Search Results (116)

This study aimed to investigate the dynamic characteristics of shafts joined by friction welding and to update their finite element models. The first five bending mode resonance frequencies, damping ratios, and mode shapes of SAE 304 steel beams, friction-welded at three different rotational speeds (1200, 1500, and 1800 rpm), were determined using the Experimental Modal Analysis method. This approach allowed for an examination of how the dynamic properties of friction-welded beams change at varying rotational speeds. A slight decrease in resonance frequency values was observed with the transition from lower to higher rotational speeds. The largest difference of 3.28% was observed in the first mode, and the smallest difference of 0.19% was observed in the second mode. Different trends in damping ratios were observed for different modes. In the first, second, and fourth modes, damping ratios tended to increase with increasing rotational speeds, while they tended to decrease in the third and fifth modes. The largest difference was calculated as 52.83% in the third vibration mode. However, no significant change in mode shapes was observed for different rotational speeds. Based on the examined Modal Assurance Criterion (MAC) results, cross-comparisons of the mode shapes obtained for all three different speeds yielded a minimum similarity of 93.8%, reaching up to 99.9%. For model updating, a Frequency Response Assurance Criterion (FRAC)-based method utilizing frequency response functions (FRFs) was employed. Initially, a numerical model of the welded shaft was created using MATLAB-R2015a, based on the Euler–Bernoulli beam theory. Since rotational coordinates were not used in the EMA analyses, static model reduction was performed on the numerical model to reduce the effect of rotational coordinates to translational coordinates. For model updating, experimentally obtained FRFs from EMA and FRFs from the numerical model were used. The equivalent modulus of elasticity and equivalent density of the friction weld region were used as updating parameters. Successful results were achieved by developing an algorithm that ensured the convergence of the numerical model’s FRFs and natural frequencies. 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

The mechanics of an elastic sheet reinforced with fiber mesh is investigated when undergoing bilateral in-plane bending and stretching. The strain energy of FRC is formulated by accounting for the matrix strain energy contribution and the fiber network deformations of extension, flexure, and torsion, where the strain energy potential of the matrix material is characterized via the Mooney–Rivlin strain energy model and the fiber kinematics is computed via the first and second gradient of deformations. By applying the variational principle on the strain energy of FRC, the Euler–Lagrange equilibrium equations are derived and then solved numerically. The theoretical results highlight the matrix and meshwork deformations of FRC subjected to bilateral bending and stretching simultaneously, and it is found that the interaction between bilateral extension and bending manipulates the matrix and network deformation. It is theoretically observed that the transverse Lagrange strain peaks near the bilateral boundary while the longitudinal strain is intensified inside the FRC domain. The continuum model further demonstrates the bidirectional mesh network deformations in the case of plain woven, from which the extension and flexure kinematics of fiber units are illustrated to examine the effects of fiber unit deformations on the overall deformations of the fiber network. To reduce the observed matrix-network dislocation in the case of plain network reinforcement, the pantographic network reinforcement is investigated, suggesting that the bilateral stretch results in the reduced intersection angle at the mesh joints in the FRC domain. For validation of the continuum model, the obtained results are cross-examined with the existing experimental results depicting the failure mode of conventional fiber-reinforced composites to demonstrate the practical utility of the proposed model. Full article

In this contribution, the classical Cauchy first-gradient elastic theory is used to solve the equilibrium problem of a bidimensional (2D) reinforced elastic structure under small displacements and strains. Such a 2D first-gradient continuum is embedded with a reinforcement, which is modeled as a zero-thickness interface endowed with the elastic properties of an extensional Euler–Bernoulli 1D beam. Modeling the reinforcement as an interface eliminates the need for a full geometric representation of the reinforcing bar with finite thickness in the 2D model, and the associated mesh discretization for numerical analysis. Thus, the effects of the 1D beam-like reinforcements are described through proper and generalized boundary conditions prescribed to contiguous continuum regions, deduced from a standard variational approach. The novelty of this work lies in the formulation of an interface model coupling 1D and 2D continua, based on weak formulation and variational derivation, capable of accurately capturing stress distributions without requiring full geometric resolution of the reinforcement. The proposed framework is therefore illustrated by computing, with finite element simulations, the response of the reinforced structural element under uniform bending. Numerical results reveal the presence of jumps for some stress components in the vicinity of the reinforcement tips and demonstrate convergence under mesh refinement. Although the reinforcement beams possess only axial stiffness, they significantly influence the equilibrium configuration by causing a redistribution of stress and enhancing stress transfer throughout the structure. These findings offer a new perspective on the effective modeling of fiber-reinforced structures, which are of significant interest in engineering applications such as micropiles in foundations, fiber-reinforced concrete, and advanced composite materials. In these systems, stress localization and stability play a critical role. 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

The shallow, soft subsea formations, characterized by low strength and poor stability, lead to complex interactions between the screw motor drilling tool and the wellbore wall during directional drilling, complicating the accurate evaluation of the tool’s deflection capability. To address this issue, this paper proposes an integrated mechanical analysis method combining three-dimensional finite element analysis and transient dynamic analysis. By establishing a finite element model using 12-DOF (degree-of-freedom) spatial rigid-frame Euler–Bernoulli beam elements, coupled with well trajectory coordinate transformation and Rayleigh damping matrix, a precise description of drill string dynamic behavior is achieved. Furthermore, the introduction of pipe–soil dynamics and the p-y curve method improves the calculation of contact reaction forces between drilling tools and formation. Case studies demonstrate that increasing the tool face rotation angle intensifies lateral forces at the bit and stabilizer, with the predicted maximum dogleg severity within the first 10 m ahead of the bit progressively increasing. When the tool face rotation angle exceeds 2.5°, the maximum dogleg severity reaches 17.938°/30 m. With a gradual increase in the drilling pressure, the maximum bending stress on the drilling tool, maximum lateral cutting force, and stabilizer lateral forces progressively decrease, while vertical cutting forces and bit lateral forces gradually increase. However, the predicted maximum dogleg severity increases within the first 10 m ahead of the bit remain relatively moderate, suggesting the necessity for the multi-objective optimization of drilling pressure and related parameters prior to actual operations. Full article

Magnetic soft continuum robots (MSCRs) have broad application advantages in vascular intervention; however, current MSCRs still face challenges in navigating the narrower and tortuous structure of the cerebral vasculature. To address this challenge, we propose a tapered MSCR (T-MSCR), which is designed to facilitate smooth navigation through microvascular structures via its miniature tip. Specifically, to optimize its bending ability, we combine the Gray Wolf Optimizer (GWO) with the Euler–Bernoulli beam theory and introduce a Discrete GWO (DGWO) approach to optimize the distribution of magnetic particles within the T-MSCR. We then demonstrate the optimization process of the T-MSCR’s bending ability, comparing and analyzing its deflection angle and deformation characteristics, highlighting its capability to enter microvasculars. Furthermore, we demonstrate the magnetic steering and path selection capabilities of T-MSCR in a two-dimensional vascular model and its navigation performance in real-scale human vascular models. Finally, biocompatibility tests confirm that T-MSCR exhibits no toxicity to human cells, thereby laying a solid foundation for its clinical application. The proposed T-MSCR design and optimization are expected to provide a more efficient and feasible solution for future cerebrovascular interventions. 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

Constructed wetlands (CWs) are cost-effective and sustainable systems for wastewater treatment, but their hydraulic performance remains a critical challenge. In this study, a lab-scale baffled horizontal subsurface flow constructed wetland was modeled using Computational Fluid Dynamics to investigate the effects of aeration strategies on hydraulic performance, focusing on aeration rates and positions. A gas–liquid two-phase flow system was modeled using the Euler–Euler approach with the Darcy–Forchheimer model in OpenFOAM, simulating 15 cases with varying aeration rates (0.1–0.3 m³/day) and positions (middle of channels vs. bends at the ends of baffles). Results show that the introduction of aeration influenced hydraulic efficiency (HE) and the Morrill Dispersion Index (MDI). Without aeration, the baseline HE was already high (HE = 0.9297) due to the optimized baffle configuration. However, aeration further improved performance, with HE increasing to 0.9594 and MDI decreasing from 1.6087 to 1.4000 when aeration was applied at bends (Position C) at 0.3 m³/day. Aeration at bends was more effective than mid-channel aeration, promoting uniform flow distribution and reducing short-circuiting. These findings highlight the importance of aeration positioning and provide insights for optimizing CW design to balance energy consumption and hydraulic performance. Full article

High-speed passenger carriages with a long and light carriage body are sensitive to vertical vibration because the bending mode eigenfrequency falls within the most sensible frequency interval for the human being. Anti-bending bars (ABBs) are a passive means to raise the eigenfrequency of the bending mode of the carriage body beyond the sensitive limit, ameliorating ride comfort. ABBs are two bars fixed via vertical supports under the carriage chassis on the longitudinal beams. ABBs resist the bending of the carriage body and can, therefore, increase the bending eigenfrequency beyond the sensitive limit, as necessary. In this paper, a new model for the ABBs, which takes into account the longitudinal stiffness of the ABBs, the three-direction stiffness of the fastening between the ABBs and the vertical supports and the vertical vibration modes of the ABBs via the Euler–Bernoulli beam theory and modal analysis, is incorporated in the 10 degrees of freedom model of a passenger carriage; this is to study the effect of the ABBs upon the running behaviour and ride comfort according to the specific regulations in the field. First, the frequency response functions (FRFs) of the passenger carriage with an ABB system are calculated and analysed, and then, the root mean square (r.m.s.) acceleration and the comfort index are evaluated in the carriage body centre in the context of a parametric study. The longitudinal stiffness of the fastening is critical to ensure the effectiveness of the ABB system. However, the effect of decreasing in the longitudinal stiffness of the fastening can be compensated by adopting longer ABBs. Full article

With the ever-growing demand for high-speed optical communications, microwave photonics, and quantum key distribution systems, compact electro-optic (EO) modulators with high extinction ratios, large bandwidth, and high tuning efficiency are urgently pursued. However, most integrated lithium–niobate (LN) modulators cannot achieve these high performances simultaneously. In this paper, we propose an improved theoretical model of a chip-scale electro-optic (EO) microring modulator (EO-MRM) based on X-cut lithium–niobate-on-insulator (LNOI) with a hybrid architecture consisting of a 180-degree Euler bend in the coupling region, double-layer metal electrode structure, and ground–signal–signal–ground (G-S-S-G) electrode configuration, which can realize highly comprehensive performance and a compact footprint. After parameter optimization, the designed EO-MRM exhibited an extinction ratio of 38 dB. Compared to the structure without Euler bends, the increase was 35 dB. It also had a modulation bandwidth of 29 GHz and a tunability of 8.24 pm/V when the straight waveguide length was 100 μm. At the same time, the proposed device footprint was 1.92 × 10⁴ μm². The proposed MRM model provides an efficient solution to high-speed optical communication systems and microwave photonics, which is helpful for the fabrication of high-performance and multifunctional photonic integrated devices. Full article

Ride comfort is an important requirement that passenger rail vehicles must meet. Carbody–anti-bending system is a relatively new passive method to enhance the ride comfort in passenger rail vehicles with long and light carbody. The resonance frequency of the first bending mode (FBM) of such vehicle is within the most sensitive frequency range that affects ride comfort. Anti-bending bars consist of two bars that are mounted under the longitudinal beams of the carbody chassis using vertical supports. When the carbody bends, the anti-bending bars develop moments in the neutral axis of the carbody opposing the bending of the carbody. In this way, the carbody structure becomes stiffer and the resonance frequency of the FBM can be increased beyond the upper limit of the discomfort range of frequency, improving the ride comfort. The theoretical principle of this method has been demonstrated employing a passenger rail vehicle model that includes the carbody as a free–free Euler–Bernoulli beam and the anti-bending bars as longitudinal springs jointed to the vertical supports. Also, the method feasibility has been verified in the past using an experimental scale demonstrator system. In this paper, a new model of the carbody–anti-bending bar system is proposed by including three-directional elastic elements (vertical and longitudinal direction and rotation in the vertical–longitudinal plane) to model the fastening of the anti-bending bars to the supports and the vertical motion of the anti-bending bars modelled as free–free Euler–Bernoulli beams connected to the elastic elements of the fastening. In the longitudinal direction, the anti-bending bars work as springs connected to the longitudinal elastic elements of the fastening. The modal analysis method is applied to point out the basic properties of the frequency response functions (FRFs) of the carbody–anti-bending bars system, considering the bounce and FBMs of both the carbody and the anti-bending bars. A parametric study of the FRF of the carbody shows that the vertical stiffness of the fastening should be sufficiently high enough to eliminate the influence of the modes of the anti-bending bars upon the carbody response and to reduce the anti-bending bars vibration in the frequency range of interest. Longitudinal stiffness of the elastic elements of the fastening is critical to increase the bending resonance frequency of the carbody out of the sensitive range. Longer anti-bending bars can improve the capability of the anti-bending bars to increase the bending resonance without the risk of interference effects caused by the bounce and bending modes of the anti-bending bars. Full article

As wind turbines increase in size, blades become longer, thinner, and more flexible, making them more susceptible to large geometric nonlinear deformations, which pose challenges for aeroelastic simulations. This study presents a nonlinear aeroelastic model that accounts for large deformations of slender, flexible blades, coupled through the Actuator Line Method (ALM) and Geometrically Exact Beam Theory (GEBT). The accuracy of the model is validated by comparing it with established numerical methods, demonstrating its ability to capture the bending–torsional coupled nonlinear characteristics of highly flexible blades. A bidirectional fluid–structure coupling simulation of the IEA 15MW wind turbine under uniform flow conditions is conducted. The effect of blade nonlinear deformation on aeroelastic performance is compared with a linear model based on Euler–Bernoulli beam theory. The study finds that nonlinear deformations reduce predicted angle of attack, decrease aerodynamic load distribution, and lead to a noticeable decline in both wind turbine performance and blade deflection. The effects on thrust and edgewise deformation are particularly significant. Additionally, nonlinear deformations weaken the tip vortex strength, slow the momentum exchange in the wake region, reduce turbulence intensity, and delay wake recovery. This study highlights the importance of considering blade nonlinear deformations in large-scale wind turbines. Full article

This paper proposes a distributed passivity-based control scheme for the consensus and vibration suppression of multiple space manipulators holding flexible beams. A space manipulator holding a flexible beam is essentially a rigid–flexible underactuated system. The bending deformation of the flexible beam is discretized by employing the assumed modes method. Based on Lagrange’s equations of the second kind, the dynamics model of each manipulator holding a flexible beam is established. By connecting such underactuated systems with the auxiliary Euler–Lagrange systems, a distributed passivity-based controller is designed under undirected communication graphs. To suppress flexible vibration effectively, a distributed controller with the feedback of the velocity of deflection at the free end of the flexible beam is proposed to achieve the manipulator synchronization and vibration suppression simultaneously. The stability of the proposed controller is analyzed with LaSalle’s invariance principle. Numerical simulations and experiments are conducted to show the effectiveness of the designed controllers. Full article

For wide flange box sections, conventional Euler–Bernoulli beam theory with maintaining the cross-section planarity may lead to underestimation of axial stresses. Axial stresses in cross-section flanges may have a non-uniform distribution due to shear pliability, decreasing in value from the flange–web junction to the middle area of the flange. This phenomenon leads to the introduction of an effective flange width with a uniform distribution of original maximum stress. Furthermore, the introduction of flange curvature makes it even more complex due to the varying lever arm of each flange part with respect to the neutral bending axis. Because of this, in some cases, it is hard to predict where the flange’s highest normal stress value will appear. In this paper, the shear lag effect on wide curved box sections is analyzed through parametric numerical analysis using the FEA software Dlubal RFEM 5, together with visual programming performed in Rhino Grasshopper. This study investigates the interaction of the shear lag effect and plane section hypothesis, which can be simplistically represented as a reduction in the impact of shear lag and the activation of a larger part of the flange of a wide-flange beam in the structural system of a continuous beam. The results suggest that for higher flange curvature and higher width to length ratio, this effect is more prominent. Full article