Search Results (6,141)

In this study, a detection method utilizing nonlinear ultrasonic guided waves is presented to tackle the difficulties in detecting localized damage and weakening in bonded composite structures. For a three-layer structure made of polystyrene, acrylic resin, and aluminum plate, dispersion equations for ultrasonic guided waves were developed using the spring model and wave equation. The A1-S1 mode was selected by examining the material parameters’ influence on the adhesive layer’s dispersion curves. The finite element method was employed to simulate the propagation characteristics of ultrasonic guided waves within the composite structure. The error between the theoretically calculated and simulated group velocities was less than 5.15%. As the propagation distance increased, both the nonlinearity coefficient and the amplitude of the second-order harmonic showed an upward trend. This indicates a significant accumulation effect at the second harmonic of nonlinear guided waves. Compared to without adhesive layer weakening, localized and overall weakening resulted in higher amplitudes of the second-order harmonic. Experimental testing of ultrasonic guided waves was conducted to investigate the nonlinear properties of the composite structure. The error between the experimentally measured and theoretically calculated group velocities was less than 6.96%. The experimental results corroborated the propagation accumulation effect of the second-order harmonic amplitude. Full article

The operational effectiveness of Architectural, Engineering, and Construction (AEC) consultants, whose services have a substantial impact on project execution and results, depends on effective risk management. Using 336 survey responses from professionals in the construction industry, such as consultants, contractors, and employers working on a range of infrastructure and building projects, this study validates a hybrid Partial Least Squares Structural Equation Modeling–Artificial Neural Network (–ANN) approach. In order to ensure both causal analysis and predictive insights for AEC consultant performance assessment, this study combines PLS–SEM and ANN to develop an integrated performance evaluation framework. While ANN ordered their relative relevance in a non-linear predictive model, the PLS–SEM analysis found that the two most important predictors of consultant performance were communication and relationship management (G03) and document and record management (G06). The hybrid approach is a more efficient and data-driven tool for evaluating AEC consultants than traditional regression models since it accurately captures both causal links and predictive performance. These results contribute to a robust and sustainable framework for performance evaluation in the AEC sector by offering practical insights into risk reduction and operational improvement. Full article

In this work, we analyze the suitability of the State-Dependent Riccati Equation (SDRE) suboptimal nonlinear control formulation for the implementation of body-fixed hovering of a spacecraft in the highly nonlinear environment engendered by the faint force fields around single- and multi-body Near-Earth Objects (NEOs), a class of Small Solar System Bodies with high relevance either in scientific, economic, or planetary defense-related aspects. Our results, addressing the hovering of a spacecraft around relative equilibrium points on the effective potential of the Near-Earth Asteroid (16) Psyche and of the much smaller main body (called Alpha) of the triple NEA system (153591) 2001SN263, show that the known effectiveness offered by the flexibility engendered by state-dependent factorization of nonlinear models is also effective when applied in these faint and highly nonlinear force fields. In fact, this work is a qualitative evaluation of the suitability of using SDRE in the highly disturbed environment around Small Solar System Bodies, which has never been undertaken before. We intend to prove that this method is adequate. For real missions, it is necessary to make deeper studies. In particular, our results show the flexibility granted by the SDRE approach in the trade off between maneuvering time against fuel consumption, a central aspect in such space missions. For instance, our simulations showed control effort and time of convergence for two controlled trajectories around (16) Psyche ranging from a half-time convergence with ∼20 times lower cost. Analogously, for the much smaller bodies in the (153591) 2001SN263 triple system, we got two trajectories in which one of them may converge ∼10 times faster but with up to ∼100 times higher cost. Full article

This investigation focuses on the study of the fractional damped Burgers’ equation by using the natural residual power series method coupled with the new iteration transform method in the context of the Caputo operator. The equation of Burgers under the damped context is useful when studying one-dimensional nonlinear waves involving damping effect, and is used in fluid dynamics, among other applications. Two new mathematical methods that can be used to obtain an approximate solution to this complex non-linear problem are the natural residual power series method and the new iteration transform method. Therefore, it can be deduced that the Caputo operator aids in modeling of the fractional derivatives, as it provides a better description of the physical realities. Thus, the objective of the present work is to advance the knowledge accumulated on the behavior of solutions to the damped Burgers’ equation, as well as to check the applicability of the proposed approaches to other nonlinear fractional partial differential equations. Full article

This paper investigates a general class of variable-kernel discrete delay differential equations (DDDEs) with integral boundary conditions and impulsive effects, analyzed using Caputo piecewise derivatives. We establish results for the existence and uniqueness of solutions, as well as their stability. The existence of at least one solution is proven using Schaefer’s fixed-point theorem, while uniqueness is established via Banach’s fixed-point theorem. Stability is examined through the lens of Ulam–Hyers (U-H) stability. Finally, we illustrate the application of our theoretical findings with a numerical example. Full article

Over the past 70 years since the founding of the People’s Republic of China, urban development has achieved remarkable progress but also encountered severe atmospheric pollution, which has become a significant obstacle to high-quality urban development. Understanding the interaction mechanisms between urban development and atmospheric pollution is thus crucial for promoting sustainable urban construction. This paper explores these mechanisms by analyzing the interplay between urban population, industry, space, social development, and pollution through a theoretical framework. Using a simultaneous equations model and the Three-Stage Least Squares (3SLS) method, it examines these relationships and further investigates threshold effects. The findings reveal a nonlinear relationship with significant thresholds: (1) High levels of PM_2.5, population size, and industrial agglomeration can shift from exacerbating pollution to enabling governance, though excessive thresholds reverse this trend. (2) PM_2.5 mediates the impact of spatial sprawl, environmental regulation, and population dynamics, oscillating between governance and pollution effects. (3) Industrial agglomeration and spatial sprawl show variable impacts on pollution mitigation depending on pollution intensity and urban thresholds. These findings provide critical insights into the intricate dynamics between urban development and atmospheric pollution, emphasizing the importance of adopting differentiated strategies based on specific urban thresholds. Ultimately, this research contributes to the broader goal of harmonizing economic growth, social development, and environmental sustainability in urban areas, serving as a valuable reference for cities worldwide facing similar challenges. Full article

Nanofluids, with their enhanced thermal properties, provide innovative solutions for improving heat transfer efficiency in renewable energy systems. This study investigates a numerical simulation of bioconvective flow and heat transfer in a Williamson nanofluid over a stretching wedge, incorporating the effects of chemical reactions and hydrogen diffusion. The system also includes motile microorganisms, which induce bioconvection, a phenomenon where microorganisms’ collective motion creates a convective flow that enhances mass and heat transport processes. This mechanism is crucial for improving the distribution of nanoparticles and maintaining the stability of the nanofluid. The unique rheological behavior of Williamson fluid, extensively utilized in hydrometallurgical and chemical processing industries, significantly influences thermal and mass transport characteristics. The governing nonlinear partial differential equations (PDEs), derived from conservation laws and boundary conditions, are converted into dimensionless ordinary differential equations (ODEs) using similarity transformations. MATLAB’s bvp4c solver is employed to numerically analyze these equations. The outcomes highlight the complex interplay between fluid parameters and flow characteristics. An increase in the Williamson nanofluid parameters leads to a reduction in fluid velocity, with solutions observed for the skin friction coefficient. Higher thermophoresis and Williamson nanofluid parameters elevate the fluid temperature, enhancing heat transfer efficiency. Conversely, a larger Schmidt number boosts fluid concentration, while stronger chemical reaction effects reduce it. These results are generated by fixing parametric values as $0.1<\varpi <1.5, 0.1<\mathit{Nr}<3.0, 0.2<\mathrm{Pr}<0.5, 0.1<\mathit{Sc}<0.4, \mathrm{and} 0.1<\mathit{Pe}<1.5.$ This work provides valuable insights into the dynamics of Williamson nanofluids and their potential for thermal management in renewable energy systems. The combined impact of bioconvection, chemical reactions, and advanced rheological properties underscores the suitability of these nanofluids for applications in solar thermal, geothermal, and other energy technologies requiring precise heat and mass transfer control. This paper is also focused on their applications in solar thermal collectors, geothermal systems, and thermal energy storage, highlighting advanced experimental and computational approaches to address key challenges in renewable energy technologies. Full article

Due to irregular hydrodynamic–aerodynamic coupling, the modeling and simulation of near-surface flight are extremely complex. For the present study, a practical dynamic model and a complete motion simulation method for the solution of such problems were established for engineering applications. A discrete non-linear time-varying dynamics model was employed in order to ensure the universality of the method; thereafter, force models—including gravity, aerodynamic, hydrodynamic, control, and thrust models—were established. It should be noted that a non-linear approach was adopted for the hydrodynamic model, which reflects the influences of waves in real-world situations; in addition, a Proportional–Integral–Derivative (PID) control law was added to realize closed-loop simulation of the motion. Considering a take-off flight as a study case, longitudinal three Degrees of Freedom (DoF) motion was simulated. The velocity, angle of attack, height, and angular velocity were selected as the state vectors in the state–space equations. The results show that, with the equilibrium state as the initial setting for the motion, reasonable time–history curves of the whole take-off phase can be obtained using the proposed approach. Furthermore, it is universally applicable for aircraft operating under hydrodynamic–aerodynamic coupling scenarios, including amphibious aircraft, seaplanes, Wing-in-Ground-Effect (WIGE) aircraft, and Hybrid Aerial–Underwater Vehicles (HAUVs). Full article

In this study, a novel symbolic regression-based empirical equation has been developed to compute the joint roughness coefficient (JRC) value based on the statistical parameters of rock joints. The symbolic regression was adopted to map the nonlinear function, which represents the relation between the JRC and statistical parameters of the rock joint, based on the collected rock joint dataset. It is not necessary to presume the mathematical function form of the empirical equation, which is used to fit the rock joint data while using symbolic regression. The collected rock joint samples from the literature were used to investigate and illustrate the developed symbolic regression-based empirical equation. The performance of the developed empirical equation was compared to the traditional empirical equation. The results show that the generalization performance of the developed empirical equation is better than the traditional empirical equation. They proved that the symbolic regression-based empirical equation characterized the roughness property of rock joints well and that symbolic regression could be used to capture the complex and nonlinear relationship between JRC and the statistical parameters of rock joints. The developed symbolic regression-based empirical equation provides a scientific and excellent tool to estimate the JRC value of rock joints. Full article

This study aimed to investigate the structure-borne sound suppression of a strongly/weakly excited curved panel. Quadratic nonlinear resonance can induce anti-symmetric modal responses to replace symmetric modal responses, even though the physical panel dimensions and excitation distribution are symmetric. Unlike cubic nonlinear resonance, quadratic nonlinear resonance can be induced regardless of whether the panel vibration amplitude is small or large. As the sound radiation efficiency of anti-symmetric responses is much lower than that of symmetric responses, this quadratic nonlinear resonance effect is thus used for sound suppression. A set of multimode formulations was developed from the nonlinear structural governing equation and sound radiation efficiency equation. The quadratic nonlinear resonant responses and some other nonlinear responses were computed from the multimode formulations. Modal convergence studies and parametric studies were performed to understand the effects of various parameters on the quadratic nonlinear responses and sound suppression. The results showed that when the panel was strongly excited, the difference between the peak sound levels in the linear and nonlinear cases was up to 12 dB, and when the panel was weakly excited, the difference was up to 6 dB. Full article

In the process of energy harvesting, vibration energy harvesting still has several disadvantages, including a high-threshold excitation and a narrow working bandwidth. Therefore, a 2-degrees-of-freedom piezoelectric energy harvester is proposed. By introducing a nonlinear magnetic force to the system, the working bandwidth and the energy-harvesting efficiency of three magnetically coupled piezoelectric cantilever beams can be effectively improved. In this paper, a mathematical model consisting of three electrically coupled magnetically coupled piezoelectric cantilever beam systems is established, and the governing equations of electric coupling are solved numerically and verified experimentally. The dynamic characteristics under different excitations and frequencies are studied. The experiment shows that the working bandwidth can be increased by controlling the distance between three pairs of circular magnets and changing the excitation and frequency to induce resonance. Thus, the self-power requirement of micro-power devices can be realized. Overall, this study provides a promising solution for improving the performance of piezoelectric energy harvesters and offers theoretical insights for designing vibrating piezoelectric energy harvesters. Full article

An efficient linearization method for solving a system of nonlinear equations was developed, showing good stability and convergence properties. It uses an unconventional and simple strategy to improve the performance of classic methods by a full-rank update of the Jacobian approximates. It can be considered both as a discretized Newton’s method or as a quasi-Newton method with a full-rank update of the Jacobian approximates. A solution to the secant equation presented earlier was based on the Wolfe-Popper procedure. The secant equation was splitted into two equations by introducing an auxiliary variable. A simplified algorithm is given in this paper for the full-rank update procedure.It directly solves the secant equation with the pseudoinverse of the Jacobian approximate matrix. Numerical examples are shown for demonstration purposes. The convergence and efficiency of the suggested method are discussed and compared with the convergence and efficiency of classic linearization methods. Full article

In this paper, we use an existing fixed point iterative scheme to approximate a class of generalized $\alpha$-nonexpansive mapping in Banach spaces. We also prove weak and strong convergence results for the mapping using the AG iterative scheme. An example of a generalized $\alpha$-nonexpansive mapping is given to show the validity of the claims. We apply the main results to the approximation of solution of a mixed type Voltera–Fredholm functional nonlinear integral equation and to the spread of HIV modeled in terms of a fractional differential equation of the Caputo type. Full article

In this article, we define a new class of noncommuting self mappings known as the S-operator pair. Also, we provide the existence and uniqueness of common fixed point results involving the S-operator pair satisfying the $(F,\phi ,\psi ,Z)$-contractive condition in m-metric spaces, which unifies and generalizes most of the existing relevant fixed point theorems. Furthermore, the variables in the m-metric space are symmetric, which is significant for solving nonlinear problems in operator theory. In addition, examples are provided in order to illustrate the concepts and results presented herein. It has been demonstrated that the results can be applied to prove the existence of a solution to a system of integral equations, a nonlinear fractional differential equation and an ordinary differential equation for damped forced oscillations. Also, in the end, the satellite web coupling problem is solved. Full article

This research focuses on the dynamic analysis of an oscillating conveyor mechanism using numerical methods to solve nonlinear differential equations that govern its motion. The system under study is modeled by a second-order differential equation of the form $R\left(t\right){\displaystyle \frac{d{\omega }_1}{dt}}+Q\left(t\right){\omega }_1^2\left(t\right)=W\left(t\right)$, where R(t), Q(t), and W(t) are time-dependent functions representing system parameters such as resistance, damping, and external driving forces. To solve these equations, we employed a numerical approach based on Euler’s method, which discretizes the time domain into small steps h and approximates the derivatives of angular velocity and angular displacement. The angular velocity ${\omega }_{k+1}$ and angular displacement ${\phi }_{k+1}$ are updated iteratively using the formulas ${\omega }_{k+1}={\omega }_k+h\left({\displaystyle \frac{W_k}{R_k}}-{\displaystyle \frac{Q_k}{R_k}}{\omega }_k^2\right)$ and ${\phi }_{k+1}={\phi }_k+h{\omega }_k$, respectively. Initial conditions, with ${\omega }_0=0$ and ${\phi }_0=0$, were specified, and the system was simulated over a specified time range divided into N time steps. In the simulation, key parameters such as $A\left(t\right)$, B(t), D(t), E(t), F(t), $H\left(t\right)$, N(t), M(t), $Q\left(t\right)$, $R\left(t\right)$, and $W\left(t\right)$ were evaluated at each time step based on the system’s geometry and the angular displacements. Due to the complexity of the system, analytical solutions were impractical, so the Runge–Kutta method was employed for higher accuracy in the integration process. The results from the numerical simulations were validated by comparing them with theoretical expectations, and the system’s dynamic behavior was visualized using time-series and 3D plots. The simulation demonstrated that the system’s stability and accuracy were highly dependent on the time step h, with smaller values providing more precise results at the cost of increased computational time. The research confirms the applicability of numerical methods in solving complex nonlinear differential equations for dynamic systems and provides insights into the system’s behavior under various operating conditions. Full article