Acta Mechanica最新文献

Liquid sloshing within partially filled tanks of large liquid cargo ships has been a major concern in marine engineering. An arbitrary Lagrangian–Eulerian (ALE) finite element (FE) method is proposed to simulate three-dimension large-amplitude liquid sloshing in ellipsoidal tanks, and its effectiveness is verified by experiments. Firstly, a scheme of the fractional step algorithm for solving the Navier–Stokes (NS) equations, combining with the characteristic-based split (CBS), in the ALE framework is constructed. Then a deft and effective mesh moving and update strategy is designed for large-amplitude liquid sloshing in ellipsoidal tanks. Subsequently, computer programming and numerical simulation are carried out and the obtained results show excellent agreements with the experiments. Finally, the nonlinear phenomena for large amplitude liquid sloshing in ellipsoidal tanks under the external excitations are investigated and the multi-modal characteristics of liquid nonlinear sloshing is revealed through a combination of numerical simulations and the ground physical experiment.

A size-dependent post buckling analysis of functionally graded (FG) microbeams is conducted by using an analytical solution based on a reformulated strain gradient elasticity theory (RSGET). The nonlinear behavior of post buckling is considered by employing the von-Karman nonlinear strain–displacement relation. The microstructure-dependent behavior of the microbeam is captured by the RSGET which incorporated both couple stress and strain gradient effects using one size-dependent parameter for each. The material properties of the FG microbeam changed along the thickness direction, which are described using a power law relation. Based on the principle of minimum potential energy, the equations of equilibrium and boundary conditions of the Euler–Bernoulli microbeam are obtained. The post buckling response of FG mcirobeams with different boundary conditions are analytically derived. Moreover, the effects of the length scale parameter, material gradient index, length-thickness ratio and Poisson's ratio on the post buckling responses are studied. In addition, the total critical pressure for the FG array structures is estimated. These results are helpful for designing FG-MEMS devices.

This work presents the vibration and buckling analyses for a sandwich arch with Titanium alloy face sheets and a metal foam core via a new porosity-dependent model. Porous aluminum core consists of six layers so that each of them reinforce by graphene platelets (GPLs) with different values of porosity to achieve a piece-wise functionally graded media. The mathematical modelling is formulated to reveal nonlinear responses of the porous sandwich arch embedded in an elastic nonlinear medium. The higher-order equations of motion are achieved by taking Hamilton’s principle within the framework of the von Kármán nonlinear hypothesis. Afterwards, the established nonlinear problems are solved analytically with the aid of a perturbation-based technique implementing the Galerkin procedure. The investigation results show effects of the weight fraction of GPLs, porosity distribution, geometrical characters and foundation stiffness on nonlinear vibration and buckling of the porous sandwich arch.

Effects of external magnetic field, microstructural effects and thermal effects on the dispersion and attenuation feature of elastic waves as well as the reflection and transmission behavior of coupled waves are studied in the paper. The microstructure effects are reflected by the dipolar gradient elasticity. The heat conduction behavior is modeled by non-Fourier law with the fractional order derivatives. The Lorentz force due to the external magnetic field is derived by the electromagnetic induction law and Maxwell equation. The numerical results are provided in the case of incident P wave. It is found that the microstructure effect induces the dispersive feature of elastic waves, while the dispersion and attenuation features are both induced by the thermal effects. The external magnetic field does not contribute to the dispersion but only influence on the amplitude of speed. The fractional order heat conduction only has evident influences on the propagation of thermal wave.

In this work, the doubly periodic shear layers are employed to underpin the vortex dynamics associated with the perturbed free shear layers using the lattice Boltzmann method with the Bhatnagar–Gross–Krook collision model. The effect of (i) width between shear layers, (ii) modes of perturbation, (iii) the strength of perturbation, and (iv) thickness of a shear layer on roll-up formation, vortex interactions, pairings, and the generation of thin filaments is studied in detail with the evolution kinetic energy, enstrophy, and palinstrophy for Reynolds number, (text {Re}=30,000). The formation of thin vorticity braids and vortex merging causes the production of vorticity gradients and a rise in the palinstrophy. No compelling interplay is observed with corotating or counter-rotating vortices for a minimum separation distance ((S_1)) between two opposite vorticity strips. The counter-force from each layer creates a jet whose properties differ from those of a single shear layer. However, the evolution of multiple pairs of shear layers produces smaller vortices of lower strength and enhances the growth of palinstrophy and decay of kinetic energy and enstrophy. The rise in the momentum thickness is observed for the interactive flows ((S_2 le S_1)), while the non-interactive flow ((S_2 > S_1)) shows constant momentum thickness. The increased perturbation strength quickens the roll-up of shear layer and enhances the growth of palinstrophy. Thick shear layers evolves with dipole-like structures and slows down the decay of kinetic energy and enstrophy compared to thin shear layer flows. It generates family of thin vortex filaments and influences the rapid growth of vorticity gradients and positive Okubo–Weiss-Q-quantity.

This study investigates the quasi-static and dynamic compressive mechanical properties of polyamide-6 at different temperatures (25–85 ℃) and strain rates (2.6 × 10⁻⁴–3.2 × 10³ s⁻¹) by using a universal testing machine and a split Hopkinson pressure bar device. The variation of mechanical properties with temperature and strain rate is analyzed. The results show that the stress–strain response of polyamide-6 at different temperatures and strain rates includes viscoelastic deformation, yield behavior, and strain hardening behavior. Under some experimental conditions, polyamide-6 has constant stress flow states, which are related to temperature and strain rate. The mechanical properties of polyamide-6 are significantly affected by temperature and strain rate. The elastic modulus, yield strength, and energy absorption property increase with an increase of strain rate, but decrease with an increase of temperature. The formulas of yield strength and elastic modulus are given, and a modified constitutive model is given to describe the stress–strain response of polyamide-6. The predicted results of the model are in good agreement with the experimental data at different temperatures and strain rates.

Functionally graded (FG) laminated micro/nanostructures reinforced with graphene nanoplatelets (GPLs) stand as one of the most promising candidates for composite structures due to the excellent thermo-mechanical properties. Meanwhile, thermoelastic damping (TED) is one of the key factors to lower quality factor in micro/nanoresonators. Nevertheless, the classical TED models fail to explain the thermo-mechanical behavior considering the influences of the size-dependent effect and the thermal lagging effect. To fill these gaps, the present study aims to investigate TED analysis of FG laminated microplate resonators reinforced with GPLs in the frame of the modified strain gradient theory and the three-phase-lag heat conduction model. Four patterns of GPLs distribution including the UD, FG-O, FG-X and FG-A pattern distributions are taken into account, and the effective material properties of the plate-type nanocomposite are evaluated according to the Halpin–Tsai model. The energy equation and the motion equation based on the Kirchhoff microplate model are solved, and then, the closed-from analytical expression of TED is obtained by complex frequency technique. A detailed parametric study has been conducted to discuss the influence of the material length-scale parameter, the phase-lag parameters and the total weight fraction of GPLs on the TED. Results demonstrated that the energy dissipation of FG laminated microplate resonators reinforced with GPLs is determined by the size-dependent effect, the thermal lagging effect and the total weight fraction of GPLs. This results are helpful to the design of FG laminated microplate resonators reinforced with GPLs with high-performance for theoretical approach.

This paper is concerned with a linear theory of thermopiezoelectricity in which the second gradient of the displacement, the second gradient of the electric potential and the second temperature gradient are included in the classic set of independent constitutive variables. The present paper is based on Green–Naghdi thermomechanics. The introduction of the entropy flux tensor leads to constitutive equations that depend on the second temperature gradient. The fundamental boundary-initial-value problems are formulated and the uniqueness of the solution is studied. Two applications of the theory are presented. We study the problem of a concentrated charge density acting in an unbounded region, as well as the effects of a concentrated heat source.

The aerodynamic characteristics of flapping rotary wings (FRWs) have received considerable attention in design. In this study, optimizations of aerodynamic performance and kinematics of FRWs over the parameter space are explored. A well-validated Quasi-Steady model is employed to estimate the aerodynamic characteristics of FRWs in hovering flight, and a genetic algorithm is utilized for optimizing. It is assumed that flapping and pitching motion are given by motion parameters actively, while rotation is produced passively. Our results show that the optimal kinematic parameters are independent of flapping frequencies. The maximum lift comes from the high rotational speed caused by the small pitching amplitude, and the maximum power factor is from the large pitching amplitude. The dimensionless optimization of the flapping velocity as reference velocity is comparable to the dimensional results. The optimization model proposed in this study can be applied to the actual model for qualitative analysis. Rotational equilibrium power factor can reach more than 80% of the maximum value without rotation equilibrium constraint, but which rotational status can achieve the maximum power factor depends on the pitching angle at the mid-downstroke (α_d). This study is helpful for the kinematic parameter design and further research of FRWs.