Acta Mechanica最新文献

Metastructures with high-static-low-dynamic stiffness (HSLDS) resonators are effective in generating low-frequency bandgaps but face limitations due to narrowing in widths of low-frequency bandgaps at lower frequencies. In this research, a one-dimensional graded quasi-zero-stiffness (QZS) metastructure with tunable HSLDS resonators is proposed to broaden the low-frequency bandgap. The tunable HSLDS resonator integrates a tunable negative stiffness element with a positive stiffness element in parallel, allowing for stiffness contraction and adjustments. A mathematical model is developed to predict the bandgap followed by a parametric study for optimization. Results show that the proposed graded QZS metastructure achieves a 81.4% increase in low-frequency bandgap width compared its uniform counterpart, highlighting its superior performance for low-frequency broadband vibration suppression.

The nonlocal continuum mechanics theory effectively incorporates scale effects and microstructural characteristics of materials into macroscopic mechanical properties, addressing the coupling between macro- and microscale phenomena. Despite its advantages, current computational methods for solving nonlocal elasticity problems face significant challenges: The original volume integral formulation is mathematically complex, while the equivalent differential form still presents numerical difficulties, particularly for complex geometries and boundary conditions in nanoscale structures. This study proposes a novel finite element-differential quadrature (FE-DQ) hybrid method for analyzing the buckling behavior of graphene-equivalent nanoplates. The method combines the geometric flexibility of finite elements with the high-order accuracy of differential quadrature, overcoming limitations of existing approaches. Through comprehensive validation against established results, we demonstrate the method's accuracy and efficiency. Based on the obtained results, the effects of size, nonlocal parameters, and biaxial load ratios on the nonlocal behavior of buckling loads were investigated. The findings indicate that the nonlocal effects on buckling loads decrease with increasing size, while they intensify with higher nonlocal parameters. In contrast, the biaxial load ratio exhibits negligible influence on the nonlocal effects of buckling loads. These results not only validate the effectiveness of the proposed FE-DQ method for nanoscale structural analysis but also provide valuable insights for the design and application of graphene-based nanostructures in flexible electronics, sensors, and nanocomposite materials.

We employ an effective medium model to investigate the effects of embedded heavy hard spheres as local resonators on the dynamic instability of metacomposite columns subjected to a follower force. Classical formulas for the dynamic buckling of the flutter response of a conventional elastic column subjected to a follower force are extended to a heavy hard sphere-filled metacomposite column under a follower force. The effects of embedded heavy hard spheres on the critical load and the associated flutter frequency of the instability mode are examined for two specific metaelastic composite columns. Our results show that the embedded heavy hard spheres as local resonators have a moderate effect on the flutter frequency but do not affect the critical load for dynamic instability of the metacomposite column under a follower force.

This paper presents a novel viscoelastic foundation model for the first time, for the damped vibration analysis of functionally graded sandwich beams. The proposed viscoelastic foundation is established by two layers: the visco-Winkler layer and the visco-Pasternak layer. Each layer involves two coefficients, including the coefficient of elasticity and the coefficient of viscosity. Both hard- and soft-core functionally graded sandwich beams are considered in detail. The governing equations of motion are generated using Reddy’s third-order shear deformation theory and Hamilton’s principle. Navier’s technique is used to achieve complex eigenvalues and eigenvectors of the damped vibration of the beams. The correctness and efficiency of the current algorithm are authenticated through a comparison study; then the proposed algorithm and calculation program are employed to explore the damped vibration characteristics of the sandwich beams. A detailed numerical analysis is carried out to illustrate the effects of several coefficients on the damped vibration characteristics of the sandwich beams. The outcomes of this study showed that the influences of the damping coefficients are substantial on the damped vibration behaviors of the sandwich beams.

In this paper, the nonlinear free vibration behavior of the composite functionally gradient piezoelectric semiconductor (FGPS) rectangular beam resting on the Pasternak foundation is studied on the basis of the nonlinear strain–displacement relation and the theory of piezoelectric semiconductor. The nonlinear constitutive equations are presented, and the strain energy, kinetic energy and virtual work of the composite FGPS beam are derived. On account of the condition of charge continuity and Hamilton’s principle, the governing equations of the system are obtained. The author provides several numerical examples to display the effect of the initial electron concentration, functionally gradient index, thermal load, elastic foundation parameter and geometric parameter on the nonlinear vibration frequency and damping characteristic of the composite FGPS beam. The main innovation of the paper is that the different performances between the linear vibration responses and the nonlinear vibration responses are illustrated. Also, the thermal effect has a momentous influence on the natural frequency, but an unimportant influence on the damping characteristic of the composite FGPS beam.

In this study, we present a novel mathematical model for a thermally conducting, homogeneous, and isotropic Kelvin–Voigt-type circular microplate resonator, grounded in Kirchhoff's Love plate theory and incorporating nonlocal thermomass motion. The model leverages ramp-type heat conduction to thermally load the resonator, revealing significant impacts on temperature increase and drift velocity components. By developing and solving the governing equations within the Laplace transform domain, we analyze a ceramic microplate's response to thermal loads. Numerical results demonstrate the influence of thermoviscoelastic parameters and ramp-time heat on various physical fields, including deflection distributions, displacement, temperature, radial thermal moment, and radial stress. The findings highlight the pronounced effect of viscosity on these physical aspects, providing valuable insights into the time-dependent behavior of the resonator.

Sliding electrical contacts are critical components in electrical connectors, brushes, and slip rings, with their performance directly influencing the reliability and stability of these equipment. Sliding electrical contact equipment operate in complex multi-field coupling environments involving Joule heating, frictional heating, thermal expansion, and sliding contact on rough surfaces. Current researches on the multi-field coupling mechanisms in sliding electrical contact are limited. This paper presents a numerical approach based on the boundary integration method to investigate the electro-thermo-mechanical coupling effects at the contact asperities of rough surfaces. The surface profile-dependent friction coefficient is considered through friction experiments. Using Fourier transform and the conjugate gradient method, the temperature, displacement, contact pressure, and electrical contact resistance (ECR) are calculated. The underlying influence mechanisms of surface parameters and loading conditions on the contact area, temperature rise, and ECR are systematically analyzed. This numerical approach provides insights into the multi-field coupling behavior in rough surface sliding electrical contacts.

In the present article, based on the first-order shear deformation theory (FSDT) and strain gradient theory (SGT), vibrational characteristics of plate-type microstructures made of functionally graded materials (FGMs) with arbitrary shape are numerically investigated. To this end, first, the governing equations are obtained within the frameworks of Mindlin’s SGT and FSDT. The relations are presented in a vector–matrix form so as to use in a numerical approach. Also, the developed SGT-based formulation can be reduced to various simplified theories including MCST and MSGT. Then, the variational differential quadrature (VDQ)-transformed method is applied to the variational statement of problem in the solution procedure. FG microplates under various edge conditions are considered whose free vibration response is analyzed. The developed approach can be used to address the problem for various geometries. Natural frequencies of FG skew, triangular and sector plates are computed, and the effects of thickness-to-length-scale parameter and vibration mode number on the results are studied. It is shown that natural frequencies are considerably decreased by increasing the thickness-to-length-scale parameter ratio.

This pioneering study introduces a novel framework for analyzing the magneto-thermoelastic behavior of rotating viscoelastic nanorods, significantly advancing the modeling of nanoscale systems. By uniquely integrating the Kelvin–Voigt viscoelastic model with the Klein–Gordon nonlocal elasticity theory, this work captures intrinsic length and time-scale effects, enabling precise representation of small-scale interactions—a critical leap beyond existing approaches. The newly proposed model innovatively combines thermomass motion, internal heat sources, magnetic forces, and viscoelastic energy dissipation, establishing a comprehensive and robust framework for evaluating the nonlinear mechanical behavior of nanorods. Key contributions include the incorporation of viscoelastic energy dissipation, magnetic forces, drift velocity, and thermoviscoelastic relaxation times into a unified model, delivering unprecedented predictive accuracy for nanoactuators, sensors, and energy-harvesting systems. This addresses longstanding challenges in nanomechanical and nanoelectronic device design by providing practical solutions to enhance stability, mitigate overheating risks, and optimize performance. The governing equations, derived and solved using the Laplace transform technique, offer new insights into the effects of parameters such as drift velocity, rotation, thermoviscoelastic relaxation times, and internal heat source frequency, as demonstrated through graphical results. By bridging critical gaps in the literature, this work sets a new benchmark for nanoscale system reliability and performance across industries. Its novel integration of multiple physical phenomena and advanced theoretical frameworks distinguishes it from prior studies, paving the way for future research into anisotropic and heterogeneous nanostructures.

Microstructure evolution of materials over space and time is typically studied through the solution of Cahn–Hilliard (CH)-type diffusion and deformation equations. In this work, a numerical framework implemented in commercial software, Abaqus as user element (UEL) and user material (UMAT), is presented to model the complex material behavior during microstructure evolution. This is done by formulating the system’s free energy that comprises chemical, interfacial, and elastic strain energy and phase separation dynamics. The elastic strain energy is expressed as a function of species concentration based on Khachaturyan’s elasticity theory. The species evolution is governed by the fourth-order CH equation and is subsequently transformed into two second-order equations amenable to traditional ({mathcal {C}}^0) finite elements. A detailed Abaqus implementation is provided, enabling researchers and scientists to solve problems involving similar physics. The numerical examples demonstrate the effectiveness of the proposed algorithm in addressing both phase separation with and without coupled elastic deformation. The source code is made available in the Appendix.