Tunable Wave Propagation Research Articles

Rest length controlled tunable band structure in periodic tensegrity metastructure – a numerical study using a novel consistent stiffness and mass formulation

Elastic wave propagation in various periodic metastructures and its application to wave filtering, vibration isolation, acoustic cloaking, etc., have gained significant attention among researchers in recent years. Despite the presence of band gaps, traditional lattice structures lack dynamic tunability. The solution lies in using tensegrity as unit cells. This article presents analysis of tunable wave propagation through a metastructure formed by tessellation of a 2D tensegrity unit cell in one dimension. Equations of motion of the unit cell are derived with consideration of flexibility and distributed mass of the bars, which is often neglected in the literature. The formulation is extended for wave dispersion analysis using the Floquet–Bloch theory. Next, the order of the formulation is reduced for decoupled analysis of symmetric and antisymmetric modes. The dispersion relations for different modes have been validated with nonlinear as well as linearized frequency response analysis under impulse load. Next, the effect of rest length of strings and alternating arrangement of bars on band gaps is studied in detail.

Greek Key Inspired Fractal Metamaterials with Superior Stretchability for Tunable Wave Propagation

Stretchable materials that can sustain a large deformation are in high demand, because they find broad applications ranging from stretchable energy storage devices to tunable noise and vibration devices. One main challenge is creating strain‐releasing mechanisms from inherently brittle materials. This work explores a new approach to designing stretchable metamaterials, using a "kerfing" pattern inspired by the ancient Greek Key configuration. The kerfing architecture allows for substantial in‐plane elongation. In‐plane tensile experiments show an ≈8‐times increase in stretchability when the kerfing width is enlarged four times. With higher‐order fractal patterns, the fractal lattice exhibits a stretchability of up to ≈520%, far beyond the inherent deformability of the brittle constituent. Moreover, this design also enables the tunability of various mechanical properties, including stiffness, strength, toughness, and Poisson's ratio. Ashby‐type plots are presented, revealing the relationships between stretchability and other mechanical properties to aid in the design and fabrication of advanced engineering materials. To demonstrate a vital application of the achieved stretchability, elastic wave propagation in the proposed kerfing metamaterials is studied. Simulations indicate that multiple broad phononic bandgaps arise in these structures as the fractal order increases. These bandgaps prove to be adjustable not only through the fractal lattice geometry but also by means of applied mechanical loading. This investigation highlights the potential of fractal‐based layouts as a promising avenue for designing cutting‐edge stretchable metamaterials with customizable mechanical properties and functionalities.

Vibration isolation of a self-powered piezoelectric pipe conveying fluid composed of laminated fiber-reinforced composites

Based upon the wave manipulating characteristics of phononic crystals (PCs), this paper aims to isolate flexural vibration of laminated composite pipes conveying fluid by introducing a self-powered periodic piezoelectric design. The pipe is composed of three layers of fiber-reinforced composites along the thickness, and is periodically attached with a number of shunted piezoelectric sensor/actuator pairs along the axis. A negative proportional feedback strategy is adopted to amplify the sensing voltage to the actuators, which can generate periodic active stiffness to the pipe and thus enable tunable wave propagation and frequency band gap (BG). The dynamical equation of motion for a single piezoelectric laminated pipe conveying fluid is deduced from classical laminated beam theory as well as one-dimensional piezoelectric constitution. The BG distribution and amplitude transmission of topological structure are obtained by the spectral element method (SEM). Numerical results demonstrate that the present self-powered piezoelectric PC design can achieve excellent vibration isolation effect for the laminated composite pipe conveying fluid. Major parameter regulations including cross-ply angle, lamina sequence, feedback control gain, geometry of piezoelectric layers and fluid effect are examined. Free vibration and stability of the system are also discussed to perfect the vibration isolation design.

Synthesizing and reconfiguring metastable modular metamaterials for adaptive wave propagation control

This research uncovers new insights and novel methodology to synthesize tunable wave propagation characteristics in a metastable modular metamaterial by reconfiguring the modules and system metastable states. The reconfigurable criteria of the one-dimensional (1D) metastable modular metamaterial are rigorously investigated to provide insights on the tunability of such metamaterials. A sufficient condition for reconfigurability is derived analytically, following the numerical solutions of the sufficient and necessary condition. An inverse problem is then formulated to achieve desirable band structures via switching the modular internal configurations and metastable states in one-dimensional and two-dimensional (2D) metamaterials. Exploiting the correlation between the unique on-off feature of the modules’ metastable states and the binary nature of the Genetic Algorithm (GA) approach, GA is utilized to decide the reconfiguring action of each module to achieve the desired band structure. With this method, we show that wave propagation in 1D and 2D metastable modular metamaterials can be controlled adaptively by on-demand reconfiguration of the modules.

Pressure diffusion wave and shear wave in gels with tunable wave propagation properties

Gels are composed of cross-linked polymer network and solvent. Gels are both ubiquitous in nature and widely applied in engineering applications. In this work, we develop a physics-based dynamic theory to investigate the tunable wave propagation properties of gels. Gels are soft and can generate large deformation. The constitutive relation takes account the coupled large deformation and diffusion of gels. The dynamic governing equations take account the relative motions between the polymer network and solvent, which leads to a pressure diffusion wave similar to the “slow pressure wave” in the classical Biot’s poroelastodynamics. It is different from the pressure wave in pure solid or pure liquid. The phase velocity, group velocity and attenuation coefficient are analyzed at different frequencies and propagating directions for both pressure wave and shear wave. We show that the wave propagation properties of gels are not only related to the material properties including the crosslink density and the interaction property between solvent and polymer, but also can be tuned by different mechanical loading conditions and chemical stimuli. It is also predicted that the constrained swollen gel exhibits anisotropic wave propagation properties, which leads to the splitting of the pressure wave and shear wave propagating through it. The theory provides a general frame for fundamental understanding and quantitative characterization of the dynamic behaviors of gels.

Tunable wave propagation in octa-chiral lattices with local resonators

This paper aims to investigate the wave behavior of the octa-chiral lattices with local resonators and tunable wave propagation properties with different chiral geometrical dimensions. The octa-chiral lattices are assembled with the repeat unit cells and the unit cell contains a ring and eight slender elastic massless ligaments which are rigidly connected to the ring. The ring has a heavy disk with its surrounding soft elastic annulus. The dynamic equations of the lattices are established with the principle of the Lagrangian method. The wave behaviors of the lattices are calculated by solving the eigenvalue problem governing the wave harmonic propagation with the application of the Bloch’s theorem. By calculating the band structures and the phase and group, we investigate the effects of the chiral geometry and resonators on the formation of the low-frequency band-gaps and the directional frequency-dependent energy flow. The phase and group velocities show that the maxima wave propagation speeds are along the ±45°. While, the phase velocities and the group velocities trend to be identical with the increase of the chiral angles. The findings suggest that we can tune the anisotropic wave behavior to the isotropic wave characterization with special structural design on the chiral geometry.

Instability-Induced Pattern Transformation in Soft Metamaterial with Hexagonal Networks for Tunable Wave Propagation

Instability-induced pattern transformations of the architectured multi-phase soft metamaterial under bi-axial compression were explored. The soft metamaterial is composed of two phases: a soft matrix and a reinforcing hexagonal network embedded in the matrix. Equi-biaxial loading is found to induce both micro- and macro- instabilities in the networked architecture. Two types of instability patterns were observed, dependent upon the architecture geometry and the material combination. The critical strain for triggering instability and the two resulting types of patterns was derived, and a theoretical criterion for the transition between the two patterns was determined. Type I patterns retain the original periodicity of the architecture but wrinkles the network walls whereas Type II patterns transform the overall periodicity of the architecture while bending the network walls. Elastic wave propagation analysis was performed for the two distinct patterns under both stressed and stress-free conditions: a change in band gaps is found for both instability-induced pattern transformations, but differs for each type due to their dramatic difference in structure transformation (i.e. Type I wall wrinkling vs. Type II periodicity switching). The distinguished mechanical behavior and the rich properties of this category of multi-phase soft metamaterial can be used to design new smart materials with switchable functionalities controllable by deformation.

Tunable wave propagation by varying prestrain in tensegrity-based periodic media

This paper investigates the dynamic properties of one, two and three-dimensional tensegrity-based periodic structures introduced in Rimoli and Pal (2017), which are here termed as tensegrity beams, plates and solids, respectively. We study their linear wave propagation properties and show that in each case, these properties can be significantly altered by the prestrain in the cables. As the prestrain is varied, we observe jumps in the wave velocities at two critical prestrain values, which define transitions between the three distinct phases of these structural assemblies. At low cable prestrains, the wave speeds are zero as the lattices have zero effective stiffness. At moderate prestrains, the wave speed is nonzero and finally, at prestrain levels where the bars buckle, the wave speeds change to a near constant value. Dispersion analysis on these beams, plates and solids reveal unique properties such as very low wave velocities compared to their constituent material and the existence of flat bands at low frequencies. Furthermore, we find that shear waves travel faster than longitudinal waves in tensegrity solids in a range of cable prestrains. Finally, we verify the key observations through detailed numerical simulations on finite tensegrity solids.

Tunable Wave Propagation in Granular Crystals by Altering Lattice Network Topology

We develop a framework for wave tailoring by altering the lattice network topology of a granular crystal consisting of spherical granules in contact. The lattice topology can alternate between two stable configurations, with the spherical granules of the lattice held in stable equilibrium in each configuration by gravity. Under impact, the first configuration results in a wave with rapidly decaying amplitude as it propagates along a primary chain, while the second configuration results in a solitary wave propagating along the primary chain with no decay. The mechanism to achieve such tunability is by having energy diverted to the granules adjacent to the primary chain in the first case but not the second. The tunable design of the proposed network is validated using both numerical simulations and experiments. In terms of potential applications, the proposed bistable lattice network can be viewed either as a wave attenuator or as a device that allows higher amplitude wave propagation in one direction than in the opposite direction. The lattice is analogous to a crystal phase transformation due to the change in atomic configurations, leading to the change in properties at the macroscale.

Tunable Wave Propagation in Superconducting Microstrip Line Based on Ferroelectric Thin Films

The microwave propagation characteristics in superconducting microstrip line supported by ferroelectric layer are theoretically investigated. The control of propagation constant and attenuation coefficient of the waveguide with biasing electric field is analyzed using the spectral domain method. The dependence of propagation characteristics on thickness of ferroelectric thin film as well as operating frequency for different applied electric fields is studied. The variation of propagation constant with temperature is also investigated. This method of analysis can be easily implemented in the design of tunable microwave devices.

Tunable wave propagation in linear ferrite film bound by Kerr-type media

The propagation of electromagnetic waves in a structure of a linear ferrite film bound by nonlinear dielectric substrate and cladding is analyzed. The nonlinear medium is taken to be of refractive index of the form, n 2 ( E ) = n 0 2 + α | E | 2 , where E is the electric field. The dependence of energy flow on the direction of propagation (non-reciprocity) as well as on the strength of the biasing magnetic field is established.