Search Results (280)

For systems such as the van der Pol and van der Pol–Duffing oscillators, the study of their oscillation is currently a very active area of research. Many authors have used the bifurcation method to try to determine oscillatory behavior. But when the system involves n separate delays, the equations for bifurcation become quite complex and difficult to deal with. In this paper, the existence of periodic oscillatory behavior was studied for a system consisting of n coupled equations with multiple delays. The method begins by rewriting the second-order system of differential equations as a larger first-order system. Then, the nonlinear system of first-order equations is linearized by disregarding higher-degree terms that are locally small. The instability of the trivial solution to the linearized equations implies the instability of the nonlinear equations. Periodic behavior often occurs when the system is unstable and bounded, so this paper also studied the boundedness here. It follows from previous work on the subject that the conditions here did result in periodic oscillatory behavior, and this is illustrated in the graphs of computer simulations. Full article

This paper presents a modeling framework for hysteretically nonlinear piezoelectric composite beams using functional differential equations (FDEs). While linear piezoelectric models are well established, they fail to capture the complex nonlinear behaviors that emerge at higher electric field strengths, particularly history-dependent hysteresis effects. This paper develops a cascade model that integrates a high-dimensional linear piezoelectric composite beam representation with a nonlinear Krasnosel’skii–Pokrovskii (KP) hysteresis operator. The resulting system is formulated using a state-space model where the input voltage undergoes a history-dependent transformation. Through modal expansion and discretization of the Preisach plane, we derive a tractable numerical implementation that preserves essential nonlinear phenomena. Numerical investigations demonstrate how system parameters, including the input voltage amplitude, and hysteresis parameters significantly influence the dynamic response, particularly the shape and amplitude of limit cycles. The results reveal that while the model accurately captures memory-dependent nonlinearities, it depends on numerous real and distributed parameters, highlighting the need for efficient reduced-order modeling approaches. This work provides a foundation for understanding and predicting the complex behavior of piezoelectric systems with hysteresis, with potential applications in vibration control, energy harvesting, and precision actuation. Full article

This study applies the Conformable Laplace Adomian Decomposition Method (CLADM) to solve generalized time-fractional Korteweg–de Vries (KdV) models, including seventh- and fifth-order models. CLADM combines the conformable fractional derivative and Laplace transform with the Adomian decomposition technique, offering analytic approximate solutions. Numerical and graphical results, generated using MATLAB R2020a 9.8.0.1323502, validate the method’s efficiency and precision in capturing fractional-order dynamics. Fractional parameters $\mathsf{\varrho }$ significantly influence wave behavior, with higher orders yielding smoother profiles and reduced oscillations. Comparative analysis confirms CLADM’s superiority over existing methods in minimizing errors. The versatility of CLADM highlights its potential for studying nonlinear wave phenomena in diverse applications. Full article

Waste and chemicals generated from industry have been a major source of pollution and a prominent threat to human health via the food chain; hence, an efficient and durable material that can be used to detoxify polluted soil and water bodies is necessary to attain ecosystem equity and security. This study hypothesized that biochar (BC) made from poultry manure (PM) through pyrolysis and fortification with iron (Fe–BC) can be used to remove methyl orange dye from aqueous solution. Furthermore, this study evaluated the effect of solution pH on the sorption of methyl orange through batch sorption studies. The similarity in the modeled data and experimental data was measured by the standard error of estimate, whereas sorption isotherms were examined using nonlinear forms of different sorption equations. With the use of Langmuir models, a maximum sorption capacity of 136.25 mg·g⁻¹ and 98.23 mg·g⁻¹ was recorded for Fe–BC and BC, respectively. Fe–BC possessed a higher adsorption ability in comparison to BC. The pseudo-second-order best described the sorption kinetics of both adsorbents at R² = 0.9973 and 0.9999, indicating a strong interaction between MO and Fe–BC. Furthermore, the efficiency with which MO was removed by the absorbent was highest at lower pH (pH = 4). It is therefore concluded that Fe–BC can be used as an effective and environmentally friendly material for detoxification of wastewater; however, further research on the application and usage of biochar modified techniques for enhancing adsorption efficacy on a large scale should be encouraged. Full article

Especially in real-world circumstances with uneven road surfaces and impulsive shocks, nonlinear dynamic effects in vehicle systems can greatly skew biometric data utilized to track passenger and driver physiological states. By creating a thorough multibody human–seat–chassis model, this work tackles the effect of vehicle-induced vibrations on the accuracy and dependability of biometric measures. The model includes external excitation from road-induced inputs, nonlinear damping between structural linkages, and vertical and angular degrees of freedom in the head–neck system. Motion equations are derived using a second-order Lagrangian method; simulations are run using representative values of a typical car and human body segments. Results show that higher vehicle speed generates more vibrational energy input, which especially in the head and torso enhances vertical and angular accelerations. Modal studies, on the other hand, show that while resonant frequencies stay constant, speed causes a considerable rise in amplitude and frequency dispersion. At speeds ≥ 50 km/h, RMS and VDV values exceed ISO 2631 comfort standards in the body and head. The results highlight the need to include vibration-optimized suspension systems and ergonomic design approaches to safeguard sensitive body areas and preserve biometric data integrity. This study helps to increase comfort and safety in both traditional and autonomous car uses. Full article

This study presents high-fidelity numerical simulations of the shock-accelerated single-mode Richtmyer–Meshkov instability (RMI) in a light helium layer confined between two interfaces and surrounded by nitrogen gas. A high-order modal discontinuous Galerkin method is employed to solve the two-dimensional compressible Euler equations, enabling detailed investigation of interface evolution, vorticity dynamics, and flow structure development under various physical conditions. The effects of helium layer thickness, initial perturbation amplitude, and incident shock Mach number are systematically explored by analyzing interface morphology, vorticity generation, enstrophy, and kinetic energy. The results show that increasing the helium layer thickness enhances vorticity accumulation and interface deformation by delaying interaction with the second interface, allowing more sustained instability growth. Larger initial perturbation amplitudes promote earlier onset of nonlinear deformation and stronger baroclinic vorticity generation, while higher shock strengths intensify pressure gradients across the interface, accelerating instability amplification and mixing. These findings highlight the critical interplay between layer confinement, perturbation strength, and shock strength in governing the nonlinear evolution of RMI in light fluid layers. Full article

Proper orthogonal decomposition (POD) is a widely used linear dimensionality reduction technique, but it often fails to capture critical features in complex nonlinear flows. In contrast, clustering methods are effective for nonlinear feature extraction, yet their application in dimensionality reduction methods is hindered by unstable cluster initialization and inefficient mode sorting. To address these issues, we propose a clustering-based dimensionality reduction method guided by POD structures (C-POD), which uses POD preprocessing to stabilize the selection of cluster centers. Additionally, we introduce an entropy-controlled Euclidean-to-probability mapping (ECEPM) method to improve modal sorting and assess mode importance. The C-POD approach is evaluated using the one-dimensional Burgers’ equation and a two-dimensional cylinder wake flow. Results show that C-POD achieves higher accuracy in dimensionality reduction than POD. Its dominant modes capture more temporal dynamics, while higher-order modes offer better physical interpretability. When solving an inverse problem using sparse sensor data, the Gappy C-POD method improves reconstruction accuracy by 19.75% and enhances the lower bound of reconstruction capability by 13.4% compared to Gappy POD. Overall, C-POD demonstrates strong potential for modeling and reconstructing complex nonlinear flow fields, providing a valuable tool for dimensionality reduction methods in fluid dynamics. Full article

The present research analyzed the nonlinear vibration of a CNTRC embedded in a nonlinear Winkler–Pasternak foundation in the presence of an electromagnetic actuator and mechanical impact. A higher-order shear deformation beam theory was applied to various models, as well as Euler–Bernoulli, Timoshenko, Reddy, and other beams, using a unified NSGT. The governing equations were obtained based on the extended shear and normal strain component of the von Karman theory and a Hamilton principle. The system was discretized by means of the Galerkin–Bubnov procedure, and the OAFM was applied to solve a complex nonlinear problem. The buckling and bending problems were studied analytically by using the HPM, the Galerkin method in combination with the weighted residual method, and finally, by the optimization of results for a simply supported composite beam. These results were validated by comparing our results for the linear problem with those available in literature, and a good agreement was proved. The influence of some parameters was examined. The results obtained for the extended models of the Euler–Bernoulli and Timoshenko beams were almost the same for the linear cases, but the results of the nonlinear cases were substantially different in comparison with the results obtained for the linear cases. Full article

This review summarizes the application of physics-informed neural networks (PINNs) for solving higher-order nonlinear partial differential equations belonging to the nonlinear Schrödinger equation (NLSE) hierarchy, including models with external potentials. We analyze recent studies in which PINNs have been employed to solve NLSE-type evolution equations up to the fifth order, demonstrating their ability to obtain one- and two-soliton solutions, as well as other solitary waves with high accuracy. To provide benchmark solutions for training PINNs, we employ analytical methods such as the nonisospectral generalization of the AKNS scheme of the inverse scattering transform and the auto-Bäcklund transformation. Finally, we discuss recent advancements in PINN methodology, including improvements in network architecture and optimization techniques. Full article

The thick-walled thickness effect in layered-symmetrical structure is very important for considering the external thermal heating on the surface of functionally graded material (FGM) plates. Dynamic thermal vibration with advanced shear correction on the FGM plates are presented. The third-order shear deformation theory (TSDT) is included to calculate the values of advanced shear correction for the thick plates based on the displacement assumed in the middle symmetry plane. The values of advanced shear correction coefficient are in nonlinear variation with respect to the power-law index value for FGM. The dynamic stresses are calculated when the displacements and shear rotations are obtained for the given natural frequency of displacements, frequency of applied heat flux and time. The natural frequencies of sinusoidal displacements and shear rotations are obtained by using the determinant of the coefficient matrix in the fully homogeneous equation. Only the numerical dynamic results of displacements and stresses subjected to sinusoidal applied heat loads are investigated. The heating study in symmetry structure of FGMs to induce thermal vibration is interesting in the field of engineering and materials. The center displacements can withstand a higher temperature of 1000 K and a power-law index of 5, for which the length-to-thickness ratio 5 is better than that for 10. Full article

The order of convergence for Jarratt-type methods in solving nonlinear equations is determined without relying on Taylor expansion. Unlike previous studies, we depend solely on assumptions about the derivatives of the involved operator up to the second order. The proof presented in this paper is independent of the Taylor series expansion, thereby reducing the need for assumptions about derivatives of higher order of the involved operator and enhancing the applicability of these methods. The method’s applicability is broadened by employing the concept of generalized conditions in local convergence analysis and majorizing sequences in semi-local analysis. This study includes numerical examples and basins of attraction for the methods. Full article

This paper investigates the bifurcation dynamics and optical soliton solutions of the integrable quintic Kundu–Eckhaus (QKE) equation with an M-fractional derivative. By adding quintic nonlinearity and higher-order dispersion, this model expands on the nonlinear Schrödinger equation, which makes it especially applicable in explaining the propagation of high-power optical waves in fiber optics. To comprehend the behavior of the connected dynamical system, we categorize its equilibrium points, determine and analyze its Hamiltonian structure, and look at phase diagrams. Moreover, integrating along periodic trajectories yields soliton solutions. We achieve this by using the simplest equation approach and the modified extended Tanh method, which allow for a thorough investigation of soliton structures in the fractional QKE model. The model provides useful implications for reducing internet traffic congestion by including fractional temporal dynamics, which enables directed flow control to avoid bottlenecks. Periodic breather waves, bright and dark kinky periodic waves, periodic lump solitons, brilliant-dark double periodic waves, and multi-kink-shaped waves are among the several soliton solutions that are revealed by the analysis. The establishment of crucial parameter restrictions for soliton existence further demonstrates the usefulness of these solutions in optimizing optical communication systems. The theoretical results are confirmed by numerical simulations, highlighting their importance for practical uses. Full article

Aiming at the limitations of existing multisensor fault diagnosis methods for rolling bearings in real industrial scenarios, this paper proposes an innovative intuitionistic fuzzy weighted least squares twin support higher-order tensor machine (IFW-LSTSHTM) model, which realizes a breakthrough in the noise robustness, adaptability to the working conditions, and the class imbalance processing capability. First, the multimodal feature tensor is constructed: the fourier synchro-squeezed transform is used to convert the multisensor time-domain signals into time–frequency images, and then the tensor is reconstructed to retain the three-dimensional structural information of the sensor coupling relationship and time–frequency features. The nonlinear feature mapping strategy combined with Tucker decomposition effectively maintains the high-order correlation of the feature tensor. Second, the adaptive sample-weighting mechanism is developed: an intuitionistic fuzzy membership score assignment scheme with global–local information fusion is proposed. At the global level, the class contribution is assessed based on the relative position of the samples to the classification boundary; at the local level, the topological structural features of the sample distribution are captured by K-nearest neighbor analysis; this mechanism significantly improves the recognition of noisy samples and the handling of class-imbalanced data. Finally, a dual hyperplane classifier is constructed in tensor space: a structural risk regularization term is introduced to enhance the model generalization ability and a dynamic penalty factor is set to set adaptive weights for different categories. A linear equation system solving strategy is adopted: the nonparallel hyperplane optimization is converted into matrix operations to improve the computational efficiency. The extensive experimental results on the two rolling bearing datasets have verified that the proposed method outperforms existing solutions in diagnostic accuracy and stability. Full article

Offshore wind turbines serve as critical infrastructure components in marine renewable energy systems, enabling sustainable energy extraction within offshore engineering frameworks. Monopile foundations for offshore wind turbines in deep-water environments are subjected to strong nonlinear wave actions. This study introduces a novel composite monopile foundation specifically designed for deep-sea applications, with its fully nonlinear hydrodynamic performance systematically investigated using potential flow theory. The novel hybrid monopile incorporates a concrete-filled double-skin steel tubular (CFDST) configuration to reduce pile diameter at water level. In the numerical model, the higher-order boundary element method (HOBEM) is implemented to resolve boundary value problems at each temporal iteration. Following numerical validation, nonlinear wave loading and run-up characteristics for the CFDST hybrid structure are quantified, while the limitations of Morison’s equation for large-scale structures under strongly nonlinear wave conditions are concurrently assessed. Results indicate that CFDST implementation effectively attenuates both nonlinear hydrodynamic forces and wave run-up amplitudes, enabling safer and more economical design approaches for deep-water offshore wind turbine foundations. Full article

This article introduces a novel iterative solver with memory, derived from Newton’s scheme, for nonlinear scalar equations. The key innovation lies in integrating memory into the iterative process, enhancing the convergence rate without increasing the quantity of functional evaluations compared to conventional two-point solvers. The proposed method achieves a superior R-order of convergence by adaptively utilizing past iterates to refine the current approximation. A rigorous theoretical analysis is presented to establish the convergence properties of the method. Extensive computational experiments demonstrate that the method with memory not only accelerates convergence but also enhances accuracy with fewer iterations. These findings suggest that the proposed solver has significant potential for applications in scientific computing and numerical optimization, where efficient and high-order iterative methods are crucial. Full article