Mechanical Wave Propagation Research Articles

Two types of interaction phenomena of the lump wave for nonlinear model of Rossby waves

In this paper, we show the interaction phenomena about the first-order lump wave and multiple solitons by four theorems. The interaction phenomena are divided into two types, one type is absorbing collision phenomenon and the other type is elastic collision phenomenon. Six sets of dynamic plots over time are showed the phenomenon of absorbing interactions with energy transfer process, the phenomenon of elastic interactions with restoration of the initial state after collision. We apply the four theorems to an equation which can characterize the Rossby waves’ amplitude, this equation can be used to describe the resonance phenomenon of Rossby waves. Different test functions with the same parameter values can present different wave-wave interaction properties. This study contributes to in-depth investigation of the mechanism of lump wave generation, evolution and interaction.

Nonlinear generalized piezothermoelasticity of spherical vessels made of functionally graded piezoelectric materials

The present study investigates the thermoelastic response of a heterogeneous piezoelectric sphere under thermal shock loading. Boundary conditions as well as loading are considered as symmetric; thus, the response of the sphere is expected to be symmetric. All of the properties of the thick-walled sphere, including mechanical, electrical and thermal properties, are considered dependent on the radial position, except for the relaxation time, which is considered a constant value along the radius. The governing equations of the sphere have been derived under heterogeneous anisotropic assumptions. The general form of the second law of thermodynamics, which is nonlinear in nature, and is called nonlinear energy equation is used. The number of the established equations is three, which includes the motion equation, energy equation and Maxwell electrostatic equation of Maxwell. These equations are obtained in terms of radial displacement, temperature difference and electric potential. The energy equation is derived based on Lord and Shulman theory with a single relaxation time. In the next step, by introducing dimensionless variables, the governing equations are provided in dimensionless presentation. Then these equations have been discretized using generalized differential quadrature method. Also, in order to follow the solution of the equations in time domain, Newmark method has been used. Since the system of equations is nonlinear, Picard algorithm is applied as a predictor-corrector mechanism to solve the nonlinear system of equations. Then numerical results are presented to investigate the propagation of mechanical, thermal and electric waves inside the heterogeneous sphere and also their reflection from the outer surface of the sphere. By examining the results, it can be seen that mechanical and thermal waves propagate with a limited speed, while the speed of electric wave propagation is infinite.

Assorted optical solitons of the (1+1)- and (2+1)-dimensional Chiral nonlinear Schrödinger equations using modified extended tanh-function technique

In this research article, the (1+1)- and (2+1)-dimensional Chiral nonlinear Schrödinger equations (CNLSEs) are studied, which play an important role in the development of quantum mechanics, particularly in the field of quantum Hall effect. Our primary goal is to obtain the analytical solutions utilizing novel methodology, particularly the modified extended tanh-function technique. We concentrate on the search to solitary wave solutions inside the (1+1)- and (2+1)-dimensional CNLSEs, which are relevant in domains such as optics, electro-magnetic wave propagation, plasma physics, optics and quantum mechanics. Our objective is to increase knowledge of this equation and give insight into the behavior of solitary waves by employing a novel mathematical technique. This will be accomplished by displaying our findings in 2D and 3D graphics. We believe that our results would pave a way for future research generating optical memories based on the nonlinear solitons.

The site-city interaction effect uncertainty on structural responses and its application to fragility analysis of buildings in Shanghai CBD

Seismic fragility analysis is a crucial tool for assessing the seismic performance of buildings. In areas with dense clusters of tall buildings, the significant site-city interaction (SCI) effect alters wave propagation mechanisms, influencing the seismic fragility of structures. However, a significant increase in computational workload results from the need for detailed modeling of sites and building clusters for the SCI analysis. To address this challenge, this work first investigates the minimum number of earthquake waves required to characterize SCI-induced response changes. The Central Business District of Shanghai is analyzed. A table for the recommended minimum number for a given accuracy requirement and prediction reliability is provided. Moreover, a seismic fragility analysis method considering the SCI effect is proposed for low-rise buildings. The case study indicates that, buildings with similar height will exhibit various fragility changes after considering SCI. For the complete damage state, the mean intensity value of the fragility curve can be 14.4 % smaller than that without SCI. In addition, this approach provides significant computational workload reduction. For the case study, the computational workload of the proposed method is roughly 1/50 of that using traditional IDA method.

Experimental Study on the Design and Cutting Mechanical Properties of Bionic Pruning Blades

This study focuses on existing pruning equipment; cutting blades show cutting resistance and lead to high energy consumption. Using finite element (FEA) numerical simulation technology, the branch stress wave propagation mechanism during pruning was studied. The cutting performance of the bionic blade was evaluated with cutting energy consumption as the test index and the branch diameter and branch angle as the test factors, respectively. The test results showed that the blades imitating the mouthparts of the three-pecten bull and the beak of the woodpecker performed well in pruning, and the energy consumption during cutting was reduced by 18.2% and 16.3% compared to traditional blades, making these blades significantly better. These two blades also effectively reduced the cutting resistance and branch splitting by optimizing the edge angle design and increasing the slip-cutting action. In contrast, the imitation shark’s tooth blade increased cutting energy consumption by 14.4% due to the large amount of cutting resistance in the cutting process when cutting larger-diameter branches, making it unsuitable for application in the pruning field. Therefore, the blades imitating the mouthparts of the three pectins and the beak of the woodpecker have significant advantages in reducing the cutting resistance and improving the pruning quality. These findings provide an important theoretical reference for the development of energy-efficient pruning equipment.

Application Practice of SHPB Experimental Technology in "Blasting Engineering" Teaching

The course of "Blasting Engineering" is a highly practical professional course in the field of civil engineering. In order to help students deeply understand and comprehend the propagation and attenuation mechanism of stress waves during rock blasting process, as well as the influence of rock dynamic characteristics on blasting rupture effect, SHPB impact compression experimental technology is introduced into the teaching of "blasting engineering". Firstly, the structure, experimental process, and principles of SHPB equipment were introduced, allowing students to have a better understanding of the experimental principles of SHPB and the theoretical calculation methods of rock dynamic parameters. Then, by combining SHPB experiments with the theoretical course of "Blasting Engineering", the teaching mode can solve students' difficulties in learning blasting theory, exercise their scientific research and exploration abilities, expand their innovative thinking, and cultivate their ability to propose and solve key scientific problems. This helps to unleash students' subjective initiative in conducting experimental research independently and improve teaching effectiveness.

Propagation of periodic director and flow patterns in a cholesteric liquid crystal under electroconvection

The electroconvection of liquid crystals is a typical example of a dissipative structure generated by complicated interactions between three factors: convective flow, structural deformation, and the migration of charge carriers. In this study, we found that the periodic structural deformation of a cholesteric liquid crystal propagates in space, like a wave, under an alternating-current electric field. The existence of convection and charge carriers was confirmed by flow-field measurements and dielectric relaxation spectroscopy. Given that the wave phenomenon results from electroconvection, we suggest a possible model for describing the mechanism of wave generation. The validity of the model was examined using the Onsager variational principle. Consequently, it was suggested that wave generation can be described by four effects: the electrostatic potential, mixing entropy, anisotropic friction due to charge migration, and viscous dissipation of the liquid crystal.

Elastic wave insulation and propagation control based on the programmable curved-beam periodic structure

AbstractCurved-beams can be used to design modular multistable metamaterials (MMMs) with reprogrammable material properties, i.e., programmable curved-beam periodic structure (PCBPS), which is promising for controlling the elastic wave propagation. The PCBPS is theoretically equivalent to a spring-oscillator system to investigate the mechanism of bandgap, analyze the wave propagation mechanisms, and further form its geometrical and physical criteria for tuning the elastic wave propagation. With the equivalent model, we calculate the analytical solutions of the dispersion relations to demonstrate its adjustability, and investigate the wave propagation characteristics through the PCBPS. To validate the equivalent system, the finite element method (FEM) is employed. It is revealed that the bandgaps of the PCBPS can be turned on-and-off and shifted by varying its physical and geometrical characteristics. The findings are highly promising for advancing the practical application of periodic structures in wave insulation and propagation control.

Analytic solutions for effective elastic moduli of isotropic solids containing oblate spheroid pores with critical porosity

AbstractAccurate characterization for effective elastic moduli of porous solids is crucial for better understanding their mechanical behaviour and wave propagation, which has found many applications in the fields of engineering, rock physics and exploration geophysics. We choose the spheroids with different aspect ratios to describe the various pore geometries in porous solids. The approximate equations for compressibility and shear compliance of spheroid pores and differential effective medium theory constrained by critical porosity are used to derive the asymptotic solutions for effective elastic moduli of the solids containing randomly oriented spheroids. The critical porosity in the new asymptotic solutions can be flexibly adjusted according to the elastic moduli – porosity relation of a real solid, thus extending the application of classic David‐Zimmerman model because it simply assumes the critical porosity is one. The asymptotic solutions are valid for the solids containing crack‐like oblate spheroids with aspect ratio < 0.3, nearly spherical pores (0.7 < < 1.3) and needle‐like prolate pores with > 3, instead of just valid in the limiting cases, for example perfectly spherical pores (= 1) and infinite thin cracks (0). The modelling results also show that the accuracies of asymptotic solutions are weakly affected by the critical porosity and grain Poisson's ratio , although the elastic moduli have appreciable dependency of and . We then use the approximate equations for pore compressibility and shear compliance as inputs into the Mori–Tanaka and Kuster–Toksoz theories and compare their calculations to our results from differential effective medium theory. By comparing the published laboratory measurements with modelled results, we validate our asymptotic solutions for effective elastic moduli.

Study on the evolution characteristics of coal mass spalling during coal and gas outbursts

The process of coal and gas outbursts (called outbursts for short) are commonly accompanied by coal mass spalling and fragmentation, but the formation mechanism of spalling is still unclear. To clarify this mechanism, this research constructs multi-layered combined coal-rock mass model. Based on the stress wave propagation mechanism, it’s found that outbursts initially start from ‘weak layer’. Besides, there are two significant results by analyzing the process of unloading waves formed by sudden pressure relief of the excavation face. Firstly, in the axial direction, due to the internal impact of the coal mass during the unloading wave propagation, the load shock wave is formed. The tensile stress is formed on the surface of the coal mass, resulting in rapid damage to the coal mass and even multi-layered spalling. Secondly, in the radial plane, permanent standing surfaces will be formed when the unloading wave catches up with the plastic load wave. Under effect of the unloading wave, internal impact will occur a series of load shock wave, resulting in the formation of multi-layered spalling in the radial plane. In addition, the attenuation law of the load shock wave generated by the internal impact in multi-layered coal mass is also analyzed, results showed that the thickness of coal mass spalling formed far away from the free surface will increase. Finally, the three-dimensional dynamic damage path and the spindle shape damage area formation mechanism in coal mass under external dynamic load are analyzed, which provides a new idea for elucidating the outbursts mechanism.

Non-Linear Plasma Wave Dynamics: Investigating Chaos in Dynamical Systems

This work addresses the significant issue of plasma waves interacting with non-linear dynamical systems in both perturbed and unperturbed states, as modeled by the generalized Whitham–Broer–Kaup–Boussinesq–Kupershmidt (WBK-BK) Equations. We investigate analytical solutions and the subsequent emergence of chaos within these systems. Initially, we apply advanced mathematical techniques, including the transform method and the G′G2 method. These methods allow us to derive new precise solutions and enhance our understanding of the non-linear processes dominating plasma wave dynamics. Through a systematic analysis, we identify the conditions under which the system transitions from orderly patterns to chaotic behavior. This investigation provides valuable insights into the fundamental mechanisms of non-linear wave propagation in plasmas. Our results highlight the dynamic interplay between non-linearity and variation, leading to chaos, which may be useful in predicting and potentially controlling similar phenomena in practical applications.

Interaction between the core and the edge for ion cyclotron resonance heating based on artificial absorption plasma model

In numerical simulations of the ion cyclotron range of frequencies (ICRF) wave heating scheme, core solvers usually focus on wave propagation and absorption mechanisms within the core plasma region. However, the realistic scrape-off layer (SOL) plasma is usually simplified, making it difficult to have deeper understanding of wave propagation and absorption within the SOL. In this work, we employ a cold plasma assumption and an artificial absorption mechanism based on the approach of reference (Zhang et al 2022 Nucl. Fusion 62 076032), to study wave propagation and absorption in the realistic SOL plasma of the EAST. During the exponential decay of the total coupled power with respect to the toroidal mode numbers, several fluctuations are observed in the case of low collisional frequencies. The fluctuations may be caused by the cavity modes associated with specific toroidal mode numbers. Due to the presence of cut-off densities, the edge power losses and the total coupled power exhibit different behaviors before and after the cut-off layer is “open”. Furthermore, the simulation results obtained from the kinetic model in reference (Zhang et al 2022 Nucl. Fusion 62 076032) is discussed. This suggests that both the core-edge combined model and the artificial mechanism are capable of simulating wave propagation and absorption.

The Relationship between Cardiomyocyte Action Potentials and Ion Concentrations: Machine Learning Prediction Modeling and Analysis of Spontaneous Spiral Wave Generation Mechanisms

The changes in cardiomyocyte action potentials are related to variations in intra- and extracellular ion concentrations. Abnormal ion concentrations can lead to irregular action potentials, subsequently affecting wave propagation in myocardial tissue and potentially resulting in the formation of spiral waves. Therefore, timely monitoring of ion concentration changes is essential. This study presents a novel machine learning classification model that predicts ion concentration changes based on action potential variation data. We conducted simulations using a single-cell model, generating a dataset of 850 action potential variations corresponding to different ion concentration changes. The model demonstrated excellent predictive performance, achieving an accuracy of 0.988 on the test set. Additionally, the causes of spontaneous spiral wave generation in the heart are insufficiently studied. This study presents a new mechanism whereby changes in extracellular potassium ion concentration leads to the spontaneous generation of spiral waves. By constructing composite myocardial tissue containing both myocardial and fibroblast cells, we observed that variations in extracellular potassium ion concentration can either trigger or inhibit cardiomyocyte excitation. We developed three tissue structures, and by appropriately adjusting the extracellular potassium ion concentration, we observed the spontaneous generation of single spiral waves, symmetrical spiral wave pairs, and asymmetrical double spiral waves.

Identification of bored pile defects utilizing torsional low strain integrity test: Theoretical basis and numerical analysis

The torsional low strain integrity test (TLSIT), known for its advantages such as a smaller detection blind zone, improved identification of shallowly buried defects, stable phase velocity for signal interpretation, and better adaptability for existing pile testing. However, it lacks a comprehensive understanding of the authentic three-dimensional (3D) strain wave propagation mechanism, particularly wave reflection and transmission at defects. To address this gap, a novel 3D theoretical framework is introduced in this context to model the authentic 3D wave propagation during the TLSIT. The proposed approach is validated by comparing its results with those obtained from 3D finite element method (FEM) simulations and simplified 1D (one-dimensional) and 3D analytical solutions. Additionally, a parametric study is conducted to enhance insights into the formation mechanism of high-frequency interference observed during the TLSIT. Finally, a defect identification study is performed to provide guidance for interpreting the wave spectrum in terms of defect characteristics.

Experimental study on the propagation mechanism of acetylene-air detonation waves in a unilaterally intermittently constrained channel

This study experimentally explores the propagation mechanisms of acetylene/air detonation waves within a channel intermittently constrained on one side, utilizing soot foil and high-speed schlieren photography to capture the cellular structure and shock-flame evolution. The experiments revealed that the detonation waves traverse the semi-enclosed channel with various discrete wall configurations on the side in three distinct propagation modes: (I) periodic detonation failure and re-initiation; (II) single extinction and re-initiation; (III) non-extinction. Mode I occurs exclusively when the open area ratio exceeds 0.85, while detonation tends to favour Mode II when the gaps between discrete walls exceed three times the cell size; otherwise, it tends towards Modes III. The re-initiation mechanism of detonation involves curvature shocks inducing local explosions of reactive mixtures through multiple Mach reflections off the discrete walls. The self-sustained propagation mechanism of the detonation wave is maintained by the interaction of strong transverse shocks reflected from discrete walls with the inherent transverse waves within the detonation structure, sustaining the instability of the cellular detonation.

A study of asymmetric guided wave propagation mechanism in elbow and prediction of elbow erosion degree based on SAFE and GA-LSSVM methods

Aiming at the problems of complex sensor layout, low detection accuracy when using guided wave to detect the elbow’s erosion degree, this research presents a new approach based on asymmetric guided wave and Genetic Algorithm-Least Support Vector Machine (GA-LSSVM). The program for calculating elbow’s dispersion curve was compiled using the semi-analytical finite element (SAFE) method. Through numerical simulation, it is found that the bending mode in the guided wave signal at the outer arch back position of the receiving end decreases with the increase of the erosion degree, which leads to the decrease of the signal’s time domain energy. Finally, The GA-LSSVM model were used to predict various elbow specimens’ residual wall thickness, and the results shows the high prediction accuracy. The average accuracy of predicting the new elbows is 87.63%. This research provides a feasible scheme for detecting elbow’s erosion degrees in engineering.

Phase velocity shifts of shear surface waves in flexoelectric wave-guide clamped on piezomagnetic base

Surface acoustic wave devices featuring periodic layers of piezomagnetic and piezoelectric-flexoelectric layers are subject to intense investigation. In miniaturized devices, large strain gradients are possible that produce significant flexoelectric fields in piezoelectric components. In the present theoretical research, surface acoustic wave transference has been manifested in a flexoelectric waveguide clamped over a piezomagnetic base. This endeavor involves the formulation and solution of coupled magneto-electro-elastic field equations governing the structure’s behavior. Coupled magneto-electro-elastic field equations for the structure have been derived and solved utilizing analytical techniques. By accounting for pertinent boundary conditions, the dispersion relations characterizing the velocity of surface waves, both in scenarios with and without electrodes have been obtained. Based on proper numerical examples, the frequency and phase velocity spectrum have been plotted offering insights into key parameters i.e. modal frequency, phase velocity, and wave attenuation. The outcomes of the theoretical study may be helpful in providing insights into mechanical wave propagation in coupled piezoelectric/piezomagnetic structures.

Numerical modeling of cavity collapse water hammer in pipeline systems: Internal mechanisms and influential factors of transient flow and secondary pressure rise dynamics

This study explores the dynamics of pressure wave propagation and cavitation in pressurized pipelines during and after the rapid closure of the pipeline's end ball valve, utilizing a three-dimensional computational fluid dynamics approach with the method of characteristics, validated against Bergant and Simpson's experimental data of three degrees of cavitation. It innovatively examines transient pressure dynamics through both energy transformation and wave propagation perspectives, focusing on the phases of water column separation and coalescence, and the dynamics of flow interruption bubbles. The research delves into the detailed mechanisms of pressure wave propagation and further assesses the effects of physical factors. Key findings include: (1) As initial inlet velocities increase, cavitation starts earlier, extends further, and intensifies, with higher final volume fractions near the valve, indicating that higher velocities exacerbate cavitation. Higher inlet velocities also correlate with more intricate and expansive vortex formations. (2) Secondary pressure surges in water hammer result from the superposition of two-stage positive pressure waves. Initially, positive pressure waves within the conduit reflect twice from air pockets and the upstream boundary, remaining positive. Subsequently, they interact with secondary positive pressure waves reflected by the valve, causing a secondary pressure surge. (3) The fluid flow is laterally symmetry in the pipe cross section, except for minor local asymmetrical spikes in areas with vapor bubbles. Velocity discrepancies are notable near the pipe walls due to vapor accumulation, primarily on the upper wall due to buoyancy. This accumulation may narrow the flow area, possibly accelerating the water passing by. (4) Lower flow velocities, downward inclines, and slower valve closures diminish secondary pressure rise amplitudes in water hammer events, while reduced static heads intensify cavitation despite lessening pulse amplitudes. These findings offer valuable insights for the design and operational guidance of complex hydraulic systems during transient processes in urban water supplies.

Guided wave propagation in a high-speed rotating concrete shell reinforced by advanced nanocomposites

This paper investigates the propagation of guided waves in a high-speed rotating concrete shell reinforced with graphene oxide powders (GOP) using higher-order shear deformation theory (HSDT). The study addresses the complexities introduced by initial hoop tension and provides a comprehensive analytical solution procedure. Concrete shells are widely used in various engineering applications due to their robustness and durability; however, their mechanical performance can be significantly enhanced by the incorporation of GOP, which improves the material properties, such as tensile strength and modulus of elasticity. The analysis begins with the formulation of the governing equations based on HSDT, which accurately captures the effects of transverse shear deformation and rotary inertia, crucial for high-speed rotating structures. The presence of initial hoop tension, resulting from the centrifugal forces in the rotating shell, is integrated into the model to reflect real-world conditions. The modified equations are then solved analytically to obtain the dispersion relations for the guided wave modes. The results reveal that the inclusion of GOP significantly alters the wave propagation characteristics, enhancing the shell’s ability to transmit high-frequency waves with minimal attenuation. The initial hoop tension is found to shift the frequencies of the guided wave modes, indicating a coupling effect between the mechanical loading and wave propagation. This study provides valuable insights into the dynamic behavior of reinforced concrete shells in high-speed rotational environments, offering a potential pathway for the design of advanced structural components in aerospace, automotive, and civil engineering applications.

Time/frequency domain analysis of detonation wave propagation mechanism in a linear rotating detonation combustor

Controlling the rotating detonation combustor (RDC) is crucial for enhancing propulsion system safety, efficiency, and overall performance. Swift and precise identification of the operational mode of RDC is of great significance for refining the propulsion dynamics of detonation-based technologies. In this study, two-dimensional numerical simulations are performed to investigate time-domain characteristics and frequency-domain characteristics of various operational modes of the RDC, hydrogen–air mixtures are used as fuel, and fast Fourier transformation (FFT) is applied to the analysis of frequency-domain. The alteration of the RDC operational mode is achieved through adjustments to the chemical equivalent ratio (ER) of the fuel, spanning from 0.52 to 3.50. Our findings reveal four distinct operational modes within this equivalent ratio range: ignition failure (ER ≤ 0.52 and ER ≥ 3.50), collision failure (ER = 0.85, 1.60 and 1.65), single wave (0.53 ≤ ER ≤ 0.80 and 1.70 ≤ ER ≤ 3.40) and multiple wave mode (0.90 ≤ ER ≤ 1.50). For the ignition failure mode, the detonation waves in RDC decouple from the flame and fail after ignition. In the collision failure mode, the inability of detonation waves to propagate sustainably within the RDC is evident. Frequency-domain analysis underscores the significance of a characteristic low-frequency (0.3 kHz) in distinguishing this mode from others. For single wave mode, it represents the steady and continuous propagation of a detonation wave in the RDC. Frequency-domain analysis reveals characteristic frequencies approximately equal to integer multiples of the propagation frequency (fD), where fD ∼ 10fD serves as the primary characteristic frequencies. The multiple wave mode can be categorized into two subtypes: the forward and reverse single detonation waves appear alternately or the forward and reverse single detonation waves finally co-direction double detonation waves. In the former subtype, characteristic frequencies are integer multiples of the fD, but the amplitude distribution is different with single wave mode. In contrast, primary characteristic frequencies of the latter subtype are fD ∼ 4fD, accompanied by two adjacent characteristic frequencies near each integer multiples of fD. These findings promise advancements in the controllability of RDC and lay the foundations for the development of RDC control systems.