Acta Mechanica最新文献

This study presents a theoretical framework to calculate the influence of image forces on the strength of Frank-Read (FR) sources near free surfaces. We present a line tension model that explicitly incorporates image stress forces to establish the critical conditions of a FR source operation at various distances from the surface. A quasi-static nested loop (QNL) computational framework is developed to calculate the critical stress of FR source operation, and predictions are validated against discrete dislocation dynamics (DDD) simulations. Our analysis identifies a critical threshold surface proximity below which image stresses dominate, preventing the stable formation of a bowed-out segment regardless of the applied stress. Additionally, we derive a generalized analytical model expressing source strength as a function of both segment length and surface distance, capturing the transition from surface-dominated to bulk-dominated activation regimes. These findings provide insights into the mechanisms behind size-dependent phenomena in confined crystals (e.g., microbeams, thin films), such as enhanced yield strength, stochastic strength variability, and strain avalanche. The proposed approach contributes to the development of more accurate constitutive models and DDD simulations of microscale plasticity in confined crystalline volumes by providing a more accurate assessment of dislocation source strength in the presence of free surfaces.

To design and optimize piezoelectric quasicrystal (PQC) surface acoustic wave (SAW) devices, a detailed study of surface wave propagation—specifically Rayleigh and Love waves—in PQC-layered structures with weak interfaces is conducted. A hybrid Legendre–Laguerre polynomial approach is developed to analytically solve the wave dynamic equations in these structures, overcoming the limitations of traditional Laguerre polynomial methods. The interplay between piezoelectric effects and weak interface characteristics is thoroughly analyzed. Notably, new phenomena are uncovered: weak interfaces in the phonon and phason fields reduce structural stiffness, whereas weak interfaces in the electric field increase it. These effects are especially prominent at frequencies exhibiting significant dispersion. Additionally, the weak interface is found to diminish the piezoelectric coupling of phonon modes in Love waves. The findings provide a strong theoretical basis for the design and optimization of PQC-based SAW devices.

Film bulk acoustic resonators (FBARs) are essential in RF front-end applications due to their high performance, microsize, and ease of integration. This paper presents a one-dimensional analytical model for predicting the nonlinear forced vibrations of thickness–extensional AlN FBARs based on nonlinear piezoelectric theory. The model incorporates geometric and material nonlinearities, viscous damping, and electrode mechanical effects. Analytical expressions are derived to describe the excitation frequency–current relationship, including the effects of an external circuit. The influences of driving voltage, higher-order elastic constants, viscous damping, and electrode materials on the nonlinear frequency response are examined. Results indicate that increasing voltage strengthens nonlinear effects, leading to resonance frequency hardening and response multi-stability. The critical voltage marking the transition from linear to nonlinear behavior is also identified. Additionally, electrode properties, fourth-order elastic constants, and damping significantly affect the nonlinear response. Proper electrode and circuit design can mitigate nonlinear effects and extend the linear operating range. The proposed analytical model serves as an efficient tool for predicting nonlinear FBAR vibrations, providing valuable insights for device optimization.

The present study is concerned with a numerical investigation of the stochastic and stationary behavior of fiber-reinforced composite plates with uncertainty about the mechanical and material properties, fiber orientation, and external force. The uncertainty quantification is applied using the Neumann–Monte Carlo Simulation (NMC) and spectral stochastic finite element method (SSFEM) to obtain the estimates of the statistical moments of the solution for composite plate bending problems. The Neumann series acts to obtain the approximation of the inverse of the stochastic stiffness matrix. Fibers derived from the blade of buriti leaves are used to develop volumetric and laminar composites. A composite formed by epoxy mold is used, leading to local variations in mechanical properties such as structural stiffness matrix in structural responses. The finite element formulation (FEM) utilizes spectral stochastic discretization, and a truncated polynomial expansion approximates the random coefficients of the equation system. In the abstract variational problem (AVP), the generalized Hermite functions with unknown coefficients matrix represent the structural variability. The numerical case illustrates the methods’ features, where the uncertainty’s impact is in fiber orientation, volumetric fraction, and vertical displacement. The uncertainty quantification methods are discussed considering that the set of random variables composes a Uniform, Normal, and Gamma distribution. After verifying the convergence of the numerical solution, the first- and second-order statistical moments of the vertical and angular displacement estimators are discussed for the system subjected to the two uncertainty quantification methods.

The focus of this work is on the time-dependent creep behavior of a rotating multi-layered disk with imperfect bonding and variable thickness composed of functionally graded magneto-electro-elastic (FGMEE) under axisymmetric thermal and humidity fields, a centrifugal body force, and electric and magnetic potentials. Norton’s law was considered as the creep basic model, where the creep parameters are power functions of radius. The electrical, mechanical, magnetic, and hygrothermal characteristics of the material change as functions through the radial direction. A differential equation involving creep strains was developed utilizing equilibrium, electrostatic, and magnetostatic equations. Firstly, the creep strain was eliminated, and the primitive stresses, displacement, and electromagnetic potentials were derived analytically. Next, employing Prandtl-Reuss relations, an analytical solution was formulated to determine the creep stress rate and rate of electromagnetic potentials under steady-state hygrothermal conditions. Finally, in several numerical examples, the history of various fields was determined utilizing an iterative approach. The results show the considerable effect of grading index, imperfect bonding, hygrothermal loading, and boundary conditions on the response of the disk.

For the first time, this article provides essential knowledge about the required inner radius-to-pipe radius ratio for selecting the optimal graphene sheet distribution pattern. This selection aims to improve resistance against divergence while enhancing both linear and nonlinear natural frequencies for oscillating fluid-filled composite pipes reinforced with graphene sheets (GRC pipes) exposed to a thermal environment. In this context, the equations of motion are presented based on the Euler–Bernoulli beam model, taking into account geometric nonlinearity through von Karman nonlinear strains. The flow is assumed to be fully developed, making the plug flow model applicable. The refined Halpin–Tsai rules are used to specify the mechanical properties of GRC. The nonlinear discretized equations of motion, obtained through the Galerkin projection method, are analyzed using the method of multiple scales to derive the linear and nonlinear natural frequencies, as well as the associated nonlinearity coefficient. The effects of inner radius-to-pipe radius ratio, in conjunction with the graphene sheet distribution pattern, layer arrangement, flow speed, and environmental temperature on the outcomes are illustrated. For the first time, it is demonstrated that the radius ratio significantly affects the optimal distribution pattern for a GRC pipe, leading to improved performance against divergence, along with enhanced linear and nonlinear natural frequencies. The relationship between these two factors is critical. Thus, this article clarifies the impacts of the radius ratio and the graphene sheet distribution pattern on the linear and nonlinear free oscillation characteristics of fluid-filled GRC pipes, offering valuable insights for engineering designers. Additionally, the significance of layer arrangement for fluid-filled GRC pipes exposed to a thermal environment is highlighted.

Considering the Volterra viscoelastic model, dynamical boundary value problems for a half-space with a cut are presented. Using the methods of contour integration and integral transforms, the problems are reduced to first kind singular integral equations with respect to jumps of the displacement component. Using the method of orthogonal polynomials, the singular integral equation is reduced to an infinite system of linear algebraic equations. The quasi-completely regularity of the obtained systems is proved, and the method of reduction for approximate solutions is developed.

Wind-induced vibrations pose a significant global challenge in the electric power transmission sector. The alternating shedding of Von Kármán vortices, resulting from airflow around overhead power cables, induces oscillations that can lead to cable failure due to fatigue, if they are not properly understood and controlled. In this context, it is of special concern the ability to predict the dynamic behavior of these cables, which are systems with high modal density. This study presents an improved and integrated experimental/numerical method to identify elastic and dissipative parameters of overhead power cables, using a novel receptance expression, experimental data and nonlinear optimization techniques. The receptance expression (which relates displacement and force in the frequency domain) is of analytical nature, the fidelity of which is verified in comparison to a formulation developed via the finite element method. Experimental data are collected from discrete harmonic sweep and impact tests, performed on a conductor cable in a laboratory bench under five different tensile loads. The ensuing results show that the bending stiffness tends to increase with tensile load while the equivalent material loss factor tends to decrease, which is consistent with reports in the pertinent literature. It is shown that the proposed method proves to be a consistent, efficacious and meaningful alternative for thesimultaneous and flexible estimation of stiffness and damping parameters of overhead power cables, contributing to advance the subject beyond its current state.

This research investigates the mechanical behavior of nanomaterials under various physical conditions by integrating fractional-order viscoelasticity, nonlocal elasticity theory, and Maxwell’s electromagnetic relations. The study aims to accurately model the viscoelastic characteristics of nanomaterials using fractional calculus, specifically the Riemann–Liouville fractional derivative, to capture internal damping effects. The nonlocal elasticity theory is employed to account for nanoscale size effects by incorporating a nonlocal parameter that describes the influence of strain at different locations on the stress experienced at a given point. The governing equations for nanobeams subjected to magnetic fields are derived using Hamilton’s principle and further simplified through nonlocal couple stress theory. To solve the resulting complex differential equations, the homotopy perturbation technique (HPT) is applied, providing approximate analytical solutions. The study considers various boundary conditions, including simply supported (S–S), clamped-simply supported (C-S), and clamped–clamped (C–C), to ensure a comprehensive understanding of structural responses. The developed model is validated, by comparing the obtained results with benchmark results, and the outcomes are tabulated to confirm the effectiveness of the approach. These findings contribute to the development of advanced nanostructures, offering valuable insights for applications in nanotechnology and material science.

This research surveys the flutter instability and vibration analysis of hybrid laminated composite truncated conical shells subjected to fluid flow. The study explores the effect of the presence of a viscous fluid on the frequency of the cone and its velocity in inducing flutter and divergence instability. The simultaneous combination of several controlling parameters, including fluid velocity, layering configuration, and the number of layers, aids in adjusting the natural frequency of the system to the optimal condition. In this study, a third-order shear displacement field assumption is utilized, and the fluid force is applied as external work using a linear stress–strain relationship, with governing equations derived from Hamilton’s principle. The extracted equations are converted into discrete equations for numerical solution using a systematic differential quadrature method employing the Kronecker delta function. To calculate the properties of graphene, the Halpin–Tsai model is used, while the rule of mixtures is applied to estimate the mechanical properties of carbon nanotubes. The validation of the results is conducted in cases involving a cylinder containing fluid. The impact of parameters such as radius, various arrangements of nanotubes and graphene in thickness, weight percentage of nanotubes, fluid velocity, and viscosity on the issue is also examined. In the fluid analysis, the results indicate that as the fluid velocity increases, the natural frequency decreases, and at critical velocity, the phenomenon of divergence occurs. This point marks the onset of the interweaving of vibrational modes, leading to the flutter phenomenon. The extent of the impact of each parameter is detailed in the results section.