Propagation Characteristics Of Elastic Waves Research Articles

Anisotropy and dispersion of elastic waves in periodically multilayered anisotropic media

The propagation characteristics of elastic waves in general periodically multilayered media formed by alternate arrangement of two or more arbitrarily-anisotropic materials are comprehensively studied. Combining with the state-space formalism for obtaining the wave solutions to the constituent layers, the Floquet-Bloch theorem for providing the periodic relations between neighboring unit cells, the method of reverberation-ray matrix (MRRM) is employed to derive the general dispersion equations of the periodically multilayered anisotropic media. By solving the dispersion equations in cases of all possible sorts of wavenumber components, the complete anisotropic and dispersion characteristics of elastic waves can be provided. By numerical examples, the slowness and the phase velocity curves are provided to summarize the innovative anisotropic characteristics of elastic waves in three coordinate planes. The effects of the anisotropic parameters on the slowness/phase velocity curves have also been discussed. Moreover, all kinds of dispersion curves including the frequency-related and phase velocity-related curves along the directions perpendicular, parallel, and oblique to the layering are provided to reflect the general dispersion characteristics of elastic waves from various viewpoints. It is found that the innovative anisotropy characteristics of elastic waves in the periodically multilayered anisotropic media include that the slowness curves have periodicity in the thickness direction and the least positive period decreases with the increasing of frequency. As the frequency becomes big enough, the slowness/phase velocity curves show interactions between the modes within the overlapping neighboring periods. The common dispersion characteristics of elastic waves along various directions include the symmetry of wavenumber, the asymptotic of the wavelength and the phase velocity curves to the frequency lines corresponding to zero wavenumber, as well as the cutoff property of the phase velocities of the lowest three basis modes. The waves in oblique directions are special in that the mode transition and repulsion due to the zone folding effect of periodicity along thickness as well as the cutoff property of higher-than-third-order overtones along layering are simultaneously in effective.

Broadband vibration attenuation study and wave propagation analysis of extended arrow tetragonal lattice structure

In order to reduce vibration and noise with wide frequency, a new extended arrow tetragonal lattice topology is proposed. The band gap characteristics are discussed by combining the finite element method and Bloch’s theorem. The generation principle of band gap is explained by vibration mode analysis. By topological optimization of the structure, band gap has obvious optimization effect. The propagation characteristics of elastic waves with a specific frequency in the structure are studied from the point of view of energy. Finally, the band gap frequency range is compared with the transmission function, and the stress cloud diagram is analyzed. The research shows that the structure has good band gaps and can play a good role in vibration and noise reduction. Through the topological design of the structure, the band gap frequency range of the structure is optimized, which provides a new design idea for wide frequency vibration attenuation.

Elastic wave propagation and vibration characteristics of diamond-shaped metastructures

Elastic wave propagation and vibration characteristics of diamond-shaped metastructures

Innovative structural design of chiral lattices with low frequency wide multiple band gaps and vibration suppression

In order to achieve low-frequency vibration and noise reduction, this paper proposes an innovative structure based on the four-ligament chiral structure. The band gap characteristics and the principle of band gap generation are numerically analyzed by using the finite element method. By optimizing the proposed structure, the band gap is obviously transferred to the low frequency. The propagation characteristics of elastic waves with a specific frequency on the passband in the proposed structure are studied. Finally, the calculated band gap frequency range is compared with the finite element simulation results, and the two correspond perfectly. The research shows that the proposed structure has a good bandgap frequency range, which can play a good role in suppressing vibration transmission, and by improving the chiral structure of the basic four ligaments, the bandgap frequency range of the structure can be transferred from a high frequency to low frequency, which provides ideological guidance and scheme for the structural design of metamaterial that suppress low-frequency waves.

Characteristics of Elastic Wave Propagation in Fluid-Saturated Porous Media Based on the Model of Soil Mechanics

Characteristics of Elastic Wave Propagation in Fluid-Saturated Porous Media Based on the Model of Soil Mechanics

Finite-amplitude nonlinear waves in inertial amplification metamaterials: Theoretical and numerical analyses

The motivation of this study is to understand the unique characteristics of finite-amplitude elastic wave propagation in an inertial amplification (IA) system coupled with a Duffing resonator and leverage the unique opportunities offered by the IA mechanism and nonlinearities to achieve the modulation of elastic waves. Based on the assumption of the perturbation method, the effective range of the wave amplitude was investigated, which is usually ignored. Meanwhile, the obvious phenomenon of bandgap transition (between the single resonance bandgap and hybrid bandgap) is observed with varying IA levels. In particular, we demonstrated a new phenomenon of negative wave propagation and an obvious standing-wave mode in this system. Here, an analytical investigation of the amplitude-dependent and IA-dependent nonlinear dispersion is conducted based on the perturbation approach. Numerical simulations using the time-domain finite element method and Gaussian pulse excitation were performed to validate the nonlinear dispersion and negative motion of the wave packet. The research results can be used to tune wave propagation in metamaterials and provide ideas for the design of metamaterials, which can be used in practical circumstances for different energy transfer needs.

Ultra-low-frequency multi-broadband and vibration suppression mechanism of innovative star-shaped hybrid metamaterials

Metamaterials with low-frequency band gap have always been the focus of research. For this reason, many researchers have proposed many structural design schemes. In this paper, an innovative star-shaped hybrid metamaterial structure is proposed. Based on Bloch's theorem and finite element method, a dynamic model of the proposed structure is established, the band gap characteristics of the proposed structure are analyzed, and the generation mechanism of band gap is discussed with the mode shape of specific frequency. Then, the propagation characteristics of elastic wave in the proposed structure are analyzed by using the dispersion surface and group velocity images, and the attenuation region of vibration transmission in the finite periodic structure is consistent with the frequency range of band gap. Finally, the relationship between band gap and structure parameters is explored. The results show that the proposed structure has good band gap characteristics in the frequency range of 1000 Hz, the lowest frequency of band gap reaches 60.207 Hz, and the total band gap width accounts for 54.463%. This research opens up an ideological route for the design of low frequency metamaterial structures.

Isolation Effect of P-Wave By Double-Layer Wave Impeding Barrier in Unsaturated Foundations

Wave impeding block (WIB) barriers are often used to reduce vibration from different sources, but traditional vibration isolation of WIB has been limited to homogeneous materials and single-phase elastic or two-phase saturated foundations by many researchers. In fact, soils in nature are usually tri-phase unsaturated materials, and the propagation characteristics of elastic waves in unsaturated medium are completely different from those in single-phase elastic medium or two-phase saturated porous medium. In addition, the conventional WIB barrier has better vibration isolation only at low frequencies. Therefore, this paper improves the vibration isolation of the WIB by double-layer WIB with the same thickness on the basis of traditional WIB. Based on the wave theory of unsaturated porous media and elastic media, and according to the Helmholtz principle, we can obtain the solution of surface vertical displacement after setting double-layer WIB in unsaturated foundation, and then the isolation effect of double-layer WIB in unsaturated foundation under [Formula: see text]-wave incidence is investigated. The wave impedance ratio at the interface between WIB and unsaturated soil and wave impedance ratio at the interfaces among the layers of WIB is first analyzed on the vibration isolation effect of double-layer WIB, and the wave impedance ratio corresponding to the optimal vibration isolation effect of WIB barrier is achieved. Then the key factors such as incidence angle, incidence frequency, saturation, thickness, and burial depth of the double-layer WIB are evaluated on its vibration isolation properties. Finally, the isolation effects of single-layer homogeneous WIB and double-layer non-homogeneous WIB with the same thickness are compared. For the same thickness isolation barrier, the vibration isolation efficiency of double-layer WIB is 42.73% higher than single-layer at the incidence angle of [Formula: see text]–[Formula: see text]. The double-layer WIB has better isolation effect at low, medium and high frequencies than single-layer WIB.

Propagation of terahertz elastic longitudinal waves in piezoelectric semiconductor rods

Terahertz elastic waves travelling in piezoelectric semiconductors (PSs) with the deformation-polarization-carrier coupling have a huge potential application in elastic wave-based devices. To reveal wave propagation characteristics of terahertz elastic waves in rod-like PS structures, we present three typical rod models based on the Hamilton principle and the linearization of the nonlinear current, which are extensions of the classical, Love, and Mindlin-Herrmann rod models for elastic media to those for PS materials. Using the derived equations, the analytical dispersion relations of the elastic longitudinal waves propagating in an n-type PS rod are obtained, which can be reduced to those for piezoelectric and elastic rods by sequentially dropping the corresponding electron- and piezoelectricity-related terms. The Mindlin-Herrmann rod model is more accurate for analysis of terahertz elastic longitudinal wave in rod-like PS structures. The effects of the interaction between the piezoelectricity and semiconducting properties on the dispersion behaviors of terahertz elastic longitudinal waves are investigated in detail. Numerical results show that both phase and group velocities have a 50%-60% reduction in the terahertz range in comparison with those in the low frequency range, and the effective tuning range of the initial electron concentration is different for longitudinal waves with different frequencies. It lays the theoretical foundations for the design of terahertz elastic wave-based devices.

Integrated analysis of bandgap optimization regulation and wave propagation mechanism of hexagonal multi-ligament derived structures

In this paper, a new class of multi-ligament derived structures is proposed. Based on the finite element method and Bloch's theorem, the bandgap characteristics and transmission properties of different derived structures are comprehensively analyzed, and the bandgap opening and closing mechanism and the vibration and noise reduction capability of the structure are explained by stress cloud diagrams and vibration modes. Then, a better bandgap is obtained by structural optimization and active frequency modulation. Finally, the propagation characteristics of elastic waves in different derived structures are investigated separately. The results show that the multi-ligament derived structure has excellent bandgap performance and can obtain better vibration and noise reduction capability through bandgap adjustment and active strain modulation, which greatly improves its engineering practicality. The comprehensive analysis of wave propagation in this paper provides a theoretical basis and technical means for the improvement and design of metamaterials.

Elastic wave propagation characteristics in unsaturated double-porosity medium under capillary pressure

Rock pores often contain two-phase or multi-phase fluids, so it is important to understand how the wave-induced fluid pressure diffusion affects dispersion and attenuation of elastic waves for resource exploration. To describe the propagation of elastic wave in a double-porosity medium saturated by two-phase fluids, a wave propagation model, including both global and local flow mechanisms and considering the effect of capillary pressure, is derived. The dispersion and attenuation characteristics of three longitudinal waves (P1, P2, P3) and one transverse wave (S wave) are investigated by analyzing a plane wave, and the effects of physical parameters, such as inclusion radius, water saturation, permeability and porosity, on the propagation characteristics of P1 wave are investigated. Theoretical analysis shows that the model derived in this work can be degenerated into the Biot model under specific conditions. According to the numerical simulation results, due to the coupling of global flow and local flow, the P1 wave velocity may decrease below the Gassmann-Wood limit. The physical explanation of this phenomenon is as follows: when considering the effect of capillary pressure, the coupling effect of global flow and local flow will break the basic assumption that rock is undrained. The relationship between physical parameters of porous medium and the dispersion and attenuation characteristics of elastic wave is complicated and nonlinear. Compared with Santos model, elastic modulus predicted by Santos-Rayleigh model is in good agreement with the experimental data in the low frequency band, which proves that this model has good reliability in modeling the velocity field of seismic exploration.

Study on bandgap and vibration attenuation mechanism of novel chiral lattices

The chiral metamaterials have been well applied in engineering applications, but the chiral structure of a single material is difficult to achieve low-frequency sound insulation or vibration reduction. Therefore, a new chiral lattice structure is proposed in this paper. Based on the Bloch's theorem, finite element analysis is carried out, and the energy band structures of different types of structures are calculated. The principle of band gap generation of Model No.1 is emphatically analyzed. The effect of geometric parameters on the band gap is discussed. In addition, the propagation characteristics of elastic waves with a specific frequency in the structure are explored. Finally, according to the corresponding relationship between the finite element simulation of vibration transmission in finite period structures and the band gap frequency range, it is verified that the structure can effectively restrain the vibration transmission. The research results show that the structure has excellent broadband gap performance in the frequency range of 3000 Hz, and has a certain filtering effect on vibration transmission.

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.

Dispersion characteristics analysis of box girder structure based on virtual spring model and variational principle

The box girder structure is widely used in engineering. The study of its dispersion characteristics is of great significance to clarify the mechanism of its vibration propagation and sound radiation. However, its dispersion analysis is currently relies mainly on the finite element method due to the relative complexity of the box girder structure model, and although FE-based methods are an effective means to simulate the dispersion characteristics of box girder structure, they are not as favorable or convenient as the analytical or semi-analytical methods to perform a deeper investigation of the parameters and mechanisms involved in this process. Therefore, this study develops a semi-analytical method based on the energy method to analyze the dispersion characteristics of the box girder structure, with the core idea being the use of virtual springs to simulate the Bloch boundary; this successfully corrects for the complications of constructing displacement functions that satisfy Bloch boundary conditions in the traditional energy method, and it can improve the calculation efficiency. Then, the box girder structure is simplified to a spatial plate coupling model, and its dispersion control equation is established using the variational principle. This paper studies the propagation characteristics of elastic waves in a box girder, and the accuracy of the method is verified by finite element simulation.

Bandgap and Vibration Suppression Mechanisms of Novel Star‐Shaped Hybrid Metamaterials

Herein, a novel star‐shaped hybrid acoustic metamaterial structure is proposed. Based on Bloch's theorem and the finite element method, the bandgap characteristics and the bandgap formation mechanism of different combinations of structures are first analyzed. Then, the propagation characteristics of elastic waves in Model C2 are studied with focus on equal frequency contours, phase velocity, and group velocity. And the attenuation of elastic waves in the finite size structure of Model C2 illustrates that the elastic waves are effectively suppressed in the bandgap frequency range, which further confirms the perfect correspondence between the bandgap and the vibration attenuation region. Finally, the influence of structural parameters on the bandgap is analyzed, as well as the change of the bandgap when the structure undergoes large deformation, which can realize the tunability and flexibility of the bandgap. This study provides important clues for the design of vibration isolators and metamaterials, and shows the good engineering application potential of the structure for vibration isolation.

Theoretical and Experimental Investigations on the Ultra-Low-Frequency Broadband of Quasi-Static Metamaterials

This paper proposes an I-shaped radial elastic metamaterial with ultra-low-frequency broadband characteristics and studies the propagation characteristics of elastic waves in their quasi-static state. Through the calculation of the dispersion relationship, the frequency response function, and the eigenmode displacement field, it is found that the ultra-low-frequency wide band gap can be generated in the quasi-static metamaterial. The wide band gap is mainly caused by modal transitions. The equivalent mass–spring model reveals the modal changes of the I-shaped radial elastic metamaterial under the surface constraints. Furthermore, by studying the directional vibration displacement field of the finite period structure, it is demonstrated that the mechanism of the ultra-low-frequency broadband (0<Reduced frequency(Ω)<0.20) is the local resonance mechanism. Subsequently, the influence of the geometric and the material parameters on the location and width of the band gap is explored numerically. Finally, based on the model, through the hammer modal experiment, it is proven that the quasi-static structure yields an ultra-low-frequency stop band of 0.1–1012 Hz. The research conclusions can be applied to mechanical engineering fields such as ultra-low-frequency vibration reduction.

Dynamic stress analysis of an elliptical cavity during elastic wave propagation in a density-inhomogeneous medium with the modulus varying as a power function

Based on the propagation characteristics of elastic waves in an inhomogeneous continuum, we investigate the dynamic stress concentration caused by an elliptical cavity defect in a complex inhomogeneous continuum with a varying shear modulus and density under the action of SH waves (shear waves with displacement in the horizontal X–Y plane). By introducing the auxiliary function and the shear modulus function to construct the wave field function, the high-order wave equation with a variable coefficient is reduced and simplified and then transformed with coordinate conversion through the conformal mapping method, which allows the standard Helmholtz equation to be solved. Based on this approach, the wave field and stress field are derived by adopting the full-space elliptical cavity scattering model, and the expression of the dynamic stress concentration factor (DSCF) is obtained. Through a numerical example, we analyze the effects of the frequency of the incident wave, the ellipticity of the elliptical cavity, and the inhomogeneity of the medium on the DSCF at the boundary of the elliptical cavity under constant or variable wave velocities. The results show that in the presence of a defect in an inhomogeneous continuum, the dynamic stress concentration that arises when subjected to external forces is profound. Additionally, the value of the DSCF is sensitive to changes in each parameter, and the medium is more likely to be damaged near the position with a larger defect boundary curvature.

The low-frequency and broadband pendulum metamaterials based on inertial amplification mechanism

Pendulum has recently been introduced into the field of elastic metamaterials because of its low-frequency vibration characteristic, which further expands the application value of such structure. However, the low-frequency and broadband performance of traditional pendulum (TB) metamaterials still need to be further improved. In this paper, a new low-frequency pendulum metamaterial is proposed, and the low-frequency elastic wave propagation characteristics of the metamaterial are studied. The study shows that compared with the TB metamaterial, it can effectively lower the bandgap (BG) of metamaterial, but greatly narrow the BG. To solve this problem, the negative inertial amplification mechanism is further proposed, and the variation law of the metamaterial BG under this mechanism is investigated. It is found that the mechanism can effectively broaden the metamaterial BG and in specific cases make it have infinite width. Meanwhile, the constraint relationship between the frequency response function of unit-cell structure and the wave vector of metamaterial is established, which is used to reveal the broadening rationale of the BGunder the negative inertial amplification mechanism. Finally, depending on the negative inertial amplification mechanism, a novel broadband pendulum metamaterial is designed based on the low-frequency pendulum metamaterial. The relationship between the broadband attenuation behavior of the metamaterial and the frequency response function of unit-cell structure is analyzed, the working mechanism of negative inertial amplification to broadband pendulum metamaterial is also discussed, and the relevant optimization design method is given at the end.

Propagation of elastic waves in metamaterial plates with various lattices for low-frequency vibration attenuation

Elastic wave propagation characteristics of elastic metamaterial plates embedded scatterer with various lattices are explored numerically and experimentally in this study, for the attenuation of in-plane longitudinal and out-of-plane flexural waves in the subwavelength frequency region. Firstly, the mathematical models of the elastic metamaterial plates are established, and the dispersion relations are derived by the plane wave expansion (PWE) method based on Bloch's theorem. Furthermore, the applicability of the irreducible Brillouin zone (IBZ) for different lattices is also investigated through iso-frequency contours. The analysis of the bandgap formation mechanism indicates that the proposed metamaterial plates can enlarge the bandgaps (BGs) in the low-frequency range by coupling Bragg and local resonance BGs. Moreover, the influences of the scatterer shapes, geometric and material parameters on the BGs are investigated, and which combination of parameters has positive significance for opening low-frequency broadband is also discussed. The results show that the vibration transmittance obtained by experiment and numerical calculation is in good agreement with the predicted results of band structures. Therefore, the elastic metamaterial plates should be promising in the application of low-frequency wave mitigation.

Time and Frequency domain analysis of elastic waves in Scanning Laser Source Technique

This study investigates the propagation characteristics of elastic waves in a metal plate with a sub-surface defect. Dynamic force simulating a laser ultrasonic source was applied on the surface of the structure, and the energy transmitted around the defect was calculated in the time domain. The numerical results revealed that the energy of the acoustic wave transmitted around the defect close to the edge of the structure is larger than that around the defect located at the center of the structure. Next, natural vibration analysis was performed assuming that the defect is located near the left wall of the structure and at the center of the structure. The frequency components of the elastic wave transmitted around the defect were also calculated. The results show that the form of defect resonance and the resonance frequency are different depending on the defect location.