the effects of the chiral angles on the width and position of the band gap distributions are carefully studied. Especially, the mechanism of formation of the band gap are also analyzed by investigating the vibrational mode calculated by the commercial finite element software. The group velocities are calculated to analyze the effects of the geometrical parameters on the directional frequency-dependent energy flows in the structures. We also use the commercial finite element software to simulate the directional wave behaviors in the structure. We find that the first mode of the elastic wave spread only along certain specific directions in the auxetic chiral structure. The speed of wave propagation will be reduced, and the direction of wave propagation rotates counterclockwise when the chiral angle increases.

Analysis of temperature-dependent wave propagation for programmable lattices

This study focuses on temperature-dependent wave propagation in hexagonal and square lattices, which has potential application in the design of programmable lattices. To obtain the thermal effect on the wave behaviors of the lattices, temperature fields are applied to the structures and the thermal responses of the structures are analyzed. Furthermore, the temperature-dependent wave propagation behaviors are investigated in terms of the distributions of band gaps, and phase and group velocities, based on Bloch's theorem and the principle of the finite element method. In particular, directional wave propagation and energy flow are carefully investigated. We find that increasing temperature generates negative axial forces along the elements and decreases the branches of frequencies in the band structures. The phase and group velocities show the maxima amplitude of wave propagation in the 0°, 180°, ± 60° and ± 120° directions of the hexagonal lattice. The cooling process makes the energy flow focus in these directions, while the heating process allows the energy flow of the wave propagation focus in these directions at first and then makes it dispersed. The results can be used to tune wave propagation utilizing temperature-dependent wave behavior in the lattices.

On the directional wave propagation in the tetrachiral and hexachiral lattices with local resonators

The wave propagation in the tetrachiral and hexachiral lattices with local resonators are investigated and the wave behaviors with different geometrical parameters are analyzed. In this study, the tetrachiral and hexachiral lattices are assembled with the repeat unit cells and the unit cell contains a ring and a number of massless slender elastic ligaments. The ligaments are rigidly connected to the ring and the ring contains a heavy disk with its surrounding soft elastic annulus, which acts as the local resonators. The governing equations of the lattices are established by energy variation principle and the wave behaviors of the lattices are calculated by solving the eigenvalue problem with the Bloch’s theorem. The effects of chiral angles on the distributions of band gaps including the width and position are studied to investigate the effects of the chirality and local resonators on the formation of low-frequency band gaps. The first mode of the phase and group velocities are calculated to analyze the effects of the geometrical parameters on the directional frequency-dependent energy flows in the anisotropic structures. We also use the commercial finite element software COMSOL to simulate and verify the directional wave behaviors in the structure. We find that the first mode of the elastic wave spread only along certain specific directions in the tetrachiral structure. As the chiral angle increases, the speed of wave propagation is reduced, and the direction of wave propagation rotates clockwise. The hexachiral lattice exhibits effective isotropic property in the low frequency range, and the wave propagation velocity gradually decreases with the increase of the frequency of the elastic waves.

How a lipid bilayer membrane responds to an oscillating nanoparticle: Promoted membrane undulation and directional wave propagation

Mechanical forces acting on a plasma membrane are of essential importance to cellular functioning via inducing delicate change of the membrane shape with the underlying mechanism yet to be elucidated. Here, we introduce an oscillating nanoparticle (NP) interaction with a lipid bilayer membrane, using the coarse-grained simulation to investigate the dynamic membrane response to constrained mechanical stimulation, which is ubiquitous in biology. Our results demonstrate that, the membrane responds to an oscillating NP by generating nanoscale undulation waves, which immediately propagate through the membrane. In dynamics, propagation of the generated membrane undulation waves always starts from flattening of the region where the NP locates, thus producing a lateral force to propel the waves away from the point of stimulation. The speed of membrane undulation wave propagation is proportional to that of NP oscillation and accelerated by increasing the integral membrane surface tension, suggesting that both the membrane bending and stretching contribute to the energy driving the unique response of membrane undulation wave propagation.

Abnormal wave propagation behaviors in two-dimensional mass–spring structures with nonlocal effect

This paper considers the propagation of elastic waves in periodic two-dimensional mass–spring structures with diagonal springs. The second-neighbor interactions in non-diagonal directions are included to account for the nonlocal effect. The influences of the spring stiffness in the diagonal directions and the nonlocal effect on the propagation characteristics of elastic waves are then scrutinized. Through the dispersion relation curve and the equi-frequency contours, it is seen that when the diagonal spring stiffness increases, the slope of the second curve in the –M direction will not always be positive, meaning that the negative group velocity occurs. Therefore, an incident wavevector with a chosen angle to the negative group velocity can lead to the negative refraction phenomenon in the two-dimensional mass–spring structure. Another interesting phenomenon called directional radiation of elastic waves can also be achieved by adjusting the nonlocal effect. Within a certain range, the stronger the nonlocal effect in a specific direction is, the more obviously the elastic waves propagate along this direction. In this paper, we theoretically analyze and numerically simulate the phenomena of negative refraction and directional wave propagation by choosing a proper set of parameters of the two-dimensional mass–spring structure.

Wave propagation in elastic metamaterial beams and plates with interconnected resonators

In this work, new beam and plate metamaterials with interconnected local resonators are proposed. This design promotes the splitting and coupling between transverse and rotational vibration modes of the resonator chain. It produces a particular band structure with two band gaps: a wide band gap opens at the in-phase transverse natural frequency of the resonator chain and a second band gap, with narrower width, appears at higher frequencies. The Timoshenko beam and Mindlin–Reissner plate models are used to compute the band structure as well as the dynamic forced response. A parametric analysis of the band gaps is performed by varying the interconnection properties. The metamaterial plate presents a directional wave propagation pattern due to partial band gaps. In addition, a metamaterial beam manufactured by additive manufacturing is investigated. The experimental results are in agreement with the numerical predictions. Therefore, the proposed concept showed to be promising for metamaterial design aiming at creating singular band gaps with broadband absorption and directional/focalization features.

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.

Achieving directional propagation of elastic waves via topology optimization

This paper presents a study on topology optimization of novel material microstructural configurations to achieve directional elastic wave propagation through maximization of partial band gaps. A waveguide incorporating a periodic-microstructure material may exhibit different propagation properties for the plane elastic waves incident from different inlets. A topology optimization problem is formulated to enhance such a property with a gradient-based mathematical programming algorithm. For alleviating the issue of local optimum traps, the random morphology description functions (RMDFs) are introduced to generate random initial designs for the optimization process. The optimized designs finally converge to the orderly material distribution and numerical validation shows improved directional propagation property as expected. The utilization of linear two-dimension phononic crystal with efficient partial band gap is suitable for directional propagation with a broad frequency range.