Search Results (203)

The free vibration of stiffened plates analyzed using classical plate–beam theoretical theory (PBM) simplified the vibrations of stiffeners parallel to the plane of the stiffened plate as the first-order torsional vibration of the stiffener cross-section. This simplification introduces errors in both the natural frequencies and mode shapes of the structure for stiffened plates with relatively tall stiffeners. To mitigate the issue previously described, this paper proposes an enhanced plate–beam theoretical model (EPBM). The EBPM decouples stiffener deformation into two components: (1) bending deformation along the transverse direction of the stiffened plate, governed by Euler–Bernoulli beam theory, and (2) transverse deformation of the stiffeners, modeled using thin plate theory. Virtual torsional springs are introduced at the stiffener–plate and stiffener–stiffener interfaces via penalty function method to enforce rotational continuity. These constraints are transformed into energy functionals and integrated into the system’s total energy. Displacement trial functions constructed from Chebyshev polynomials of the first kind are solved using the Ritz method. Numerical validation demonstrates that the EBPM significantly improves accuracy over the BPM: errors in free-vibration frequency decrease from 2.42% to 0.63% for the first mode and from 9.79% to 1.34% for the second mode. For constrained vibration, the second-mode error is reduced from 4.22% to 0.03%. This approach provides an effective theoretical framework for the vibration analysis of structures with high stiffeners. Full article

During the service life of a supersonic aircraft, panels are susceptible to damaged boundary supports and unexpected attached masses, which can critically alter their flutter characteristics. This paper proposes a novel two-stage assumed mode method to efficiently analyze the modal properties and expanded flutter envelopes of such compromised structures. In the first stage, the bending modes of a Euler–Bernoulli beam under elastic supports in two orthogonal directions are combined to construct the assumed modes of the intact panel, forming a modal matrix that satisfies geometric boundary conditions and establishing the baseline dynamic model. In the second stage, the method is reapplied to derive the generalized eigenvalue problem for the panel with attached masses, accurately capturing the modified mode shapes and frequencies. Subsequently, based on the principle of virtual work and first-order piston theory, the generalized aerodynamic forces are formulated. These are then incorporated into the flutter equations, which are solved in the frequency domain using the p-k method. The results demonstrate that elastic supports generally lower flutter velocities and frequencies. However, an interesting finding is that a centrally attached mass of 0.03 kg (≈10% of the panel mass) can increase the flutter speed by about 10%, whereas the same mass placed off-center may reduce it by roughly 2%. Furthermore, the proposed 9-point damper layout is shown to raise the flutter speed of an elastically supported panel with an off-center mass by up to 18% and the flutter frequency by over 13%, thereby recovering and even exceeding the design flutter boundary. Full article

The present paper concerns a new formulation of the optimal design problem of I-shaped multistep steel beam elements, based on the study of the plastic strain spread occurring in the relevant elements, with the aim of determining the length involved by the plastic deformation related to assigned load conditions and different constrained beam schemes. Material behavior is assumed as elastic–perfectly plastic, and the hypothesis of plane cross-sections is accepted. The functions defining the plastic strain spread are analytically obtained in the framework of Euler–Bernoulli beam theory. The proposed optimal design problem is a minimum volume one and the new constraint imposed on the length of the plasticized portion ensures that the minimum volume beam element also represents a maximum plastic dissipation one. Furthermore, the solution to the optimal design problem guarantees that the obtained multistep beam element ensures protection against brittle failure of the beam end sections, provides optimal cross-sections of the different portions belonging to Class 1 and ensures a suitable minimum value of the elastic flexural stiffness to respect the constraint on the deflection. Explicit reference is made to the so-called Reduced Beam Section (RBS), which characterizes the described multistep beam elements. Actually, the proposed formulation represents an innovative approach to obtaining an optimal beam element that really satisfies all the resistance, stiffness and ductility behavioral requirements. Some numerical applications conclude the paper, and their results are confirmed by appropriate FEM analyses in ABAQUS environment. Full article

The paper presents the analysis of the influence of the location and characteristics of supports on the static response of two-layer beams. The possibility of tangential movement at the supports was considered. Multilayer beams, which combine the advantages of different materials, are widely used in construction. The authors’ previous research showed that the stiffness of the connection between layers significantly affects the behaviour of the system. This paper demonstrates that the supports’ position is another crucial factor that influences the beams’ response, which is an issue that has not been previously considered in the literature. A two-layer system was modelled using the Euler–Bernoulli beam theory. Consistent normal displacements and tangential forces at the layer interface, which were proportional to the relative slip, were assumed. From the equilibrium equations and considered assumptions, three coupled displacement equations were derived and then solved using finite Fourier transforms. They were applied to solve beams, the two ends of which cannot move in the direction perpendicular to the beam’s axis, with at least one of the beam ends being a pinned support. To verify the method’s accuracy, several numerical examples were analysed. It was shown that both the support position and the possibility of tangential displacement at the supports have a significant impact on the static response. Additionally, the crucial role of the stiffness of the interlayer connection was confirmed. The developed approach provides a practical tool for assessing two-layer beam systems and highlights the importance of considering support conditions in the design and analysis of such structures. Full article

The dynamic behavior of a double-beam configuration subjected to a harmonic moving load was studied in this paper. The model was built to represent the wheel–track system that was composed of two infinite Timoshenko beams joined by uniformly spaced sleepers and supported by a continuous viscoelastic foundation. The response of the coupled beams to a moving harmonic excitation was first derived, after which the wheel–rail interaction was incorporated through a generalized Fourier series formulation. The associated Fourier coefficients were obtained from a finite system of algebraic equations imposed by the wheel–track contact conditions. The numerical simulation was carried out to compare the predictions of the Timoshenko and Euler–Bernoulli beam assumptions and to explore the influence of load speed and excitation frequency on the dynamic characteristics of the double-beam system. Comparative analysis reveals that Timoshenko beam theory predicts larger vertical displacements for rail, slab, and sleeper near the model’s cut-off frequencies (20 Hz and 30 Hz) than Euler–Bernoulli theory, with higher load velocities reducing the first cut-off frequency and amplifying peak amplitudes. The dynamic response exhibits two critical velocities at sub-cut-off frequencies, where rail displacements increase with load velocity, whereas this trend reverses when the load frequency meets or exceeds the cut-off frequencies, and no distinct peaks occur at 25 Hz and 40 Hz. The research findings are of great significance for the vibration propagation and vibration disaster prevention for shield tunnels during the train operation. Full article

This paper investigates the effects of shear deformation on the flutter and divergence instabilities of a cantilever beam subjected to a concentrated mass and applied dynamic couple. The beam is modeled using classical and truncated Timoshenko beam theory, accounting for both shear deformation and rotary inertia. The inclusion of rotary inertia is shown to significantly influence the dynamic response, particularly for beams with greater thickness. According to Hamilton’s principle, the equations of motion for the cantilevered beam are derived, applying both classical and truncated Timoshenko beam theories. Auxiliary functions are utilized to solve the resulting system analytically. Various numerical examples are presented, illustrating typical results to demonstrate the effectiveness of the proposed approach. The numerical findings show significant convergence and computational effectiveness. The effect of the location of a concentrated mass and the dynamic couple applied at the free end is analyzed for various beam slenderness ratios and curvature positions, emphasizing their impact on modifying the critical instability limits. To highlight the significance of shear effects, a comparison is made between the outcomes of the Timoshenko model and those of the Euler-Bernoulli beam model, showing notable variations in the anticipated divergence and flutter stability characteristics. All the examples were executed using both classical theory and the truncated Timoshenko theory, and the findings indicated a remarkable level of convergence. Finally, a numerical comparisons with literature papers was performed. The results achieved showed strong alignment. Full article

Prefabricated H-section steel composite wall columns (PHSWCs) are crucial for advancing modular steel construction, yet their elastic buckling performance lacks a universally accurate predictive model due to the complex interplay between section interaction and semi-rigid bolted connections. To address this, a comprehensive theoretical framework for elastic buckling analysis is developed in this study. The model integrates Euler–Bernoulli beam theory for the H-sections, a three-dimensional spring system to represent the stiffness of bolted connections, and the Green strain tensor to account for geometric nonlinearity. Validation against ABAQUS (2020) and ANSYS (2021 R1) shows high accuracy (average errors: 1.0% and 1.2%, respectively). Furthermore, a unified formula for the normalized slenderness ratio is derived via stepwise regression, which elegantly degenerates to the classical Euler solution under limiting conditions. The main conclusion is that this framework enables rapid and precise buckling analysis, reducing parametric study time by 95% compared to detailed finite element modeling. It establishes a bolt density coefficient threshold of η = 0.5 that separates composite from independent section behavior, with an optimal design range of η = 0.2 to 0.25, thereby offering a robust theoretical basis for PHSWC design. Full article

This study presents an analysis of transverse vibration behavior of a fluid-conveying pipe mounted on an elastic foundation, incorporating both classical analytical techniques and modern physics-informed neural network (PINN) methodologies. A partial differential equation (PDE) architecture is developed to approximate the solution by embedding the physics PDE, initial, and boundary conditions directly into the loss function of a deep neural network. A one-dimensional fourth-order PDE is employed to model governing transverse displacement derived from Euler–Bernoulli beam theory, with additional terms representing fluid inertia, flow-induced excitation, and stochastic force modelled as Gaussian white noise. The governing PDE is decomposed via separation of variables into spatial and temporal components, and modal analysis is employed to determine the natural frequencies and mode shapes under free–free boundary conditions. The influence of varying flow velocities and excitation frequencies on critical buckling behavior and mode shape deformation is analyzed. The network is trained using the Resilient Backpropagation (RProp) optimizer. A preliminary validation study is presented in which a baseline PINN is benchmarked against analytical modal solutions for a fluid-conveying pipe on an elastic foundation under deterministic excitation. The results demonstrate the capability of PINNs to accurately capture complex vibrational phenomena, offering a robust framework for data-driven modelling of fluid–structure interactions in engineering applications. Full article

Maglev trains represent an advanced form of modern rail transportation. The guideway irregularity presents a common disturbance to the safe and reliable operation of the maglev train. Variations in the air gap between the train and the guideway, induced by the guideway irregularities, exert a significant influence on the train’s dynamic performance, thereby impacting both ride comfort and operational safety. Although previous studies have acknowledged the importance of guideway irregularity, the stochastic effects on the car body vibration across different speeds have not been quantitatively assessed. To fill in this gap, this paper presents a 10-degree-of-freedom maglev train model based on multibody dynamics. The guideway is modelled via the finite element method using Euler–Bernoulli beam theory, and a linearized electromagnetic force equation is employed to couple the guideway and the train dynamics. Furthermore, the measurement data of guideway irregularity from the Shanghai Maglev commercial line are incorporated to evaluate their stochastic effect. Analysis results under varying speeds and irregularity wavelengths identify a resonance speed of 127.34 km/h, attributed to the interplay between guideway periodicity and the train’s natural frequency. When the ratio of the train speed versus irregularity wavelength satisfies the train’s natural frequency, a significant resonance can be observed, leading to an increase in train vibration. Based on the Monte Carlo method, stochastic analysis is conducted using 150 simulations per speed in 200–600 km/h. The maximum vertical acceleration remains relatively stable at 200–400 km/h but increases significantly at higher speeds. When the irregularity is present, greater dispersion is observed with increasing speed, with the standard deviation at 600 km/h reaching 2.7 times that at 200 km/h. Across all tested cases, acceleration values are consistently higher than those without irregularities within the corresponding confidence intervals. Full article

This study comprehensively investigates the dynamic vibration behavior of multilayer carbon nanotubes with stepped cross-sectional geometries under various boundary conditions, which is crucial for their advanced engineering applications. The methodology integrates classical molecular dynamics simulations to determine the bending stiffness of single-walled and multi-walled atomistic structures, which are subsequently utilized in the Euler–Bernoulli beam theory based on nonlocal elasticity for vibration analysis. The research focuses on elucidating the influence of the μ/L ratio (a key length parameter) and different support conditions on the natural frequencies and mode shapes of these nanostructures. Key findings reveal that the cross-sectional geometry significantly impacts the vibrational characteristics. A consistent trend observed across all examined boundary conditions is a decrease in natural frequencies as the μ/L ratio increases, indicating that increased free length or reduced fixed length leads to lower stiffness and, consequently, reduced natural frequencies. The study presents Frequency Response Functions (FRFs) and the first four mode shapes, which visually confirm these dynamic characteristics. Graphical representations further reinforce the sensitivity of natural frequencies to both the μ/L ratio and support conditions. The systematic analysis presented in this work provides vital data for predicting resonance phenomena, optimizing structural stability, and enabling precise control over the vibrational response of these advanced nanomaterials in diverse engineering applications. Full article

Fatigue damage of yawed wind turbine components can be caused by repeated long-term unsteady asymmetric inflow loads across the rotor swept area, necessitating fatigue load analysis to ensure the in-operation safety of wind turbines. This study investigates the impact of geometric nonlinearity on the fatigue loads of wind turbine components. The geometrically exact beam theory (GEBT), implemented in BeamDyn of OpenFAST, is employed to model full geometric nonlinearity. For comparison, ElastoDyn in OpenFAST, which uses the generalized Euler–Bernoulli beam theory for straight isotropic beams, is also utilized. Aeroelastic simulations were conducted for the national renewable energy laboratory (NREL 5 MW) and international energy agency (IEA) 15 MW wind turbines. Fatigue loads, quantified by the damage equivalent load (DEL) based on Palmgren–Miner’s rule, were analyzed for critical components, including blade out-of-plane (OOP) moments, low-speed shaft (LSS) torque, LSS bending moment (LSSBM), and tower base bending moment (TBBM). Results indicate that geometric nonlinearity significantly influences fatigue damage in critical turbine components, with significant differences observed between BeamDyn and ElastoDyn simulations. Full article

In this study, the nonlinear forced vibration response of fiber-reinforced laminated composite beams coated with functionally graded materials (FGMs) is investigated under the combined action of aero-thermoelastic loads and a concentrated harmonic excitation. The mathematical formulation is established using the Euler–Bernoulli beam theory, where von Kármán geometric nonlinearities are taken into account, along with the modified third-order piston theory to represent aerodynamic effects. By neglecting axial inertia, the resulting set of nonlinear governing equations is simplified into a single equation. This equation is discretized through the Galerkin procedure, yielding a nonlinear ordinary differential equation. An analytical solution is, then, obtained by applying the method of multiple time scales (MTS). Furthermore, a comprehensive parametric analysis is carried out to evaluate how factors such as the power-law index, stacking sequence, temperature field, load amplitude and position, free-stream velocity, and Mach number influence both the lateral dynamic deflection and the frequency response characteristics (FRCs) of the beams, offering useful guidelines for structural design optimization. Full article

This study presents an exact analytical investigation into the static response of helical single-walled carbon nanotube (SWCNT) beams based on Eringen’s differential nonlocal elasticity theory, which captures nanoscale effects arising from interatomic interactions. A key contribution of this work is the derivation of the governing equations for helical SWCNT beams, based on the nonlocal Euler–Bernoulli theory, followed by their exact analytical solution using the initial value method. To the best of the authors’ knowledge, this represents the first closed-form formulation for such complex nanostructures using this theoretical framework of nonlocal elasticity theory. The analysis considers both cantilevered and clamped–clamped boundary conditions, under various concentrated force and moment loadings applied at the ends and midpoint of the helical beam. Displacements and rotational components are expressed in the Frenet frame, enabling direction-specific evaluation of the deformation behaviour. Parametric studies are conducted to investigate the influence of geometric parameters—such as the winding angle ($\alpha$) and aspect ratio ($R/d$) and the nonlocal parameter ($R/\gamma$). Results show that nonlocal elasticity theory consistently predicts higher displacements and rotations than the classical local theory, revealing its importance for accurate modelling of nanoscale structures. The proposed analytical framework serves as a benchmark reference for the modelling and design of nanoscale helical structures such as nano-springs, actuators, and flexible nanodevices. Full article

In the research, a novel accelerometer concept leveraging the mode-localization phenomenon is put forward. The sensor measures external acceleration through monitoring changes in the relative amplitude ratio among coupled resonators. The sensing part of the presented accelerometer comprises a doubly clamped beam coupled with a cantilever beam. Its design ensures the initial bending mode of the clamped beam approximates the secondary bending mode of the cantilever. Drawing on Euler–Bernoulli beam theory, the governing formulas of the coupled resonators are deduced and analyzed via Galerkin discretization integrated with the multiple-scale method. During working in both linear as well as nonlinear operating regions, this sensor’s dynamic behavior can be tuned by adjusting the drive voltage. The obtained results demonstrate that the nonlinear dynamics increases the accelerometer sensitivity, which can be further enhanced by adjusting the coupling voltage without severe mode overlap. The presented model offers one viable method to enhance the overall performance in multi-mode MEMS accelerometers. Full article

Recordings of wind velocity and associated wind turbine (WT) power possess noise, owing to inaccurate sensor measurements, atmosphere conditions, working stops, and flaws. The measurements still contain noise even after purification, so the fit curve of the wind turbine power might be different from the datasheet. The model of wind turbine power (MWTP) is significant, owing to its utilization for predicting and managing the wind energy. There are two types of MWTP, namely the parametric and the non-parametric types. Parameter identification of the parametric MWTP can be treated as a high nonlinear optimization problem. The fitness function is to minimize the root average squared errors (RASEs) between the calculated and measured wind powers while subject to a set of parameter constraints. The non-parametric MWTP is identified through training through machine learning. In this article, machine learning, namely the support vector regression (SVR), is innovatively applied for the identification of the non-parametric MWTP. Additionally, the dynamic force and the eigen parameters of WTs at different wind velocities are studied theoretically. The theoretical model for analyzing the natural frequencies of WT is validated using two techniques, namely the finite element method and the Euler–Bernoulli beam theory. The simulations are executed using MATLAB. The SVR is assessed via the comparison of its results with those of three parametric MWTP, viz. the 5-, 6-parameter logistic functions, and the modified hyperbolic tangent. It can be affirmed that the SVR execution is excellent and can produce the non-parametric MWTP with a RASE less than other algorithms by 0.4% to 93.8%, with a small computation cost. Full article