Acta Mechanica最新文献

In this paper, three modified Leslie–Gower predator–prey models with two time delays are considered based on the original Leslie–Gower predator–prey model. Taking the time delay as a bifurcation parameter, when Hopf bifurcation occurs, the critical value corresponding to time delay is obtained. By using normal form theory and central manifold argument, the direction of Hopf bifurcation and the stability of bifurcation periodic solution can be determined. The time delay affects the stability of the positive equilibria. When the time delay exceeds the critical value, the positive equilibria change from stable to unstable and bifurcate out a set of periodic solutions. Finally, numerical simulation is performed to support theoretical analysis.

A pioneering study conducted by Egbers and Rath [Acta Mech. 111 pp. 125–140 (1995)] experimentally captured spiral waves to elucidate the transition in the wide-gap spherical Couette flow. However, the physical field quantities of the spiral waves corresponding to light patterns of various intensities, as obtained in the experiment, remain unclear, and we have yet to move beyond the understanding that the reflected light from shear-sensitive flake tracers responds to a flow that appears at the transition. In this study, the experiment to visualize spiral waves using aluminum flakes, as performed by Egbers and Rath, was numerically reproduced by solving the translational and rotational motions of the particles in a spiral wave. First, the spiral wave in a spherical Couette flow with an aspect ratio (eta =1/2) was numerically calculated using the Newton–Raphson method. Subsequently, the image that was numerically reproduced from the spiral wave was compared with an experimentally visualized image. The torque acting on the inner sphere and the phase angular velocity of the spiral waves with various wavenumbers were provided. Attempts have been made to determine the instantaneous physical quantity that corresponds to the light and dark patterns observed in the flow visualization. From the attempts, we concluded the orientation motion of the flakes developed in the advective history of the flow is essential to yield these patterns. Exploring the correlation between flow visualization results and shear structures may provide a new avenue for quantitatively estimating spatial structures and time scales in complex and quickly time-varying flow fields, such as turbulence.

We present a size-dependent formulation for the longitudinal vibration study of cracked thick rods based on both the strain and stress-driven local/nonlocal mixture theories of elasticity with discontinuity. Due to the presence of the crack, the rod is divided into two segments connected by a linear spring, and compatibility conditions are given to describe the geometric discontinuity caused by the crack. The equations of motion of the discrete rods are formulated based on Rayleigh rod theory, and the two classes of local–nonlocal constitutive equations are integrated into an equivalent differential form, equipped with a set of constitutive boundary conditions at two ends of the whole structure and a set of constitutive continuity conditions at the junction of the sub-structures. The differential quadrature method (GDQM), together with the interpolation quadrature formula, is introduced to solve all the equations of motion of the sub-rods, the above constraint condition and the definite integrals occurring therein, simultaneously, through which we extract the dimensionless frequencies of the cracked rods with different boundary edges. After conducting comparison studies with the existing literature, numerical studies reveal that the present local–nonlocal model with discontinuity can effectively address the softening (or hardening) phenomenon as the structure’s size reduces. Moreover, the influence of crack location, crack severity, inertia of lateral motions and nonlocal parameters on the rods’ vibration frequencies is examined in detail.

The dispersion, attenuation and bandgap feature of coupled Bloch waves in one-dimensional piezoelectric semiconductor phononic crystal are studied in the present work. In particular, the influences of PN junction are emphasized. Different from the Bloch waves in the piezoelectric phononic crystal, the Bloch wave in piezoelectric semiconductor phononic crystal is attenuated. Moreover, the existence of the carrier fields brings forth more modes of Bloch waves due to the coupling of multiple physical fields. Using the state transfer equation method, the transfer matrix of the unit cell in a one-dimensional piezoelectric semiconductor phononic crystal is derived. Combining this with Bloch theory for periodic structures, the dispersion equation for multi-field coupled Bloch waves is obtained. The dispersion, attenuation and bandgap characteristics of the coupled Bloch waves are then plotted in the complex wave number domain. It is found that the influences of the PN junction are evident and thus provide an enlightenment that the propagation feature of Bloch waves can be adjusted by the control of the PN junction.

Since Biot’s first work on acoustic waves in non-dissipative solid media, it has been known that the group velocity of bulk acoustic waves coincides with the velocity of wave energy transport. The recent studies on these types of velocities for electromagnetic waves reveal that (i) these can differ, and (ii) the superluminal group velocities may exist. The current research demonstrates that in the case of Lamb waves propagating in sandwich clamped–clamped plates, the group velocity can exceed the largest longitudinal bulk wave velocity, and, moreover, the group velocity can be infinitely large, similarly to electromagnetic waves.

In the repowering of conventional steam power plants, we face off-design conditions. In this paper, a numerical study of the steam flow in the blades of the last stage of the low-pressure turbine of the Neka thermal power plant was carried out. To analyze the steam flow in the turbine, one design mode and two off-design modes including part-load and over-load were considered. In this research, three-dimensional Reynolds-averaged Navier–Stokes equations were simulated by using Ansys CFX software. Also, the SST k-ω method was used to model the turbulent flow. According to the obtained results, the effect of steam mass flow rate changes on the low-pressure turbine performance, such as velocity triangles, pressure, Mach number, and temperature distribution on blade surfaces, flow angles, degree of reaction, back pressure, steam quality, and efficiency, was investigated. For example, the loss of isentropic efficiency of the last stage in the off-design mode was less than 0.37% compared to the design conditions. Furthermore, the changes in the degree of reaction of the blades due to the changes in the mass flow rate of the fluid were less than 3%. Validation of the numerical solution was done in two-dimensional and three-dimensional models, and the results showed that there was a good agreement between numerical simulation and experimental data.

An enhanced treatment of the free surface boundary in the incompressible smoothed particle hydrodynamics (ISPH) method using the unified semi-analytical wall (USAW) boundary is proposed in this work. The instability problem at the free surface caused by kernel truncation can be resolved by assuming some virtual particles around the surface. The pressure of the virtual particles is considered as zero to impose pressure boundary conditions on the free surface, while the pressure of free surface particles is set to be a tiny value to reduce particle accumulation. To further improve the stability, the non-penetration algorithm is employed on the USAW boundary to avoid particle penetration. Afterward, the ISPH method with the USAW boundary is utilized to simulate several free surface flow problems. The enhancement of stability as well as the accuracy of the simulations is validated firstly by the dam break tests and further studied through examples of solitary wave propagation and liquid sloshing. The numerical results are compared with available experiment data or results from other numerical methods, verifying that the improved ISPH model with the USAW boundary in this work is highly suitable for simulating free surface flow problems.

This paper establishes a two-dimensional (2-D) shear-lag model applicable to multilayer composites, aiming to analyze the stress transfer mechanism in multilayer composites under uniaxial or biaxial tensile loading. Semi-analytical solutions for the normal stress and shear stress are provided under the assumption of elastic interface conditions. An example of patch-reinforced composites is used to provide semi-analytical solutions for the normal stress and shear stress under the assumption of elastic interface conditions. The study investigated the influence of material parameters on the stress distribution within each layer of multilayer composites, including the thickness ratio, the difference in Poisson’s ratio, the thickness of the adhesive layer, the aspect ratio, and the number of layers. The results indicate that the stress distribution solutions predicted by the proposed 2-D model are in good agreement with finite element results. This model provides an effective solution method for the 2-D stress problem in multilayer composites.

A novel multifield gradient theory for magneto-electro-elastic (MEE) materials including strain, electric and magnetic potentials, and inertia gradients is presented. Then, free vibration of the functionally graded MEE (FGMEE) microbeams based on the multifield gradient theory is investigated. The material properties of the FGMEE microbeams change continuously and symmetrically along the thickness direction in terms of a power-law distribution. Four kinds of length scale parameters are adopted to capture the size effect of the FGMEE microbeams. Based on the Hamilton’s principle, the equations of motion for the FGMEE microbeams are derived, which are solved subsequently by differential quadrature method. In the numerical examples, the effects of length scale parameters, electric and magnetic loadings, foundation parameters, and material gradient index on the natural frequency are analyzed and discussed in detail.

Predicting specific location responses in nonlinear systems under random excitations is crucial for structural health monitoring, optimization design, and safety assessment. Traditional sensor-based response measurements face challenges due to limitations in quantity and installation positions, while nonlinear time history analysis suffers from high computational costs and modeling time. Simplified regression equations used in engineering often lack accuracy. This study introduces a novel Residual Improvement Deep Learning Algorithm (RIDLA) to construct high-precision prediction models for nonlinear systems subjected to random excitations. RIDLA leverages Long Short-Term Memory (LSTM) neural networks to capture nonlinear relationships in time series and iteratively improve model accuracy through interactive training with measured responses and computed residuals. This approach effectively predicts time history responses of nonlinear systems under random excitations. RIDLA’s performance is validated by predicting responses in two typical nonlinear systems: a 6-DOF nonlinear oscillator system and the interface force of a satellite–rocket connection subjected to random excitations. The results demonstrate that RIDLA provides highly accurate predictions and can be applied to other complex nonlinear systems.