Search Results (273)

To address the data acquisition limitations of traditional flow balance methods that stem from insufficient flow rate measurements, this study establishes a pipeline flow calculation model based on the pressure data and proposes a pipeline leak identification approach for product oil pipelines. Firstly, field leak tests are designed and conducted on a product oil pipeline in East China by discharging oil in a valve chamber to simulate the leak process. Subsequently, combining the Bernoulli equation with the Leapienzon formula, a calculation model is established for flow rate prediction using the pressure data monitored at the stations and valve chambers along the pipeline. By analyzing the instantaneous flow rate changes at each pipeline section and pressure drops at each station and valve chamber, a dual-parameter collaborative threshold is set based on the flow balance principle, and leaks are identified when both parameters exceed the threshold simultaneously. Finally, the proposed flow rate calculation model and leak identification method are validated with respect to the field test data. The results show that the flow rate model yields a relative error as low as 0.48%, and the leak identification method accurately captured all six leak events in the field test, indicating very good stability and accuracy, with great potential for leak identification and alarm systems for product oil pipelines in engineering applications. Full article

This paper investigates the nonlinear bending analysis of nano-beams using the physics-informed neural network (PINN) method. The nonlinear governing equations for the bending of size-dependent nano-beams are derived from Hamilton’s principle, incorporating nonlocal strain gradient theory, and based on Euler–Bernoulli beam theory. In the PINN method, the solution is approximated by a deep neural network, with network parameters determined by minimizing a loss function that consists of the governing equation and boundary conditions. Despite numerous reports demonstrating the applicability of the PINN method for solving various engineering problems, tuning the network hyperparameters remains challenging. In this study, a systematic approach is employed to fine-tune the hyperparameters using hyperparameter optimization (HPO) via Gaussian process-based Bayesian optimization. Comparison of the PINN results with available reference solutions shows that the PINN, with the optimized parameters, produces results with high accuracy. Finally, the impacts of boundary conditions, different loads, and the influence of nonlocal strain gradient parameters on the bending behavior of nano-beams are investigated. Full article

This paper presents a novel generalization of the mth-order Laguerre and Laguerre-based Appell polynomials and examines their fundamental properties. By establishing quasi-monomiality, we derive key results, including recurrence relations, multiplicative and derivative operators, and the associated differential equation. Additionally, both series and determinant representations are provided for this new class of polynomials. Within this framework, several subpolynomial families are introduced and analyzed including the generalized mth-order Laguerre–Hermite Appell polynomials. Furthermore, the generalized mth-order Laguerre–Gould–Hopper-based Appell polynomials are defined using fractional operators and we investigate their structural characteristics. New families are also constructed, such as the mth-order Laguerre–Gould–Hopper–based Bernoulli, Laguerre–Gould–Hopper–based Euler, and Laguerre–Gould–Hopper–based Genocchi polynomials, exploring their operational and algebraic properties. The results contribute to the broader theory of special functions and have potential applications in mathematical physics and the theory of differential equations. Full article

In this paper a new generalized fractal equation for studying the behaviour of self-similar beams using the Timoshenko beam theory is introduced. This equation is established in fractal dimensions by applying the concept of fractal continuum calculus $F^{\alpha }$-CC introduced recently by Balankin and Elizarraraz in order to study engineering phenomena in complex bodies. Ultimately, the achieved formulation is a fourth-order fractal single equation generated by superposing a shear deformation on an Euler–Bernoulli beam. A mapping of the Timoshenko principle onto self-similar beams in the integer space into a corresponding principle for fractal continuum space is formulated employing local fractional differential operators. Consequently, the single equation that describes the stress/strain of a fractal Timoshenko beam is solved, which is simple, exact, and algorithmic as an alternative description of the fractal bending of beams. Therefore, the elastic curve function and rotation function can be described. Illustrative examples of classical beams are presented and show both the benefits and the efficiency of the suggested model. Full article

Under cyclic moving load action, tensile-dominant structures are prone to crack initiation due to cumulative damage effects. The presence of cracks leads to structural stiffness degradation and nonlinear redistribution of dynamic characteristics, thereby compromising str18uctural integrity and service performance. The current research on the dynamic behavior of cracked structures predominantly focuses on transient analysis through high-fidelity finite element models. However, the existing methodologies encounter two critical limitations: computational inefficiency and a trade-off between model fidelity and practicality. Thus, this study presents an innovative analytical framework to investigate the dynamic response of cracked simply supported beams subjected to moving loads. The proposed methodology conceptualizes the cracked beam as a system composed of multiple interconnected sub-beams, each governed by the Euler–Bernoulli beam theory. At crack locations, massless rotational springs are employed to accurately capture the local flexibility induced by these defects. The transfer matrix method is utilized to derive explicit eigenfunctions for the cracked beam system, thereby facilitating the formulation of coupled vehicle–bridge vibration equations through modal superposition. Subsequently, dynamic response analysis is conducted using the Runge–Kutta numerical integration scheme. Extensive numerical simulations reveal the influence of critical parameters—particularly crack depth and location—on the coupled dynamic behavior of the structure subjected to moving loads. The results indicate that at a constant speed, neither crack depth nor position alters the shape of the beam’s vibration curve. The maximum deflection of beams with a 30% crack in the middle span increases by 14.96% compared to those without cracks. Furthermore, crack migration toward the mid-span results in increased mid-span displacement without changing vibration curve topology. For a constant crack depth ratio (γ_i = 0.3), the progressive migration of the crack position from 0.05 L to 0.5 L leads to a 26.4% increase in the mid-span displacement (from 5.3 mm to 6.7 mm). These findings highlight the efficacy of the proposed method in capturing the complex interactions between moving loads and cracked concrete structures, offering valuable insights for structural health monitoring and assessment. 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

The principle of electro-analogy analysis treats a gas path structure as analogous to a circuit, offering significant potential for performance analysis in aerostatic systems. However, research on gas resistance remains in an early stage. This study investigates pipe gas resistance and its series characteristics using a slender circular pipe as the subject. First, gas resistance is redefined based on a derivation of the Bernoulli equation, resulting in formulas covering low and high speeds and a calculation model for series gas resistance. Simulations are conducted to model the pipe, focusing on the coefficient of frictional resistance at low speeds. The results provide insights into the gas resistance of pipes with varying inner diameters and related series connections. An experiment is conducted to validate predictions, indicating that, at low speeds, the defined and determined gas resistance values for pipelines with inner diameters ranging from 1 to 6 mm are largely consistent. Both gas and series gas resistances decrease as the pressure difference between the two pipe ends increases. Relative errors below 5% are typically regarded as very good, especially when dealing with complex systems. The maximum relative error between the experimentally measured single gas resistance, based on the defining formula and the simulation value, is 3.1%. Furthermore, the maximum relative errors for the measured single and series gas resistance values are 5% and 3.8%, respectively, according to the defining and determining formulas. The theoretical model is effective and reliable, providing valuable theoretical support for impedance analysis of aerostatic systems. Full article

The viscoelastic behavior of functionally graded (FG) materials significantly affects their vibration performance, making it necessary to establish theoretical analysis methods. Although fractional-order methods can be used to set up the vibration differential equations for viscoelastic, functionally graded beams, solving these fractional differential equations typically involves complex iterative processes, which makes the vibration performance analysis of viscoelastic FG materials challenging. To address this issue, this paper proposes a simple method to predict the vibration behavior of viscoelastic FG beams. The fractional viscoelastic, functionally graded porous (FGP) beam is modeled based on the Euler–Bernoulli theory and the Kelvin–Voigt fractional derivative stress-strain relation. Employing the variational principle and the Hamilton principle, the partial fractional differential equation is derived. A method based on Bernstein polynomials is proposed to directly solve fractional vibration differential equations in the time domain, thereby avoiding the complex iterative procedures of traditional methods. The viscoelastic, functionally graded porous beams with four porosity distributions and four boundary conditions are investigated. The effects of the porosity coefficient, pore distribution, boundary conditions, fractional order, and viscoelastic coefficient are analyzed. The results show that this is a feasible method for analyzing the viscoelastic behavior of FGP materials. Full article

Accurate forecasting of the remaining useful life (RUL) of aviation equipment is crucial for enhancing safety and reducing maintenance costs. This study presents a novel hybrid prognostic methodology that integrates physics-based and data-driven models to improve RUL estimations for critical aircraft components. The physics-based approach simulates long-term degradation patterns using fundamental principles such as mass conservation and Bernoulli’s equation, while the data-driven model employs a hyper tangent boosted neural network (HTBNN) to detect short-term anomalies and deviations in real-time sensor data. The integration of various models enhances accuracy, adaptability, and reliability in prognostics. The proposed methodology is assessed using NASA’s N-CMAPSS dataset for gas turbines and a fuel system test rig, demonstrating a 15% improvement in prediction accuracy and a 20% reduction in uncertainty compared to traditional methods. These findings highlight the potential for widespread application of this hybrid methodology in predictive maintenance and prognostic and health management (PHM) of aircraft systems. Full article

This paper focuses on the mathematical and numerical modeling of a non-classical macro fiber composite (MFC) piezoelectric transducer, MFC-P2, integrated with an aluminum cantilever beam for energy harvesting applications. It seeks to harness the transverse vibration energy in the environment to power small electronic devices, such as wireless sensors, where conventional power sources are inconvenient. The P2-type macro fiber composites (MFC-P2) are specifically designed for transverse energy harvesting applications. They offer high electric source capacitance and improved electric charge generation due to the strain developed perpendicularly to the voltage produced. The system is modeled analytically using Euler–Bernoulli beam theory and piezoelectric constitutive equations, capturing the electromechanical coupling in the d31 mode. Numerical simulations are conducted using COMSOL Multiphysics 6.29 to reduce the complexity of the mathematical model and analyze the effects of material properties, geometric configurations, and excitation conditions. The theoretical model is based on the transverse vibrations of a cantilevered beam using Euler–Bernoulli theory. The natural frequencies and mode shapes for the first four are determined. Depending on these, the resonance frequency, voltage, and power outputs are evaluated across a 12 kΩ resistive load. The results demonstrate that the energy harvester effectively operates near its fundamental resonant frequency of 10.78 Hz, achieving the highest output voltage of approximately 0.1952 V and a maximum power output of 0.0031 mW. The generated power is sufficient to drive ultra-low-power devices, validating the viability of MFC-based cantilever structures for autonomous energy harvesting systems. The application of piezoelectric phenomena and obtaining electrical energy from mechanical vibrations can be powerful solutions in such systems. The application of piezoelectric phenomena to convert mechanical vibrations into electrical energy presents a promising solution for self-powered mechatronic systems, enabling energy autonomy in embedded sensors, as well as being used for structural health monitoring applications. Full article

The grey prediction model is designed to characterize systems comprising both partially known information (referred to as white) and partially unknown dynamics (referred to as black). However, traditional GM(1,1) models are based on linear differential equations, which limits their capacity to capture nonlinear and non-stationary behaviors. To address this issue, this paper develops a generalized grey differential prediction approach based on the Bernoulli equation framework. We incorporate the Bernoulli mechanism with a nonlinear exponent n and a dynamic polynomial-driven term. In this work, we propose a new model designated as BPGM(1,1). Another key innovation of this work is the adoption of a nonlinear least squares direct parameter identification strategy to calculate the exponent and polynomial parameters in the Bernoulli equation, which achieves a higher degree of freedom in parameter selection and effectively circumvents the model distortion issues caused by traditional background value estimation. Furthermore, the Euler discretization method is utilized for numerical solving, reducing the reliance on traditional analytical solutions for linear structures. Numerical experiments indicate that BPGM(1,1) surpasses GM(1,1), NFBM(1,1), and their improved versions. By leveraging the synergistic mechanism between Bernoulli-type nonlinear regulation and polynomial-driven external excitation, this framework significantly enhances prediction accuracy for systems characterized by non-stationary behaviors and multi-scale trends. Full article

In this work, we investigate the extended numerical discretization technique for the solution of fractional Bernoulli equations and SIRD epidemic models under the Caputo fractional, which is accurate and versatile. We have demonstrated the method’s strength in examining complex systems; it is found that the method produces solutions that are identical to the exact solution and approximate series solutions. The ENDT is its ability to proficiently handle complex systems governed by fractional differential equations while preserving memory and hereditary characteristics. Its simplicity, accuracy, and flexibility render it an effective instrument for replicating real-world phenomena in physics and biology. The ENDT method offers accuracy, stability, and efficiency compared to traditional methods. It effectively handles challenges in complex systems, supports any fractional order, is simple to implement, improves computing efficiency with sophisticated methodologies, and applies it to epidemic predictions and biological simulations. Full article

Introduction: The purpose of this study is to provide foundational data for nursing care in patients with external ventricular drainage (EVD) by comparatively analyzing drainage volume in relation to intracranial pressure (ICP) and drainage catheter size. Methods: In this study, we conducted a volumetric analysis using the continuity and Bernoulli equations, considering friction forces under predefined conditions. In adults in the supine position with 37 °C CSF, the ventricular drainage volume was assessed based on the height of the EVD system, ICP levels, and EVD catheter sizes. Results: The results indicated that the CSF flow rate increased with larger catheter diameters and when the EVD system was positioned lower than the reference point (foramen of Monro). Across all catheter sizes, the minimum CSF flow occurred when the EVD system was 15 cm above the reference point, while the maximum flow was observed when it was 15 cm below the reference point. This multidisciplinary study, utilizing fluid dynamics, quantitatively estimates the drainage volume in EVD systems based on ICP and catheter size, contributing to the nursing care of EVD systems. The findings underscore the importance of developing specific nursing guidelines to improve patient safety in external ventricular drainage management and incorporating them into clinical education. Conclusions: A limitation of this study is that it does not compare with patients in clinical settings for clinical empirical validity. Therefore, a stepwise validation process is necessary. So, future studies will need to compare medical record data with the results of this study to confirm the validity of the equations presented. Full article

Fertilizer suction flow rate is an important performance parameter of the Venturi fertilizer applicator. This study aims to analyze the optimal structure of the Venturi fertilizer applicator with the goal of maximizing the suction flow rate at the same inlet and outlet pressures. A Venturi tube was used as a simplified case for investigating the Venturi injector. A calculation formula for the head loss between the inlet and outlet of the Venturi tube was derived based on the Bernoulli equation and the Darcy–Weisbach formula. Subsequently, it was modified through regression analysis based on the experimental and numerical simulation results of the flow on the Venturi tube. The optimal structure of the Venturi injector was further analyzed based on the head loss calculation formula. The optimal range for the reducing angle and expanding angle of the Venturi injector were determined to be 20–28° and 6–10°, respectively. The optimal throat diameter was identified to be 5–7 mm when the inlet flow rates were within the range of 1.5–2.5 m³/h. The optimum suction pipe diameter and throat pipe length were both equal to the throat diameter. Full article

In this paper, we define a new generalization of three-variable q-Laguerre polynomials and derive some properties. By using these polynomials, we introduce a new generalization of three-variable q-Laguerre-based Appell polynomials (3VqLbAP) through a generating function approach involving zeroth-order q-Bessel–Tricomi functions. These polynomials are studied by means of generating function, series expansion, and determinant representation. Also, these polynomials are further examined within the framework of q-quasi-monomiality, leading to the establishment of essential operational identities. We then derive operational representations, as well as q-differential equations for the three-variable q-Laguerre-based Appell polynomials. Some examples are constructed in terms of q-Laguerre–Hermite-based Bernoulli, Euler, and Genocchi polynomials in order to illustrate the main results. Full article