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This investigation is focused on the nonreciprocal transmission of the non-collinear mixing wave in a nonlinear elastic wave metamaterial. The nonlinear elastic wave metamaterial with asymmetric structure is used to break the traditional reciprocal transmission, which is composed of a nonlinear material and a linear phononic crystal. When two non-collinear shear waves following the resonant condition interact with each other, the sum frequency longitudinal wave can be generated and propagate together with fundamental and second harmonics. Based on the transfer and stiffness matrices, band gaps and transmission coefficients are derived. The changing of band structures results in manipulating elastic waves with different frequencies. In the nonreciprocal frequency region, elastic waves can propagate along the positive direction while the reverse case is prohibited. The mixing of two incident SV waves in the nonlinear elastic wave metamaterial is verified by experiments and the results can support the theoretical analysis and numerical calculations. Because of material nonlinearity and asymmetric structure, the nonlinear elastic wave metamaterial can behave as a mechanical diode. The present work shows the possibility to design nonreciprocal elastic wave device by nonlinear wave mixing methods. [ABSTRACT FROM AUTHOR]

Cloaking invisibility is a novel technique that prevents the object from being detected in the background field. The development of new artificial materials and structures promotes the emergence of new achievements in cloaking research. In this work, a broadband square cloaking configuration of elastic wave metamaterial plate is designed and fabricated by the external active control system. The approximate parameters of the flexural wave cloak can be obtained by the coordinate transformation and achieved by alternating layers of the Acrylonitrile Butadiene Styrene (ABS), polydimethylsiloxane (PDMS), and piezoelectric (PZT) patches. With the introduction of active control systems, the square cloak has a wide effective frequency range. The simulation and experimental results show that the square cloak of flexural waves exhibits a good invisible performance in the frequency region of 500–2200 Hz. Compared to the structure without active control systems, the frequency region 2200–2750 Hz is extended for the active cloak. The design and fabrication of the broadband cloak is wished to be helpful during the practical engineering. [ABSTRACT FROM AUTHOR]

In this investigation, the bandgaps and nonreciprocal transmission of the nonlinear piezoelectric phononic crystal and elastic wave metamaterial are studied. Analytical solutions for the wave motion equations with the electro-mechanical coupling are obtained. According to the continuous conditions, the stop bands and transmission coefficients of both fundamental wave and second harmonic are derived by the stiffness matrix method. Some particular examples are presented to show the nonreciprocal transmission of the nonlinear elastic waves. Additionally, nonlinear ultrasonic experiments are applied to verify the theoretical analyses and numerical simulations. This work is intended to be helpful in the design and fabrication of devices of the elastic wave diode with piezoelectric materials. [ABSTRACT FROM AUTHOR]

In this investigation, the non-reciprocal transmission in a nonlinear elastic metamaterial with imperfect interfaces is studied. Based on the Bloch theorem and stiffness matrix method, the band gaps and transmission coefficients with imperfect interfaces are obtained for the fundamental and double frequency cases. The interfacial influences on the transmission behaviour are discussed for both the nonlinear phononic crystal and elastic metamaterial. Numerical results for the imperfect interface structure are compared with those for the perfect one. Furthermore, experiments are performed to support the theoretical analysis. The present research is expected to be helpful to design tunable devices with the non-reciprocal transmission and diode behaviour of the elastic metamaterial. [ABSTRACT FROM AUTHOR]

• The effects of the initial stresses on the tunable propagation behavior in nonlinear phononic crystal and elastic wave metamaterial are presented. • The influences of the initial stresses on both in-plane and anti-plane modes are discussed. • The initial stresses can result in the movement to the low frequency regions of the central frequencies of the band gaps and the nonreciprocal zones. In this investigation, the nonreciprocal transmission of elastic waves is achieved by the combination of asymmetric structure and nonlinear material. Our attention is focused on the effects of the initial stresses on the tunable propagation behavior in nonlinear phononic crystal and elastic wave metamaterial. Different components of the initial stresses are considered for both in-plane and anti-plane modes. Based on the Bloch's law and transfer/stiffness matrix method, the corresponding band structures and transmission coefficients of the generated fundamental and second harmonic waves are calculated and discussed. We find that the central frequencies of the band gaps and the nonreciprocal zones shift towards the low frequency regions as the initial stresses increase. This present work can be expected to provide a way to tune the transmission behaviors in nonlinear elastic wave metamaterial and mechanical diodes. [ABSTRACT FROM AUTHOR]

The nonreciprocal phenomenon appears in nonlinear acoustic metamaterial which are composed of a linear phononic crystal and a nonlinear layer. Based on the nonlinear characteristics, the acoustic waves can pass in one direction and are prohibited in reverse. Naturally, people will wonder whether the nonreciprocal phenomenon can be found in nonlinear elastic wave metamaterial. Because of the coupling of the multi-displacements, this problem becomes more complicated but interesting for waves in solid. Motivated by this enlightenment, we will discuss the band gap and transmission properties of elastic waves in both linear and nonlinear periodic systems. The fundamental and double frequency waves can be generated by the interaction between SH waves and the nonlinearity of materials. According to continuity conditions of incident SH wave, the transfer matrices are derived. The stop band and transmission coefficient are obtained by Bloch's law. This research is expected to be helpful to develop new elastic wave metamaterial devices. [ABSTRACT FROM AUTHOR]

In this work, negative refraction and exceptional point (EP) in piezoelectric mechanical metamaterials are considered, which corporates with the Parity–Time (PT) symmetry. The oblique incidence of anti–plane shear wave at the interface between a homogeneous medium and phononic crystal can excite multiple refraction modes. In periodic layers, propagation characteristics are illustrated by the dispersion relation and transfer matrix method. The normal mode decomposition is developed and time average Poynting vector is used to derive the refraction angle at the interface of piezoelectric metamaterials. The beam splitting is shown with different incident angles, as well as the pure negative refraction is achieved. Due to the mechanical and electric coupling, the complex conjugate of Bloch wave number appears in the dispersion relation and degenerates to the exceptional point. In addition, a defect layer is introduced to study the transmission coefficient of two phononic crystals with different arrangements. When the gain and loss are introduced into the metamaterials, the Parity–Time symmetry system is realized and a complete transmission with a unidirectional zero reflection at exceptional point can be achieved. • The negative refraction and Parity–Time symmetry of piezoelectric mechanical metamaterial are discussed. • Poynting vector is presented to provide the elastic wave characteristics. • Experiments are performed to discuss about the beam splittin. [ABSTRACT FROM AUTHOR]

Different from the linear phononic crystals, elastic waves can exhibit more interesting phenomena in periodic structures with nonlinear properties. By the active control action, elastic wave characteristics can be tuned based on the demand in practical application. This work discusses the possibility of the active control action on elastic waves in phononic crystals with the weakly nonlinear monoatomic lattice chain. Based on the Lindstedt-Poincaré method, the approximate solution of the dispersion relation is derived. Numerical calculations are performed to discuss the influences of the active control action on wave propagation properties. In order to present the features of nonlinear elastic wave dynamics, it is mainly focused on the effects of active control accompanied by the changes of the elastic wave amplitude, nonlinear degree, hard and soft nonlinearities. It is expected to extend the analysis and design of new phononic crystal devices for both the theory and application fields. [ABSTRACT FROM AUTHOR]

The propagation of in-plane waves in piezoelectric metamaterials involves the coupling of longitudinal (i.e. quasi–pressure), transverse (i.e. quasi–shear) and electric potential waves, which can result in different exotic phenomena. In this study, the stiffness matrix method is used to analyze the dispersion relation, which contains anomalous propagation characteristics. With the coupling of electric potential, the frequency spectrum of in–plane wave shows new characteristics. The exceptional point caused by non–Hermitian operator that does not exist before also appears when the vertical wave number is imaginary. The oblique incidence of the in–plane wave at the interface between a homogeneous medium and phononic crystal can excite multiple refraction modes which include the negative refraction. The normal mode decomposition is developed to study the in-plane incidence of piezoelectric metamaterial and then the averaged Poynting vector is applied to obtain the refraction angle. Moreover, the defect layer is introduced into the phononic crystals to study the transmission coefficients with two different symmetrical arrangements. When the balanced gain and loss are considered in the metamaterial, the Parity–Time symmetry appears and brings in pairs of exceptional points to achieve complete transmission with unidirectional zero reflection. • With the coupling of electric potential, the exceptional point caused by non–Hermitian operator that does not exist before appears when the vertical wave number is imaginary. • The oblique incidence of the in–plane wave at the interface between a homogeneous medium and phononic crystal can excite multiple refraction modes which include the negative refraction. • The defect layer is introduced to study the transmission coefficients with two different symmetrical arrangements. [ABSTRACT FROM AUTHOR]

In this investigation, three-dimensional nonreciprocal transmission is realized by the combination of structural asymmetry and material nonlinearity. Analytical solutions of the coupled quasi-longitudinal (qP) and quasi-shear (qS 1 and qS 2) waves are derived. According to Bloch's law and the stiffness matrix method, we obtain the band gaps and the transmission coefficients of the fundamental and double frequency waves. We also discuss the effects of the incident azimuthal angle on the propagation behaviors in nonlinear phononic crystals and elastic wave metamaterials. This present work is expected to help design practical devices of nonreciprocal transmission with vector characteristics. • Three-dimensional nonreciprocal transmission is realized by material nonlinearities. • Analytical solutions of coupled quasi-longitudinal and quasi-shear waves are derived. • The effects of incident azimuthal angles on the propagation behaviors are discussed. [ABSTRACT FROM AUTHOR]

• The band structures are obtained by the transfer matrix method and the transmission coefficients are achieved by the stiffness matrix method. • Experiments are performed for comparison with the theoretical results. • The nonreciprocal transmission of elastic waves is realized by enlightenment of an acoustic diode. In this investigation, the nonreciprocal transmission of elastic waves is realized by enlightenment of an acoustic diode. The phenomenon can be found in a nonlinear elastic wave metamaterial which consists of a linear phononic crystal attached by a nonlinear elastic medium. The structural asymmetry and material nonlinearity break the inherent reciprocity. The multi-displacements coupling of elastic waves in solids makes the problem more complicated in mathematics, but with showing interesting physical phenomenon. The elastic waves with the fundamental and double frequencies can be generated by the interaction between an incident longitudinal wave and the material nonlinearity. Based on the Bloch's law and continuity conditions, the band structures are obtained by the transfer matrix method and the transmission coefficients are achieved by the stiffness matrix method. Especially, experiments are performed for comparison with the theoretical results. This research may be helpful to design practical devices with nonreciprocal transmission of the elastic wave metamaterial. The transmission coefficient for the incident longitudinal wave from the left boundary, which shows the fundamental and double frequency waves are zero in the frequency region with nonreciprocal transmission. Image, graphical abstract [ABSTRACT FROM AUTHOR]