Search Results (93)

In this study, nonlinear Lamb wave-based higher harmonic detection is employed to assess the tensile-induced microdamage in patch-repaired carbon fiber-reinforced polymer (CFRP) structures. With respect to the external repair design optimization model based on proxy technology, the minimum nonlinear coefficients are obtained from the optimal patch design parameters, thereby improving the tensile performance of the repaired structure and capturing the repair effect of the patch. First, the nonlinear Lamb wave propagation behaviors of patch-repaired CFRP laminates are assessed under different tensile displacements, and the accuracy of the finite-element model strategy is confirmed by experimental results. Second, on the basis of the tensile displacement induced under the highest nonlinear response, the effects of the radius, thickness and rotation angle of the patch on the secondary and tertiary nonlinear coefficients of the composite glued repair structure and the tensile damage area of the matrix are discussed. After the effects of individual parameters on the patch repair structure are analyzed, the effect of multiple target parameters on the quadratic relative acoustic nonlinearity coefficient of the patch repair structure is investigated via a Latin hypercube experimental design and the Diffuse Approximation method, and the optimal solutions for the mesh parameters of the patch repair structure are successfully obtained, which provides a reference for the multiparameter optimization of patch repair structures in engineering cases. Full article

While recent advances have successfully integrated neural networks with physical models to derive numerical solutions, there remains a compelling need to obtain exact analytical solutions. The ability to extract closed-form expressions from these models would provide deeper theoretical insights and enhanced predictive capabilities, complementing existing computational techniques. In this paper, we study the nonlinear Gardner equation and the (2+1)-dimensional Zabolotskaya–Khokhlov model, both of which are fundamental nonlinear wave equations with broad applications in various physical contexts. The proposed models have applications in fluid dynamics, describing shallow water waves, internal waves in stratified fluids, and the propagation of nonlinear acoustic beams. This study integrates a modified generalized Riccati equation mapping approach and a novel generalized $\left({\displaystyle \frac{G^{\prime }}{G}}\right)$-expansion method with neural networks for obtaining exact solutions for the suggested nonlinear models. Researchers are currently investigating potential applications of these neural networks to enhance our understanding of complex physical processes and to develop new analytical techniques. The proposed strategies incorporate the solutions of the Riccati problem into neural networks. Neural networks are multi-layer computing approaches including activation and weight functions among neurons in input, hidden, and output layers. Here, the solutions of the Riccati equation are allocated to each neuron in the first hidden layer; thus, new trial functions are established. We evaluate the suggested models, which lead to the construction of exact solutions in different forms, such as kink, dark, bright, singular, and combined solitons, as well as hyperbolic and periodic solutions, in order to verify the mathematical framework of the applied methods. The dynamic properties of certain wave-related solutions have been shown using various three-dimensional, two-dimensional, and contour visualizations. This paper introduces a novel framework for addressing nonlinear partial differential equations, with significant potential applications in various scientific and engineering domains. Full article

Transcranial focused ultrasound is a promising noninvasive technique for neuromodulation in neurological and psychiatric disorders, but accurate prediction of acoustic transmission through the skull remains a major challenge. In this study, we present a five-layer numerical human head model that integrates frequency-dependent acoustic parameters with nonlinear time-explicit dynamics to realistically capture ultrasound propagation. The model explicitly represents skin, trabecular bone, cortical bone, and brain, each assigned experimentally derived acoustic properties across a clinically relevant frequency range (0.5–5 MHz). Numerical simulations were performed in the frequency domain and time-explicit to quantify sound transmission loss and focal depth under high-intensity and high-frequency stimulation. The results show the effect of frequency, radius of curvature, and skull thickness on maximum pressure ratio, focal depth, and focus zone inside the brain tissue. Findings indicate that skull geometry, particularly radius of curvature and thickness, strongly influences the focal zone, with thinner skull regions allowing deeper penetration and reduced transmission loss. Comparison of the frequency-domain model with the time-explicit model demonstrated broadly similar trends; however, the frequency-domain approach consistently underestimated transmission loss and was unable to capture nonlinear effects such as frequency harmonics. These findings highlight the importance of nonlinear, time-explicit modeling for accurate transcranial ultrasound planning and suggest that the proposed framework provides a robust tool for optimizing stimulation parameters and identifying ideal target zones, supporting the development of safer and more effective neuromodulation strategies. Full article

This work investigates how fractionality affects the dynamical behavior of dust-acoustic shock waves that arise and propagate in a depleted-electron complex plasma. This model consists of inertial negatively charged dust grains and inertialess nonextensive distributed ions. Initially, the fluid model equations that govern the propagation of nonlinear dust-acoustic shock waves are reduced to the integer Burgers-type equations using the reductive perturbation method. Thereafter, the integer Burgers-type equations are converted to the fractional cases using a suitable transformation. For analyzing this fractional family, both the Tantawy technique and the new iterative method are implemented within the Caputo sense framework. These methods can produce highly accurate analytical approximations without necessitating stringent assumptions or intricate computational processes, in contrast to other similar methods. Numerical examples and the calculation of the absolute error demonstrate the efficacy of the suggested methodologies, emphasizing their superior precision and swift convergence. Full article

In this paper, we investigate the generalized coupled Zakharov system (GCZS), a fundamental model in plasma physics that describes the nonlinear interaction between high-frequency Langmuir waves and low-frequency ion-acoustic waves, including the influence of magnetic fields on weak ion-acoustic wave propagation. This research aims to achieve three main objectives. First, we uncover soliton solutions of the coupled system in hyperbolic, trigonometric, and rational forms, both in single and combined expressions. These results are obtained using the extended rational sinh-Gordon expansion method and the $\left({\displaystyle \frac{G^{\prime }}{G}},{\displaystyle \frac{1}{G}}\right)$-expansion method. Second, we analyze the dynamic characteristics of the model by performing bifurcation and sensitivity analyses and identifying the corresponding Hamiltonian function. To understand the mechanisms of intricate physical phenomena and dynamical processes, we plot 2D, 3D, and contour diagrams for appropriate parameter values. We also analyze the bifurcation of phase portraits of the ordinary differential equations corresponding to the investigated partial differential equation. The novelty of this study lies in the fact that the proposed model has not been previously explored using these advanced methods and comprehensive dynamical analyses. Full article

Indoor localization of fast-moving targets under asynchronous acoustic sensing is severely constrained by non-line-of-sight (NLOS) propagation and sparse anchor deployments. To overcome these limitations, we propose a trajectory reconstruction-based framework that simultaneously exploits time-of-arrival (ToA) and frequency-of-arrival (FoA) measurements. By embedding temporal continuity and motion dynamics into the localization model, we cast the problem as a constrained nonlinear least squares optimization over the entire trajectory rather than isolated snapshots. To efficiently solve this high-dimensional problem, we design an enhanced particle swarm optimization (PSO) algorithm featuring adaptive phase switching and noise-resilient updates. Simulation results under varying noise conditions show that our method achieves superior accuracy and robustness compared to conventional least squares estimators, especially for high-speed trajectories. Real-world experiments using a passive acoustic testbed further validate the effectiveness of the proposed framework, with over 90% of localization errors confined within 3 m. The method is model-driven, training-free, and scalable to asynchronous and anchor-sparse environments. Full article

This study presents the complete analysis of a (2 + 1)-dimensional nonlinear wave-type partial differential equation with anisotropic power-law nonlinearities and a general power-law source term, which arises in physical domains such as fluid dynamics, nonlinear acoustics, and wave propagation in elastic media, yet their symmetry properties and exact solution structures remain largely unexplored for arbitrary nonlinearity exponents. To fill this gap, a complete Lie symmetry classification of the equation is performed for arbitrary values of m and n, providing all admissible symmetry generators. These generators are then employed to systematically reduce the PDE to ordinary differential equations, enabling the construction of exact analytical solutions. Traveling wave and soliton solutions are derived using Jacobi elliptic function and sine-cosine methods, revealing rich nonlinear dynamics and wave patterns under anisotropic conditions. Additionally, conservation laws associated with variational symmetries are obtained via Noether’s theorem, yielding invariant physical quantities such as energy-like integrals. The results extend the existing literature by providing, for the first time, a full symmetry classification for arbitrary m and n, new families of soliton and traveling wave solutions in multidimensional settings, and associated conserved quantities. The findings contribute both computationally and theoretically to the study of nonlinear wave phenomena in multidimensional cases, extending the catalog of exact solutions and conserved dynamics of a broad class of nonlinear partial differential equations. Full article

Ultrasonic wave attenuation in biological tissues arises from complex interactions between mechanical, structural, and fluidic properties, making it essential to identify dominant mechanisms for accurate simulation and device design. This work introduces a novel integration of experimentally measured tissue parameters into time-explicit nonlinear acoustic wave simulations, in which the equations are directly solved in the time domain using an explicit solver. This approach captures the full transient waveform without relying on frequency-domain simplifications, offering a more realistic representation of ultrasound propagation in heterogeneous media. The study estimates both sound diffusivity and viscous damping parameters (dynamic and bulk viscosity) for a broad range of ex vivo tissues (skin, adipose tissue, skeletal muscle, trabecular/cortical bone, liver, myocardium, kidney, tendon, ligament, cartilage, and gray/white brain matter). Four regression models (power law, linear, exponential, logarithmic) were applied to characterize their frequency dependence between 0.5 and 5 MHz. Results show that attenuation is more strongly driven by bulk viscosity than dynamic viscosity, particularly in fluid-rich tissues such as liver and myocardium, where compressional damping dominates. The power-law model consistently provided the best fit for all attenuation metrics, revealing a scale-invariant frequency relationship. Tissues such as cartilage and brain showed weaker viscous responses, suggesting the need for alternative modeling approaches. These findings not only advance fundamental understanding of attenuation mechanisms but also provide validated parameters and modeling strategies to improve predictive accuracy in therapeutic ultrasound planning and the design of non-invasive, tissue-specific acoustic devices. Full article

Inverting seawater sound speed profiles (SSPs) using Bayesian methods enables optimal parameter estimation and provides a quantitative assessment of uncertainty by analyzing the posterior distribution of target parameters. However, in nonlinear geophysical inversion problems like acoustic tomography, calculating the posterior distribution remains challenging. In this study, a Bayesian framework is used to construct the posterior distribution of target parameters based on acoustic travel-time data and prior information. A Hamiltonian Monte Carlo (HMC) approach is developed for SSP inversion, offering an effective solution to the computational issues associated with complex posterior distributions. The HMC algorithm has a strong physical basis in exploring distributions, allowing for accurate characterization of physical correlations among target parameters. It also achieves sufficient sampling of heavy-tailed probabilities, enabling a thorough analysis of the target distribution characteristics and overcoming the low efficiency often seen in traditional methods. The SSP dataset was created using temperature–salinity profile data from the Hybrid Coordinate Ocean Model (HYCOM) and empirical formulas for SSP. Experiments with acoustic propagation time data from the Kuroshio Extension System Study (KESS) confirmed the feasibility of the HMC method in SSP inversion. Full article

In this study, a new nonlinear dynamic model was established for functionally graded material (FGM) beams with layered/porous fractal microstructures, aiming to reveal the cross-scale propagation mechanism of flexural waves under large deflection conditions. The characteristics of layered/porous microstructures were equivalently mapped to the fractal dimension index. In the framework of the fractal derivative, a fractal nonlinear wave governing equation integrating geometric nonlinear effects and microstructure characteristics was derived, and the coupling effect of finite deformation and fractal characteristics was clarified. Four groups of deflection gradient traveling wave analytical solutions were obtained by solving the equation through the extended minimal (G′/G) expansion method. Compared with the traditional (G′/G) expansion method, the new method, which is concise and expands the solution space, generates additional csch² soliton solutions and csc² singular-wave solutions. Numerical simulations showed that the spatiotemporal fractal dimension can dynamically modulate the amplitude attenuation, waveform steepness, and phase rotation characteristics of kink solitary waves in beams. At the same time, it was found that the decrease in the spatial fractal dimension will make the deflection curve of the beam more gentle, revealing that the fractal characteristics of the microstructure have an active control effect on the geometric nonlinearity. This model provides theoretical support for the prediction and regulation of the wave behavior of fractal microstructure FGM components, and has application potential in acoustic metamaterial design and engineering vibration control. Full article

The growing demand for low-frequency, broadband vibration and noise suppression technologies in next-generation mechanical equipment has become increasingly urgent. Effective negative mass locally resonant structures represent one of the most paradigmatic classes of acoustic metamaterials. Their unique elastic wave bandgaps enable efficient suppression of low-frequency vibrations, while inherent nonlinear effects provide significant potential for the design and tunability of these bandgaps. To achieve ultra-low-frequency and ultra-broadband vibration attenuation, this study employs Duffing oscillators exhibiting negative-stiffness characteristics as structural elements, establishing a bistable nonlinear acoustic-metamaterial mechanical model. Subsequently, based on the effective negative mass local resonance theory, the perturbation solution for the dispersion curves is derived using the perturbation method. Finally, the effects of mass ratio, stiffness ratio, and nonlinear term on the starting and cutoff frequencies of the bandgap are analyzed, and key geometric parameters influencing the design of ultra-low vibration reduction bandgaps are comprehensively investigated. Subsequently, the influence of external excitation amplitude and the nonlinear term on bandgap formation is analyzed using numerical computation methods. Finally, effective positive mass, negative mass, and zero-mass phenomena within distinct frequency ranges of the bandgap and passband are examined to validate the theoretically derived results. The findings demonstrate that, compared to a positive-stiffness system, the bandgap of the bistable nonlinear acoustic metamaterial incorporating negative-stiffness Duffing oscillators shifts to higher frequencies and widens by a factor of $\sqrt{2}$. The external excitation amplitude F changes the bandgap starting frequency and cutoff frequency. As F increases, the starting frequency rises while the cutoff frequency decreases, resulting in a narrowing of the bandgap width. Within the frequency range bounded by the bandgap starting frequency and cutoff frequency, the region between the resonance frequency and cutoff frequency corresponds to an effective negative mass state, whereas the region between the bandgap starting frequency and resonance frequency exhibits an effective positive mass state. Critically, the bandgap encompasses both effective positive mass and negative mass regions, wherein vibration propagation is suppressed. Concurrently, a zero-mass state emerges within this structure, with its frequency precisely coinciding with the bandgap cutoff frequency. This study provides a theoretical foundation and practical guidelines for designing nonlinear acoustic metamaterials targeting ultra-low-frequency and ultra-broadband vibration and noise mitigation. Full article

This study focuses on the analysis of soliton solutions within the framework of the time-fractional cubic–quintic nonlinear Schrödinger equation (TFCQ-NLSE), a powerful model with broad applications in complex physical phenomena such as fiber optic communications, nonlinear optics, optical signal processing, and laser–tissue interactions in medical science. The nonlinear effects exhibited by the model—such as self-focusing, self-phase modulation, and wave mixing—are influenced by the combined impact of the cubic and quintic nonlinear terms. To explore the dynamics of this model, we apply a robust analytical technique known as the sub-ODE method, which reveals a diverse range of soliton structures and offers deep insight into laser pulse interactions. The investigation yields a rich set of explicit soliton solutions, including hyperbolic, rational, singular, bright, Jacobian elliptic, Weierstrass elliptic, and periodic solutions. These waveforms have significant real-world relevance: bright solitons are employed in fiber optic communications for distortion-free long-distance data transmission, while both bright and dark solitons are used in nonlinear optics to study light behavior in media with intensity-dependent refractive indices. Solitons also contribute to advancements in quantum technologies, precision measurement, and fiber laser systems, where hyperbolic and periodic solitons facilitate stable, high-intensity pulse generation. Additionally, in nonlinear acoustics, solitons describe wave propagation in media where amplitude influences wave speed. Overall, this work highlights the theoretical depth and practical utility of soliton dynamics in fractional nonlinear systems. Full article

In response to the high cost and environmental impact of backfill materials in Xinjiang mines, an eco-friendly, large-volume composite was developed by bonding desert-sand mortar to waste concrete. A rock-filled concrete process produced a highly flowable mortar from desert sand, cement, and fly ash. Waste concrete blocks served as coarse aggregate. Specimens were cured for 28 days, then subjected to uniaxial compression tests on a mining rock-mechanics system using water-to-binder ratios of 0.30, 0.35, and 0.40 and aggregate sizes of 30–40 mm, 40–50 mm, and 50–60 mm. Mechanical performance—failure modes, stress–strain response, and related properties—was systematically evaluated. Crack propagation was tracked via digital image correlation (DIC) and acoustic emission (AE) techniques. Failure patterns indicated that the pure-mortar specimens exhibited classic brittle fractures with through-going cracks. Aggregate-containing specimens showed mixed-mode failure, with cracks flowing around aggregates and secondary branches forming non-through-going damage networks. Optimization identified a 0.30 water-to-binder ratio (Groups 3 and 6) as optimal, yielding an average strength of 25 MPa. Among the aggregate sizes, 40–50 mm (Group 7) performed best, with 22.58 MPa. The AE data revealed a three-stage evolution—linear-elastic, nonlinear crack growth, and critical failure—with signal density positively correlating to fracture energy. DIC maps showed unidirectional energy release in pure-mortar specimens, whereas aggregate-containing specimens displayed chaotic energy patterns. This confirms that aggregates alter stress fields at crack tips and redirect energy-dissipation paths, shifting failure from single-crack propagation to a multi-scale damage network. These results provide a theoretical basis and technical support for the resource-efficient use of mining waste and advance green backfill technology, thereby contributing to the sustainable development of mining operations. Full article

During deep mining engineering, coal bodies are subjected to complex geological stresses such as periodic roof pressure and blasting impacts, which may induce mechanical property deterioration and trigger severe rock burst accidents. This study systematically investigated the mechanical characteristics and failure mechanisms of coal under strain rates on two orders of magnitude through quasi-static cyclic loading–unloading experiments and split Hopkinson pressure bar (SHPB) tests, combined with acoustic emission (AE) localization and crack characteristic stress analysis. The research focused on the differential mechanical responses of coal-rock masses under distinct stress environments in deep mining. The results demonstrated that under quasi-static loading, the stress–strain curve exhibited four characteristic stages: compaction (I), linear elasticity (II), nonlinear crack propagation (III), and post-peak softening (IV). The peak strain displayed linear growth with increasing cycle, accompanied by a failure mode characterized by oblique shear failure that induced a transition from gradual to abrupt increases in the AE counts. In contrast, under the dynamic loading conditions, there was a bifurcated post-peak phase consisting of two unloading stages due to elastic rebound effects, with nonlinear growth of the peak strain and an interlaced failure pattern combining lateral tensile cracks and axial compressive fractures. The two loading conditions exhibited similar evolutionary trends in crack damage stress, though a slight reduction in stress occurred during the final dynamic loading phase due to accumulated damage. Notably, the crack closure stress under quasi-static loading followed a decrease–increase pattern with cycle progression, whereas the dynamic loading conditions presented the inverse increase–decrease tendency. These findings provide theoretical foundations for stability control in underground engineering and prevention of dynamic hazards. Full article

Fluororubber sealing products are widely used in nuclear power equipment, and the degree of degradation of their mechanical properties directly affects the sealing performance, which in turn affects the overall safety of nuclear power units. In order to quantitatively evaluate the degradation of the mechanical properties of fluororubber, the theory of ultrasonic propagation in fluororubber was studied. A second-order generalized Maxwell viscoelastic model was constructed in a small strain scenario of high-frequency harmonic vibration to describe the correlation between the mechanical properties and acoustic parameters. A nondestructive evaluation method for mechanical performance degradation using ultrasonic waves based on the nonlinear fitting of the model parameters was proposed. A control experiment was designed using O-rings that had been in service and those that had not yet been used in nuclear power, and mechanical tensile tests and electron microscopy microscopic analyses were conducted. The results showed that the overall elastic modulus of the used sealing ring (2.97 ± 0.15 GPa) was significantly higher than that of the unused sealing ring (2.75 ± 0.22 GPa), consistent with the results of the mechanical tensile tests. However, the sound attenuation coefficient of the unused sealing ring was significantly higher than that of the used sealing ring. Therefore, the ultrasonic evaluation of the mechanical performance degradation of fluororubber based on the viscoelastic model is a nondestructive testing method with engineering application potential. Full article