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Volume loss is an important method to estimate ground movement during tunnelling. However, volume loss is usually estimated by empirical methods, especially for volume loss at the tunnel face, which is a three-dimensional problem. Based on the principle of minimum total potential energy, we proposed a semi-analytical method to predict the volume loss at the tunnel face and ground surface. The proposed method provides a more direct way of estimating volume loss at the tunnel face from an energy point of view. Moreover, a new deformation mechanism was designed to describe the ground movement before the tunnel face. Based on the proposed method, we investigated the influence of the support pressure, tunnel diameter, and tunnel depth on the volume loss at the tunnel face, and other parameters related to surface subsidence. The volume loss at the tunnel face decreased with the increase in the support pressure ratio and the slurry weight. The volume loss at ground surface was generally smaller than the volume loss at the tunnel face due to the soil compression during ground movement. The bigger the tunnel diameter, the bigger the volume loss at the tunnel face. However, the volume loss at ground surface may not increase with the increase in tunnel depth, because of the soil arching effect. Moreover, the deeper the tunnel, the more obvious the influence of the support pressure ratio on volume loss. Similarly, the bigger the tunnel diameter, the more obvious the influence of the slurry weight on the volume loss.

The dynamic response of railway tracks is a key factor influencing the operational safety and reliability of rail transport. Classical analytical methods for modelling track dynamics become insufficient at higher operating speeds, as they typically assume linear behaviour and cannot account for nonlinearities present in the fastening system or in the rail track foundation response. This increases the risk of damage, leading to traffic interruptions, financial losses, and reduced safety. To support predictive maintenance, it is necessary to develop databases based on in-situ measurements, complemented with synthetic data obtained from validated analytical and semi-analytical models. This paper presents such a model, designed to analyse how the parameters of the track foundation – including stiffness and damping – affect the track’s dynamic response to loads generated by a moving railway vehicle. The model incorporates experimentally confirmed nonlinear stiffness of the fastening system, represented by a viscoelastic layer that provides continuous support for the rails.

The present study analyzed micro-polar nanofluid in a rotating system between two parallel plates with electric and magnetic fields. The fluid flow study was performed in a steady state. The governing equations of the present issue are considered coupled and nonlinear equations with proper similar variables. Numerical and new semi-analytical methods have been employed to solve the problem to define the exactness of the results. The influence of physical parameters governing the problem is investigated and illustrated in detail in the diagram. Results show that velocity profile and micro-rotation velocity increased when the magnetic parameter increased. Furthermore, the velocity is increased by increasing the rotation parameter. Also, in the case of the temperature profile, the Reynolds and Schmidt numbers have an inverse effect, and Prandtl number and Brownian motion have a direct effect. Other results indicate that concentration value declines by increasing the thermophoretic parameter and Reynolds number. Results compared to the prior research display good accuracy and efficiency. The study demonstrates that the method provides quantifiable reliable outcomes while requiring less computing work than conventional techniques. This method offers significant advantages in terms of simplicity, applicability, computational efficiency and accuracy.

Single-screw extruders (SSE) are commonly used in a wide variety of applications, ranging from polymer-extrusion to pellet additive manufacturing (PAM). Existing mathematical models focus on Newtonian and power-law rheologies to model melt flow in the last screw vanes. However, molten polymers usually follow more complex rheological patterns, and a generalized extrusion model is still lacking. Therefore, a semi-analytical model aiming at describing the flow of molten polymers in SSE is presented, to encompass a wide range of non-Newtonian fluids, including generalized non-Newtonian fluids (GNF). The aim is to evaluate the molten polymer flow field under the minimum set of dimensionless parameters. The effect of dimensionless extrusion temperature, flow rate, channel width, and height on the flow field has been investigated. A full factorial plane has been chosen, and it was found that the impact of dimensionless flow rate is the most prominent. The results were initially compared to numerical computations, revealing a strong agreement between the simulations and the proposed GNF method. However, significant deviations emerged when employing the traditional power-law model. This is particularly true at high values of flow rate and extrusion temperature: the mean error on overall flow speed is reduced from 12.91% (traditional power-law method) to 1.04% (proposed GNF method), while keeping a reasonable computational time (time reduction: 96.70%, if compared to fully numerical solutions). Then, the predicted pressure drop in the metering section was benchmarked against established literature data for industrial-scale extruders, to show the model’s accuracy and reliability. The relative errors of the traditional model range between 34.33 and 62%. The proposed method reduces this gap (errors ranging between 5.34% and 10.97%). The low computational time and high accuracy of the GNF method will pave the way for its integration in more complex mathematical models of large-scale additive manufacturing processes.

In this research, we introduce and analyze homotopy analysis method (HAM) for solving approximately linear matrix equation ∑i=1sAiXBi+C=0, where Ai,Bi(i=1,…,s),C∈Cn×n and X∈Cn×n must be determined. In this method we consider a convergence control parameter δ, and then we determine the optimum value of δ for obtaining fast convergence method. Moreover, we obtain the corresponding spectral radius of convergence factor of HAM method. Finally, we will apply this method to solve some test problems to support the theoretical results.

This study comprehensively analyzes how fractional-order calculus and externally applied magnetic fields synergistically govern the hydrodynamic behavior of electrically conducting Newtonian fluids in divergent geometries by injecting flow through the walls at varying tangential velocities. Using Caputo fractional derivatives, the nonlinear boundary value problem is addressed through a dual approach: an innovative implementation of the Adaptive Fractional Method (AFM) for analytical solutions and a high-precision finite difference scheme for numerical validation. Key observations reveal that enhancement of the Reynolds number (Re) or the fractional differentiation order suppressing near-wall velocities while amplifying core-region flow magnitudes. In contrast, increased Hartmann numbers (Ha) lead to significant attenuation of peak velocities due to interactions with the Lorentz force, which reveal a dual effect when reaching the Hartmann number of approximately 17: (i) the radial velocity profile begins to show uniformity at the center of the channel, and (ii) the velocity profile indicates the presence of two peak velocities near the channel walls. As well as when the Hartmann number surpasses approximately 26, the memory and non-local effects within the velocity field are mitigated. An increase in Ha results in the expansion of the streaklines. When the Hartmann number is low ( ), an increase in the channel divergence angle leads to a decrease in the maximum velocity and a refinement of the velocity profile. Conversely, at high Hartmann numbers ( ), augmenting the channel divergence angle produces effects on the velocity field akin to those observed with an increase in the Hartmann number, specifically reducing the velocity at the channel’s center and resulting in an M-shaped velocity profile.

Single abrasive particles ultrasonic vibration grinding serves as the foundation for investigating the ultrasonic vibration grinding process. This paper proposes an innovative semi-analytical model, known as the ultrasonic vibration grinding heat transfer analysis (UVGHTA) model, which accurately predicts the temperature field in single abrasive particles ultrasonic vibration grinding with complex motion-induced heat sources. Firstly, a Gaussian-shaped heat source model is established for the grinding zone. Then, the alternating direction implicit (ADI) scheme of the finite difference method is employed to solve the heat conduction partial differential equations with ultrasonic heat source load boundary conditions. During the numerical iteration process, a synchronized additional method for heat sources is introduced to incorporate the temperature rise caused by the continuously moving heat source into the calculations, resulting in a complete semi-analytical predictive model that accurately simulates the dynamic temperature field in ultrasonic vibration grinding. Finally, the temperature field calculation results of the proposed model are compared with the finite element software calculation results and the experimentally measured temperature values for verification. This study addresses the challenge of predicting the temperature field in single abrasive particles ultrasonic grinding and provides a new approach to predicting the work surface temperature field in the heat transfer process involving multi-dimensional motion-induced time-varying heat sources.

In order to further improve the power-generating capacity of the wave energy converter (WEC) of oscillating buoy type, this paper puts forward a novel type where the WEC can move and extract power in five degrees of freedom. We make a detailed hydrodynamic analysis of such WECs. Each buoy is modeled as a floating truncated cylinder with five degrees of freedom: surge, sway, heave, roll, and pitch, and there are relative motions among buoys in the array. Linear power take-off (PTO) characteristics are considered for simplicity. Under the linear wave theory, a semi-analytical method based on the eigenfunction expansion and Graf’s addition theorem for Bessel functions is proposed to analyze the hydrodynamic interactions among the WEC array under the action of incident waves, and the amplitude response and power extraction of the WEC array are then solved. After verifying the accuracy of hydrodynamic analysis and calculation, we make preliminary case studies, successively investigating the power-generating capacity of a single WEC, an array of two WECs, and an array of five WEC; then, we compare their results with the conventional heaving WECs. The results show that the WEC with five degrees of freedom can significantly improve the power extraction performance.

This paper is concerned with the comparison of semi-analytical and non-averaged propagation methods for Earth satellite orbits. We analyze the total integration error for semi-analytical methods and propose a novel decomposition into dynamical, model truncation, short-periodic, and numerical error components. The first three are attributable to distinct approximations required by the method of averaging, which fundamentally limit the attainable accuracy. In contrast, numerical error, the only component present in non-averaged methods, can be significantly mitigated by employing adaptive numerical algorithms and regularized formulations of the equations of motion. We present a collection of non-averaged methods based on the integration of existing regularized formulations of the equations of motion through an adaptive solver. We implemented the collection in the orbit propagation code THALASSA, which we make publicly available, and we compared the non-averaged methods with the semi-analytical method implemented in the orbit propagation tool STELA through numerical tests involving long-term propagations (on the order of decades) of LEO, GTO, and high-altitude HEO orbits. For the test cases considered, regularized non-averaged methods were found to be up to two times slower than semi-analytical for the LEO orbit, to have comparable speed for the GTO, and to be ten times as fast for the HEO (for the same accuracy). We show for the first time that efficient implementations of non-averaged regularized formulations of the equations of motion, and especially of non-singular element methods, are attractive candidates for the long-term study of high-altitude and highly elliptical Earth satellite orbits.

We propose an efficient semi-analytical method capable of modeling the propagation of flexural waves on cracked plate structures with any forms of excitations, based on the same group of vibration characteristics and validated by a non-contact scanning Laser Doppler Vibrometer (LDV) system. The proposed modeling method is based on the superposition of the vibrational normal modes of the detected structure, which can be applied to analyze long-time and full-field transient wave propagations. By connecting the vibration-based transient model to a power flow analysis technique, we further analyze the transient waves on a cracked plate subjected to different excitation sources and show the influence of the damage event on the path of the propagating waves. The experimental results indicate that the proposed semi-analytical method can model the flexural waves, and through that, the crack information can be revealed.