Archive of Applied Mechanics最新文献

The time-dependent creep behavior of a rotating multi-layered annular plate made of functionally graded piezoelectric material (FGPM) with imperfect interlayer bonding and variable thickness was investigated in this article. In addition to an externally applied axial magnetic field, the disk was exposed to axisymmetric hygrothermal loads. At clamp-free boundary condition, the disk thickness and all material properties vary radially in power-law functions. With parameters that are power functions of the radius, Norton’s law was used as the constitutive model for creep analysis. For each layer, governing equations incorporating creep strains were derived by utilizing hygrothermal field equations, equilibrium, electrostatic, strain–displacement, and stress–strain relations. First, by ignoring creep effects, analytical solutions were discovered for the initial stresses, displacements, and electric potential. Subsequently, analytical formulations for the creep stress rates and electric potential rate under steady-state hygrothermal conditions have been established employing the Prandtl–Reuss relations. Finally, the presentation of numerical examples demonstrates the impacts of axial magnetic field, angular velocity, material inhomogeneity, and interlayer bonding conditions on the creep behavior of the annular plate.

This study presents a theoretical framework for analyzing the spatial coupled flexural–torsional vibration of thin-walled beam bridges under moving train loads. The train is modeled as a dual-axle moving load series, representing front and rear wheel subsystems with constant spacing. Based on Vlasov's thin-walled beam theory, the governing equations incorporate warping stiffness, rotational inertia and additional torsional moments induced by changes in the position of the shear center—a mechanism often neglected in prior analyses. Closed-form solutions for lateral and torsional displacements are derived using Fourier and Laplace transforms. Validation against finite element method (FEM) and prior studies confirms the accuracy of the proposed theoretical method. Results show excellent agreement with both finite element simulations and existing reference solutions. Furthermore, various influencing parameters, including additional torsional moments, dual impact of train-to-bridge length ratio and speed, fixed wheelbase of a vehicle-to-inter-car distance ratio (i.e., L_c/L_d) and eccentricity, are systematically analyzed. The maximum dynamic amplification factors (DAFs) obtained when additional torsional moments are considered is 8.82% higher than that calculated without accounting for such effects, which demonstrates that incorporating additional torsional moment effects can significantly improve prediction accuracy. Vibration amplitudes exhibit a non-monotonic, sinusoidal-like trend with speed, peaking at critical vehicle-to-bridge length ratios. With each 1-m increment in fixed wheelbase L_c over the range 17 m to 19 m, the lateral displacement amplitude grows by approximately 6.16%, while the torsional displacement amplitude increases by about 6.6%. Both the lateral and torsional displacement amplitudes exhibit an approximately linear increase as a function of the load eccentricity. These findings provide a theoretical foundation for the dynamic assessment and optimization of thin-walled beam bridges under moving train loads.

This study presents a new configuration within the collinear elliptic Sitnikov five-body problem, characterized by two distinct pairs of primary bodies. Each pair exhibits symmetry in both shape and size, with the first pair having a greater magnitude than the second. All primary bodies are positioned collinearly and move along elliptical trajectories around their common center of mass. The primary aim of this research is to investigate the existence of equilibrium points and analyze their linear stability. The investigation focuses on the dependency of equilibrium points (E_{1,2}; (0,0,zeta _{1,2})) on three key factors: the mass parameter (mu ^{*}), the radiation factor q, and the eccentricity e of the elliptic orbits of primaries around their common center of mass. It is shown that the radiation factor q is constrained by the mass parameter within the range (qin (-beta , -beta /8)); (beta =2mu ^{*}/(1-2mu ^{*})). By fixing (mu ^{*}), we delineate the range of q for which the equilibrium points exist, establishing that they do not exist outside this range. The study reveals that as the eccentricity e increases toward 1, the equilibrium points (E_{1,2}) converge toward the center of mass along the (zeta )-axis, while a decrease in e toward 0 causes them to move away. Similarly, as q approaches (-beta /8), (E_{1,2}) move closer to the center of mass, and as q approaches (-beta ), they move farther away. The analysis demonstrates that all equilibrium points identified in this study exhibit linear instability. These results offer a detailed understanding of the positional dynamics of equilibrium points as a function of the mass parameter, radiation factor, and orbital eccentricity. The findings have significant implications for the fields of Celestial Mechanics and Dynamical Astronomy. Finally, the study also explores the motion of the infinitesimal mass using first return map and families of periodic orbits to reveal the system’s dynamic behavior.

Dynamic vibration absorbers with grounded negative stiffness present inter-layer installation difficulties, which limits other usage options of these absorbers. To overcome this problem, a novel dynamic vibration absorber with ungrounded lever-type negative stiffness (LN-DVA) is proposed in this study, which makes the inter-layer installation possible and improve the control performance. First, based on the equations of motion, the displacement transfer function of the controlled primary structure is established. Then, the optimal parameters of the LN-DVA are determined by applying the fixed point theory (FPT) and numerical method, respectively, in order to minimize the resonant response and the results are analyzed. It is found that the lever ratio and the mass ratio influence the values of the optimal parameters. When the lever ratio increases, the primary structure displacement decreases in the resonance region and the good control performance is achieved. Furthermore, by evaluating the control performance for harmonic and random (earthquake ground motion) vibrations reduction of primary structure displacement, it is found that the proposed LN-DVA significantly outperforms the compared DVAs without negative stiffness. In particular, the LN-DVA outperforms the DVA with grounded negative stiffness. The obtained results are relevant because they provide more control performance and practical usage options of the proposed LN-DVA.

Commercial and academic finite element software packages typically support either phase field modeling for bulk failure or cohesive zone modeling for interfacial damage. Still, an integrated and flexible framework that combines these two is not easily available in commercial software. This paper presents a phase field–cohesive zone (PF–CZ) model implemented in Abaqus, enabling simultaneous simulation of bulk and interfacial fracture within a single computational platform. This framework combines user-defined elements (UEL) for the phase field formulation that covers both brittle and ductile fractures in the bulk, and various Abaqus built-in cohesive elements with customizable traction–separation laws for the interface. A robust and implicit Newton–Raphson solution scheme combined with a staggered method is employed to solve phase and displacement unknowns, with detailed derivation of the stiffness and tangent stiffness matrices. Validation is performed via three-element tensile tests comparing results from Abaqus and MATLAB-based step-by-step calculations. The model is further demonstrated through simulations of bi-material interface fracture, ceramic matrix composite failure, and four-point bending of reinforced concrete beams. This work offers a verified and extensible framework for researchers and engineers who are new to either the phase field model or the cohesive zone model to study complex fracture scenarios in composite structures. In addition, the limitations of the phase field length scale parameter are analyzed and verified through simulation results. The source code is available at https://github.com/MCMB-Lab/AbaqusPF-CZmodel.

This study presents an innovative methodology for examining the photothermal dynamics in viscoelastic semiconductor materials featuring cylindrical cavities, employing a fractional adaptation of the Kelvin–Voigt model. By incorporating the generalized Mittag–Lefflerfunction and the nonlocal, non-singular Goufo–Caputo fractional operator, the research explores the conversion of light energy into thermal energy through absorption processes. The framework is based on the Moore–Gibson–Thompson equation and integrates the Guyer–Krumhansl nonlocal thermal length-scale concept to offer a robust model for intertwined thermal, mechanical, and optical phenomena. The investigation assesses the influences of fractional parameters, nonlocality, and viscoelastic properties on photothermal wave propagation. Findings underscore the promise of developing sophisticated optically absorbent nanostructures, which are essential for improving photothermal energy production and thermal management technologies. Furthermore, a comparative evaluation of adapted local and nonlocal photoelasticity models reveals distinctive characteristics of semiconducting materials, providing key insights into their thermomechanical interactions and opening avenues for novel advancements in energy systems, nanotechnology, and materials science.

This study presents a unified framework for the free vibration analysis of functionally graded (FG) nanobeams within Eringen’s nonlocal elasticity, consistently formulated under Euler–Bernoulli (EBT) and Timoshenko (TBT) beam theories. The canonical first-order governing equations are derived in a unified closed-form manner and solved using the Complementary Functions Method (CFM) in the Laplace domain. A comprehensive parametric study addresses four boundary conditions with variations in slenderness ratios, gradation indices, and nonlocal parameters. The primary contribution of this work lies in providing a unified closed-form canonical state-space formulation for nonlocal FG nanobeams under both EBT and TBT, and in demonstrating that the Laplace–CFM implementation offers a stable and efficient eigen-solver with consistent boundary enforcement across multiple support conditions. The resulting benchmark frequencies can serve as a reliable reference for verifying of future refined or multi-physics nanobeam models. The results confirm monotonic frequency softening with increasing nonlocal parameter and with grading toward the softer constituent. The EBT–TBT discrepancy is most pronounced for low-slenderness ratios, highlighting the role of shear deformation and rotary inertia in short/thick nanobeams, while the two theories converge as slenderness increases.

This work aims to develop a micropolar model for random fibrous networks within the framework of micropolar elasticity. The networks are composed of elastic filaments lying in a 2D domain, representative of the structural organization found in many biological materials—particularly collagen gels, which exhibit a variety of morphologies. Basing on finite element simulations of the fiber network, we upscale the microstructural response into an effective continuum behavior in the framework of Cosserat elasticity. The model treats fibers as Timoshenko beams and crosslinks as welded joints, allowing for both force and moment transmission throughout the network. A micromechanical homogenization approach is employed to evaluate the variation of the effective micropolar moduli as functions of key structural parameters, including fiber density, internal bending length, and the size of the window of analysis.