Analysis Of Wave Propagation Research Articles

Analyzing Soliton Solutions of the [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation: Comprehensive study of dark, bright, and periodic dynamics

This paper investigates the (n+1) dimensional integrable extension of the Kadomtsev–Petviashvili (KP) equation. The study focuses on extracting Auto-Bäcklund transformations for the given model using the extended homogeneous balance (HB) method in conjunction with Maple. These transformations are then employed to obtain explicit analytic solutions for the equation. Additionally, a Bilinear Bäcklund transformation is constructed based on the Hirota bilinear form, leading to the acquisition of exponential function solutions. Furthermore, complexiton solutions for the KP equation are obtained utilizing the bilinear form and the extended transformed rational function technique. The physical properties of the obtained solutions are explored through visualization techniques, including 3D, 2D, and contour plots. The analysis reveals the presence of dark, bright, and periodic solitons. The obtained solutions of the KP equation have practical applications in nonlinear optics, plasma physics, and wave propagation analysis.

Tunable multi-metamaterials intergrated with auxiliary magnetorheological resonators

In recent years, there has been a surge in interest in utilizing multi-metamaterials for various purposes, such as vibration control, noise reduction, and wave manipulation. To enhance their performance and tunability, auxiliary resonators and magnetorheological elastomers (MREs) can be effectively integrated into these structures. This research aims to formulate the wave propagation analysis of periodic architected structures integrated with MRE-based auxiliary resonators. For this purpose, cantilever MRE beams are embedded into conventional unit cells of square and hexagonal shapes. Integrating MREs into multi-metamaterial structures allows for real-time tuning of the material properties, which enables the multi-metamaterial to adapt dynamically to changing conditions. The wave propagation in the proposed architected structures is analyzed using the finite element method and Bloch’s theorem. The studied low-frequency region is significant, and the addition of MRE resonators leads to the formation of a mixture of locally resonant and Bragg-type stop bands, whereas the basic structures (pure square and hexagonal) do not exhibit any specific band gaps in the considered region. The effect of different volume fractions and applied magnetic fields on the wave-attenuation performance is also analyzed. It is shown that band gaps depend on the material parameters of the resonators as well as the applied magnetic flux stimuli. Moreover, the area of band gaps changes, and their operating frequency increases by increasing the magnetic flux around the periodic structure, allowing for the tuning of wave propagation areas and filtering regions using external magnetic fields. The findings of this study could serve as a foundation for designing tunable elastic/acoustic metamaterials using MRE resonators that can filter waves in predefined frequency ranges.

Multifield asymptotic homogenization for periodic materials in non-standard thermoelasticity

This article presents a multifield asymptotic homogenization scheme for the analysis of Bloch wave propagation in non-standard thermoelastic periodic materials, leveraging on the Green-Lindsay theory that accounts for two relaxation times. The procedure involves several steps. Firstly, an asymptotic expansion of the micro-fields is performed, considering the characteristic size of the microstructure. By utilizing the derived microscale field equations and asymptotic expansions, a series of recursive differential problems are solved within the repetitive unit cell Q. These problems are then expressed in terms of perturbation functions, which incorporate the material’s geometric, physical, and mechanical properties, as well as the microstructural heterogeneities. The down-scaling relation, which connects the microscopic and macroscopic fields along with their gradients through the perturbation functions, is then established in a consistent manner. Subsequently, the average field equations of infinite order are obtained by substituting the down-scaling relation into the microscale field equations. To solve these average field equations, an asymptotic expansion of the macroscopic fields is performed based on the microstructural size, resulting in a sequence of macroscopic recursive problems. To illustrate the methodology, a bi-phase layered material is introduced as an example. The dispersion curves obtained from the non-local homogenization scheme are compared with those generated from the Floquet-Bloch theory. This analysis helps validate the effectiveness and accuracy of the proposed approach in predicting the wave propagation behavior in the considered non-standard thermoelastic periodic materials.

Wave propagation analysis for three typical box girders: Dominant wave modes and their applications

Because of the prevalent application of bridges in transportation, problems such as vibration and noise of bridges, especially in densely populated urban areas, are increasingly arousing concerns. The vibro-acoustic behaviors of bridges are important for vibration and noise control. Although these vibro-acoustic behaviors have been reported and discussed in several studies in terms of modal analysis, this study focuses on the probe into the vibration properties of three typical box girders (BGs) from the wave motion perspective: concrete, steel–concrete composite, and steel BGs. The dispersion characteristics and mode shapes of waves propagating in BGs are identified using the wave finite element method (WFEM). This calculation method combines the finite element method (FEM) with the Bloch–Floquet theorem, and it is validated by the existing literature and FEM. The wave propagation characteristics of the three typical BGs are then compared to analyze their similarities and differences in vibration. Furthermore, the contribution of each wave mode to the whole vibration and the local vibration of BGs is determined; consequently, the important vibration mechanism can be identified and ranked in different frequency bands. Lastly, some feasible application of vibration control for BGs is given in the light of the vibration mechanism. The study results provide theoretical and practicable foundation of vibration control for BG bridges in urban rail trafficsystems

Advanced structural health monitoring and damage detection using inverse methods and perturbation stiff-ness matrix analysis

Sensor technology advancements have the health monitoring task for modern intricate structures introduce many challenges, primarily centered around the augmentation of safety margins and operational dependabil-ity. The demand for diverse systems or methodologies is, therefore, increasing. These systems or methodolo-gies should be capable of detecting damage, monitoring remotely, and conducting continuous evaluations in real-time. As part of this study, inverse techniques rooted in wave propagation analysis within structural frameworks are utilized to identify damage response vectors. Additionally, mathematical formulations grounded in minimal rank perturbation theory facilitate determining a perturbed stiffness matrix for a com-promised structure. Various excitations are included in the analysis, which is based on intricate non-linear structural modeling. Using streamlined procedures, these findings confirm the inherent versatility of a range of methodologies capable of meeting both rapid monitoring needs and exhaustive analytical needs. In addition, the proposed approach promotes the use of intelligent structures embedded with a variety of sensors that are not restricted by limitations related to sensor type or spatial deployment. Monitoring structural health and detecting damage could be significantly improved by this strategic deployment.

Preliminary Numerical Analysis of Mechanical Wave Propagation Due to Elastograph Measuring Head Application in Non-Invasive Liver Condition Assessment

The authors of this paper focused their attention on developing numerical models of mechanical wave propagation along human tissue as a result of the application of the measuring head of the FibroScan® elastograph. The FibroScan® diagnostic device is used for diagnostic testing of liver fibrosis and steatosis. This examination is carried out using an in vivo method by directly applying the surface of the ultrasonic measuring probe to the patient’s skin at the site of the liver. The authors’ idea is to use this apparatus for non-invasive testing on the liver used for transplantation. In order to do this, the measuring head cap should be modified so that its application to the liver does not result in damage as a result of mechanical wave excitation. The purpose of the manuscript was to build numerical models of the liver and the tissues surrounding the liver. Then, the corresponding numerical simulations were carried out, the results of which corresponded to the mechanical–acoustic properties of the physical models of the tissues. The obtained results were validated on a set of commercial calibrated phantoms. High agreement of the numerical models was obtained.

Analysis and Application of the Electromagnetic Wave Propagation, Fields, and Dispersion Relation in an Elliptical Chiro Plasma Waveguide Immersed in Magnetized Plasma

AbstractThis research proposes and investigates an elliptical waveguide filled with chiro plasma as its core and magnetized plasma as its clad region. The clad region is in the constant infinite magnetic field, and its direction is the same as the wave propagation in the chiro plasma elliptical waveguide. The electromagnetic wave propagation in the considered waveguide is studied. The expressions for electromagnetic field components in the chiro plasma core and magnetized plasma cladding are derived. The dispersion relations for the hybrid modes are calculated considering appropriate boundary conditions at the chiro plasma and magnetized plasma interface. The behavior of the energy flux and the dispersion curves are numerically and graphically studied. It is seen that the magnitude of the power density decreases with the increase of the cyclotron frequency and it increases with the increase of the plasma frequency and supports power flow in the backward direction for the considered mode. Furthermore, it is shown higher values of the chirality parameter cause the magnitude of the power flux to increase in the backward direction.

A multi-scale model-order reduction strategy for vibration analysis of coupled structures with local inhomogeneities

Although the wave finite-element method (WFEM) is an efficient numerical technique to analyze wave propagation characteristics and forced response of waveguides at medium and high frequencies, its application to large-scale and complex structures is still a challenge. In this paper, we introduce a model-order reduction (MOR) strategy for the WFEM to rapidly investigate the dynamics of coupled elastic systems involving one-dimensional waveguides with local inhomogeneities, such as steel bridges, fuselages and pipeline systems. The proposed method combines the advantages of mode-based component mode synthesis (CMS) and wave-based WFEM. A reduced modal basis is first established to describe the internal degrees of freedom using CMS. Subsequently, a reduced solution subspace considering the contribution of propagating and evanescent waves is constructed by the duality of Bloch’s formulations for the waveguide part, while wave scattering characteristics of the coupled element are used to quantify the influence of fixed-interface modes determined by CMS. Structural dynamic response can be then efficiently calculated using a dynamic stiffness matrix method. The performance of the MOR method in dispersion analysis and forced-response calculation is elaborately illustrated via an example of a steel beam with a diaphragm. The influence of the diaphragm on structural dynamic response is explained from the perspective of wave-propagation characteristics. Finally, the method is applied to a real steel–concrete composite girder, and the effects of the number and thickness of diaphragms on the vibration of each plate of the girder are discussed to provide some suggestions on vibration control.

Wave propagation analysis of functionally graded nanocomposite plate reinforced with graphene platelets in presence of thermal excitation

Wave propagation analysis of functionally graded nanocomposite plate reinforced with graphene platelets in presence of thermal excitation

A nonlocal strain gradient theory for wave propagation analysis in transversely isotropic elastic medium

This paper has the objective of studying the propagation of surface waves in a transversely isotropic medium based on nonlocal strain gradient theory (NSGT). A characteristics equation for the existence of surface waves is discussed. This equation could be easily reduced to the ones of the gradient strain theory, nonlocal theory and classical theory. It has also been concluded that there exist escape frequency and cut-off frequency for the wave propagating in size-dependent materials based on the NSGT. Dispersion equation for the propagation of Rayleigh-type waves at the free surface has been derived. The effect of the nonlocal parameter, the strain gradient parameter on the Rayleigh wave propagation is considered through some numerical examples.

Efficient zigzag theory-based spectral element model for guided waves in composite structures containing delaminations

Lamb wave-based structural health monitoring offers excellent potential for real-time delamination detection in laminated structures. It necessitates fast and accurate numerical simulation of guided wave interaction with delaminations. Towards this objective, we present an efficient layerwise zigzag theory (ZIGT) based time-domain spectral element for wave propagation analysis of composite beam- and panel-type structures (strips) containing delamination at arbitrary locations. The ZIGT delivers accuracy like layerwise theories by allowing slope discontinuities in the in-plane displacement field at layer interfaces while maintaining computational efficiency like equivalent single-layer (ESL) theories, making it ideal for such analyses. The high-order elemental nodes at Lobatto points have only four displacement variables, irrespective of the number of layers in the laminate. Delamination is modelled using the region approach, adapting the recently proposed hybrid point-least squares continuity method to satisfy the nonlinear displacement field continuity at the delamination fronts. The model’s efficacy is examined vis-à-vis elasticity-based elements, ESL theory-based elements, and the ZIGT-based standard finite element for free vibration and guided wave propagation responses of composite strips featuring multiple delaminations. The present model shows superior overall efficiency, accuracy, and convergence. An application of the model is also explored for identifying delamination locations from Lamb wave velocity fields.

Analysis of the interaction between torsion wave and phononic crystal in pipes

This article presents an analysis of torsional wave propagation in phononic crystal-based metamaterials. Such structures hold great promise as tools for wave manipulation. The unit cell of the presented structure was meticulously examined to obtain dispersion curves, revealing the presence of bandgaps and negative group velocities. The calculations of effective material parameters, based on eigenfrequencies, are presented to substantiate the existence of the bandgap and the negative value of group velocity. Time-domain simulations were conducted at various frequencies to analyze the wave behavior. In the case of negative group velocity, the wave inside the metamaterial propagates in the same direction as the incident wave. To verify the existence of negative velocity, a 2D Fast Fourier Transform (FFT) was performed, and the results from the 2D FFT data analysis align perfectly with the eigenfrequency analysis.

Reflection and Transmission Analysis of Surface Acoustic Wave Devices.

This paper presents a study of the propagation of surface acoustic waves in a single and periodic array of metal strip overlays on the surface of layered substrates. Responses of reflected and transmitted surface acoustic waves due to various geometric design parameters of the grating arrays are investigated. An eight-dimensional matrix formulation based on Stroh formalism is adopted to analyze wave propagation in piezoelectric layered media. The dispersion curves for aluminum-zinc oxide films on glass substrates are determined using the surface impedance tensor method. A transfer matrix in terms of the state vectors in cooperation with continuity conditions on the edges of the grating array is used to determine the reflectivity and transmittance of the horizontally propagating surface acoustic waves. The analysis and simulation results show that when the surface acoustic wave is obliquely incident on an array of gratings and the strip width is equal to the gap between strips, the constructive interference of the reflected wave occurs at odd multiples of the strip width to a wavelength ratio of 0.25. When the strip width is unequal to the gap, the constructive interference of the reflected wave is an odd multiple of the strip width to a wavelength ratio of 0.5. An increase in the number of strips concentrates the reflectivity's extreme frequencies, and an increase in the strip height increases the bandwidth of the extreme frequencies. Both of these increases strengthen the reflected wave's constructive interferences.

Bending and wave propagation analysis of axially functionally graded beams based on a reformulated strain gradient elasticity theory

Bending and wave propagation analysis of axially functionally graded beams based on a reformulated strain gradient elasticity theory

Wave Propagation and Stability Analysis for Ostrovsky and Symmetric Regularized Long-Wave Equations

This work focuses on the propagation of waves on the water’s surface, which can be described via different mathematical models. Here, we apply the generalized exponential rational function method (GERFM) to several nonlinear models of surface wave propagation to identify their multiple solitary wave structures. We provide stability analysis and graphical representations for the considered models. Additionally, this paper compares the results obtained in this work and existing solutions for the considered models in the literature. The effectiveness and potency of the utilized approach are demonstrated, indicating their applicability to a broad range of nonlinear partial differential equations in physical phenomena.

Wave propagation analysis in pre-stressed incompressible hyperelastic multi-layered plates using a plate theory

Wave propagation analysis of pre-stressed incompressible hyperelastic thin multi-layered plates is developed based on the first-order shear deformation plate theory (FSDT) with second order thickness extensibility. Variables describing the thickness-direction deformation are obtained from the incompressibility condition. The incremental theory of nonlinear elasticity is employed in conjunction with a plate theory. The multi-layered plate is assumed to be symmetric in the thickness direction. Since the plate theory has not been used for the wave propagation analysis of hyperelastic plates, the results of flexural wave modes are compared with results of the straight-crested flexural waves based on the three-dimensional (3D) elasticity theory available in the literature and the results for in-plane wave modes are compared with those developed in this study using the plane-stress elasticity theory. The dispersion curves of both extensional and flexural waves for single-layer and three-layer plates are presented and the effects of different parameters including the homogenous pre-stretch, the wave propagation direction and the plate initial thickness on the dispersion curves are discussed in detail. The results indicate that the phase speed of the extensional waves depends on the wave propagation angle due to the induced anisotropy. As the overall shear modulus of the three-layer plate increases, the phase velocity increases. Also, the effect of pre-stretch and thickness on phase speed of flexural waves is not pronounced for high frequencies.

Wave propagation analysis of functionally graded graphene origami-enabled auxetic metamaterial beams resting on an elastic foundation

Wave propagation analysis of functionally graded graphene origami-enabled auxetic metamaterial beams resting on an elastic foundation

Acoustic wave propagation in a porous medium saturated with a Kelvin–Voigt non-Newtonian fluid

SUMMARYWave propagation in anelastic rocks is a relevant scientific topic in basic research with applications in exploration geophysics. The classical Biot theory laid the foundation for wave propagation in porous media composed of a solid frame and a saturating fluid, whose constitutive relations are linear. However, reservoir rocks may have a high-viscosity fluid, which exhibits a non-Newtonian (nN) behaviour. We develop a poroelasticity theory, where the fluid stress-strain relation is described with a Kelvin–Voigt mechanical model, thus incorporating viscoelasticity. First, we obtain the differential equations from first principles by defining the strain and kinetic energies and the dissipation function. We perform a plane-wave analysis to obtain the wave velocity and attenuation. The validity of the theory is demonstrated with three examples, namely, considering a porous solid saturated with a nN pore fluid, a nN fluid containing solid inclusions and a pure nN fluid. The analysis shows that the fluid may cause a negative velocity dispersion of the fast P(S)-wave velocities, that is velocity decreases with frequency. In acoustics, velocity increases with frequency (anomalous dispersion in optics). Furthermore, the fluid viscoelasticity has not a relevant effect on the wave responses observed in conventional field and laboratory tests. A comparison with previous theories supports the validity of the theory, which is useful to analyse wave propagation in a porous medium saturated with a fluid of high viscosity.

CHARACTERISATION OF INFRAGRAVITY WAVES AND THEIR ASSOCIATED HYDRODYNAMICS PROCESSES IN MESO-MACRO TIDAL LAGOON

Infragravity (hereafter ‘IG’) waves are ocean waves related to the presence of groups in incident shortwaves. The importance of IG waves in the nearshore and their role in beach morphodynamics have been widely documented over the last few decades (Bertin et al., 2018) while in contrast, studies on characterisation of IG waves and related impacts in tidal inlets are scarce and have only recently begun to be addressed (Williams and Stacey, 2016). Nonetheless, existing studies tend to show that IG waves in tidal inlets can play an important role in the short and long-term hydro-morphodynamics of coastal lagoons. The current study presents the first large scale field measurements and analysis of IG waves propagation and characteristics in a meso-macro tidal lagoon/inlet.

Analysis of Wave Propagation in Hybrid Metamaterial Structure for Terahertz Applications

Analysis of Wave Propagation in Hybrid Metamaterial Structure for Terahertz Applications