Broadband and tunable one-dimensional strongly nonlinear acoustic metamaterials: Theoretical study

Research on the low-frequency band gap characteristics of longitudinal vibration of ship shafting based on bionic quasi-zero stiffness metamaterials

A novel one-dimensional quasi-zero-stiffness (QZS) metamaterial is proposed in this paper to acquire low-frequency band gaps to control the low-frequency longitudinal vibration of propulsion shaft using the bionic QZS as the local resonant oscillator. Firstly, the parameter design of the representative unit cell (RUC) for metamaterials using a bionic limb-shaped QZS structure is carried out and static analysis is conducted to verify its QZS property. Secondly, we model the QZS metamaterials as a lumped-mass-spring chain and derive the dispersion relationship through the Harmonic Balance method, then discuss the impact of damping, stiffness ratio, mass ratio, and excitation amplitude on this band gap. Finally, the resulting band gap is then confirmed through numerical simulations. Both the theoretical and numerical predictions show very low-frequency band gaps (about 7.5 Hz). Therefore, the proposed QZS metamaterials should be a promising solution for low-frequency wave filtering or attenuation for longitudinal vibration of ship shafting.

Spectro-spatial analysis of elastic wave propagation in nonlinear elastic metamaterial systems with damping

Different from the linear counterpart, elastic wave propagation in nonlinear elastic metamaterials with damping (EMD) systems has much more novel behaviors. It is little work that reveals the nonlinear wave propagation mechanism in the nonlinear EMD in the literature. In this paper, nonlinear EMD systems with different configurations for the nonlinear elements are constructed to study the nonlinear wave propagation characteristics based on the analytical formulation. Nonlinear wave propagation attenuation characteristics in nonlinear EMD systems are studied in the frequency-domain. Spectro-spatial characteristics of nonlinear traveling wave packet in space- and time-domain are also analyzed to reveal space frequency-domain characteristics. Influences of different configurations for the nonlinear elements on wave propagation in nonlinear EMD systems are discussed. Results shown that locations of band structures can be tuned by changing intensities of nonlinearities in the nonlinear EMD systems, which are not found in the linear system. Moreover, different configurations for the nonlinear elements can lead to localization feature emerged in a nonlinear EMD system, which indicates solitary waves causing from the interaction between dispersion and nonlinearity exist in the nonlinear systems. This interesting wave propagating properties can be used to design new devices for acoustic switches, energy harvesting, and broadband vibration control.

Experimental proof of emergent subharmonic attenuation zones in a nonlinear locally resonant metamaterial

High-performance locally resonant metamaterials represent the next frontier in materials technology due to their extraordinary properties obtained through materials design, enabling a variety of potential applications. The most exceptional feature of locally resonant metamaterials is the subwavelength size of their unit cells, which allows to overcome the limits in wave focusing, imaging and sound/vibration isolation. To respond to the fast evolution of these artificial materials and the increasing need for advanced and exceptional properties, the emergence of a new mechanism for wave mitigation and control consisting in a nonlinear interaction between propagating and evanescent waves has recently been theoretically demonstrated. Here, we present the experimental proof of this phenomenon: the appearance of a subharmonic transmission attenuation zone due to energy exchange induced by autoparametric resonance. These results pave the path to a new generation of nonlinear locally resonant metamaterials.

Emergent subharmonic band gaps in nonlinear locally resonant metamaterials induced by autoparametric resonance

With the aim of developing high-performance locally resonant metamaterials, the effect of nonlinear hyperelastic interactions between a rubberlike elastomeric local resonator and the host matrix is investigated. The results reveal a new emergent physical phenomenon not previously reported within the framework of elastoacoustic metamaterials: The appearance of a half subharmonic attenuation zone complementing the local resonance band gap around the fundamental frequency. Evidence of the emergent attenuation zone is provided by direct numerical simulations as well as semianalytical developments via the method of multiple scales. The analyses demonstrate that, in the considered nonlinear locally resonant metamaterial, the combined effects of autoparametric and local resonance induce saturation of the primary wave at certain conditions and, subsequently, promote energy exchange from a primary propagating wave to an evanescent subharmonic wave, giving rise to an additional attenuation zone. This opens new possibilities for the design of passive filtering devices for elastoacoustic waves.

Solitary waves in a granular chain of elastic spheres: Multiple solitary solutions and their stabilities

A granular chain of elastic spheres via Hertzian contact incorporates a classical nonlinear force model describing dynamical elastic solitary wave propagation. In this paper, the multiple solitary waves and their dynamic behaviors and stability in such a system are considered. An approximate KdV equation with the standard form is derived under the long-wavelength approximation and small deformation. The closed-form analytical single- and multiple-soliton solutions are obtained. The construction of the multiple-soliton solutions is analyzed by using the functional analysis. It is found that the multiple-soliton solution can be excited by the single-soliton solutions. This result is confirmed by the numerical analysis. Based on the soliton solutions of the KdV equation, the analytic solutions of multiple dark solitary waves are obtained from the original dynamic equation of the granular chain in the long-wavelength approximation. The stability of the single and multiple dark solitary wave solutions are numerically analyzed by using both split-step Fourier transform method and Runge-Kutta method. The results show that the single dark solitary wave solution is stable, and the multiple dark solitary waves are unstable.

Metastable modular metastructures for on-demand reconfiguration of band structures and nonreciprocal wave propagation

We present an approach to achieve adaptable band structures and nonreciprocal wave propagation by exploring and exploiting the concept of metastable modular metastructures. Through studying the dynamics of wave propagation in a chain composed of finite metastable modules, we provide experimental and analytical results on nonreciprocal wave propagation and unveil the underlying mechanisms that facilitate such unidirectional energy transmission. In addition, we demonstrate that via transitioning among the numerous metastable states, the proposed metastructure is endowed with a large number of bandgap reconfiguration possibilities. As a result, we illustrate that unprecedented adaptable nonreciprocal wave propagation can be realized using the metastable modular metastructure. Overall, this research elucidates the rich dynamics attainable through the combinations of periodicity, nonlinearity, spatial asymmetry, and metastability and creates a class of adaptive structural and material systems capable of realizing tunable bandgaps and nonreciprocal wave transmissions.

Ultra-low and ultra-broad-band nonlinear acoustic metamaterials

Linear acoustic metamaterials (LAMs) are widely used to manipulate sound; however, it is challenging to obtain bandgaps with a generalized width (ratio of the bandgap width to its start frequency) >1 through linear mechanisms. Here we adopt both theoretical and experimental approaches to describe the nonlinear chaotic mechanism in both one-dimensional (1D) and two-dimensional (2D) nonlinear acoustic metamaterials (NAMs). This mechanism enables NAMs to reduce wave transmissions by as much as 20–40 dB in an ultra-low and ultra-broad band that consists of bandgaps and chaotic bands. With subwavelength cells, the generalized width reaches 21 in a 1D NAM and it goes up to 39 in a 2D NAM, which overcomes the bandwidth limit for wave suppression in current LAMs. This work enables further progress in elucidating the dynamics of NAMs and opens new avenues in double-ultra acoustic manipulation.

Linear acoustic metamaterials based on resonances are generally tunable but limited by their narrow bands. Here, Fang et al. fabricate one- and two-dimensional nonlinear acoustic metamaterials with a broadband, low-frequency, response—greatly suppressing low frequency noise.