Applied Mathematics and Mechanics-English Edition最新文献

The closed-form solutions of the dynamic problem of heterogeneous piezoelectric materials are formulated by introducing polarizations into a reference medium and using the generalized reciprocity theorem. These solutions can be reduced to the ones of an elastodynamic problem. Based on the effective medium method, these closed-form solutions can be used to establish the self-consistent equations about the frequency-dependent effective parameters, which can be numerically solved by iteration. Theoretical predictions are compared with the experimental results, and good agreement can be found. Furthermore, the analyses on the effects of microstructure and wavelength on the effective properties, resonance frequencies, and attenuation are also presented, which may provide some guidance for the microstructure design and analysis of piezoelectric composites.

A prestressed elastic medium containing a mode-III crack is studied by means of the couple stress theory (CST). Based on the CST under initial stresses, a governing differential equation along with a mixed boundary value problem is established. The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method. To determine their intensity, a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial. The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor (CSIF) and the force stress intensity factor (FSIF) around the crack tips. The symmetric part of the shear stress has no singularity, and the skew-symmetric part related to the couple stress exhibits an r^−3/2 singularity, in which r is the distance from the crack tip. The initial stresses also affect the crack tearing displacement and the CSIF and FSIF.

Due to the influence of deep-sea environment, deep-sea sediments are usually heterogeneous, and their moduli of elasticity and density change as depth changes. Combined with the characteristics of deep-sea sediments, the thermo-hydro-mechanical coupling dynamic response model of heterogeneous saturated porous sediments can be established to study the influence of elastic modulus, density, frequency, and load amplitude changes on the model. Based on the Green-Lindsay generalized thermoelasticity theory and Darcy’s law, the thermo-hydro-mechanical coupled dynamic response model and governing equations of heterogeneous deep-sea sediments with nonlinear elastic modulus and density are established. The analytical solutions of dimensionless vertical displacement, vertical stress, excess pore water pressure, and temperature are obtained by means of normal modal analysis, which are depicted graphically. The results show that the changes of elastic modulus and density have few effects on vertical displacement, vertical stress, and temperature, but have great effects on excess pore water pressure. When the mining machine vibrates, the heterogeneity of deep-sea sediments has great influence on vertical displacement, vertical stress, and excess pore water pressure, but has few effects on temperature. In addition, the vertical displacement, vertical stress, and excess pore water pressure of heterogeneous deep-sea sediments change more gently. The variation trends of physical quantities for heterogeneous and homogeneous deep-sea sediments with frequency and load amplitude are basically the same. The results can provide theoretical guidance for deep-sea mining engineering construction.

This study is concerned with the three-dimensional (3D) stagnation-point for the mixed convection flow past a vertical surface considering the first-order and second-order velocity slips. To the authors’ knowledge, this is the first study presenting this very interesting analysis. Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations (ODEs) by using appropriate similarity transformation. These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language. The effects of the governing parameters on the non-dimensional velocity profiles, temperature profiles, skin friction coefficients, and the local Nusselt number are presented in detail through a series of graphs and tables. Interestingly, it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation. The numerical computations of the present work are compared with those from other research available in specific situations, and an excellent consensus is observed. Another exciting feature for this work is the existence of dual solutions. An important remark is that the dual solutions exist for both assisting and opposing flows. A linear stability analysis is performed showing that one solution is stable and the other solution is not stable. We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics. These effects are depicted in graphs and discussed in this paper. The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow, as well as on the heat transfer characteristics.

In this work, we design a twisting metamaterial for longitudinal-torsional (L-T) mode conversion in pipes through exploring the theory of perfect transmodal Fabry-Perot interference (TFPI). Assuming that the axial and radial motions in pipes can be decoupled, we find that the metamaterial can be designed in a rectangular coordinate system, which is much more convenient than that in a cylindrical system. Numerical calculation with detailed microstructures shows that an efficient L-T mode conversion can be obtained in pipes with different radii. In addition, we fabricate mode-converting microstructures on an aluminum pipe and conduct ultrasonic experiments, and the results are in good agreement with the numerical calculations. We expect that the proposed L-T mode-converting metamaterial and its design methodology can be applied in various ultrasonic devices.

The interfacial debonding between the active layer and the current collector has been recognized as a critical mechanism for battery fading, and thus has attracted great efforts focused on the related analyses. However, much still remains to be studied regarding practical methods for suppressing electrode debonding, especially from the perspective of mechanics. In this paper, a pre-strain strategy of current collectors to alleviate electrode debonding is proposed. An analytical model for a symmetric electrode with a deformable and limited-thickness current collector is developed to analyze the debonding behavior involving both a pre-strain of the current collector and an eigen-strain of the active layers. The results reveal that the well-designed pre-strain can significantly delay the debonding onset (by up to 100%) and considerably reduce the debonding size. The critical values of the pre-strain are identified, and the pre-strain design principles are also provided. Based on these findings, this work sheds light on the mechanical design to suppress electrode degradation.

Epilepsy is believed to be associated with the abnormal synchronous neuronal activity in the brain, which results from large groups or circuits of neurons. In this paper, we choose to focus on the temporal lobe epilepsy, and establish a cortex network of multiple coupled neural populations to explore the epileptic activities under electromagnetic induction. We demonstrate that the epileptic activities can be controlled and modulated by electromagnetic induction and coupling among regions. In certain regions, these two types of control are observed to show exactly reverse effects. The results show that the strong electromagnetic induction is conducive to eliminating the epileptic seizures. The coupling among regions has a conduction effect that the previous normal background activity of the region gives way to the epileptic discharge, owing to coupling with spike wave discharge regions. Overall, these results highlight the role of electromagnetic induction and coupling among the regions in controlling and modulating epileptic activities, and might provide novel insights into the treatments of epilepsy.

This paper uses the theory of planar dynamic systems and the knowledge of reaction-diffusion equations, and then studies the bounded traveling wave solution of the generalized Boussinesq equation affected by dissipation and the influence of dissipation on solitary waves. The dynamic system corresponding to the traveling wave solution of the equation is qualitatively analyzed in detail. The influence of the dissipation coefficient on the solution behavior of the bounded traveling wave is studied, and the critical values that can describe the magnitude of the dissipation effect are, respectively, found for the two cases of b₃ < 0 and b₃ > 0 in the equation. The results show that, when the dissipation effect is significant (i.e., r is greater than the critical value in a certain situation), the traveling wave solution to the generalized Boussinesq equation appears as a kink-shaped solitary wave solution; when the dissipation effect is small (i.e., r is smaller than the critical value in a certain situation), the traveling wave solution to the equation appears as the oscillation attenuation solution. By using the hypothesis undetermined method, all possible solitary wave solutions to the equation when there is no dissipation effect (i.e., r = 0) and the partial kink-shaped solitary wave solution when the dissipation effect is significant are obtained; in particular, when the dissipation effect is small, an approximate solution of the oscillation attenuation solution can be achieved. This paper is further based on the idea of the homogenization principles. By establishing an integral equation reflecting the relationship between the approximate solution of the oscillation attenuation solution and the exact solution obtained in the paper, and by investigating the asymptotic behavior of the solution at infinity, the error estimate between the approximate solution of the oscillation attenuation solution and the exact solution is obtained, which is an infinitesimal amount that decays exponentially. The influence of the dissipation coefficient on the amplitude, frequency, period, and energy of the bounded traveling wave solution of the equation is also discussed.

The coupling vibration of a hydraulic pipe system consisting of two pipes is studied. The pipes are installed in parallel and fixed at their ends, and are restrained by clips to one bracket at their middle points. The pipe subjected to the basement excitation at the left end is named as the active pipe, while the pipe without excitation is called the passive pipe. The clips between the two pipes are the bridge for the vibration energy. The adjacent natural frequencies will enhance the vibration coupling. The governing equation of the coupled system is deduced by the generalized Hamilton principle, and is discretized to the modal space. The modal correction is used during the discretization. The investigation on the natural characters indicates that the adjacent natural frequencies can be adjusted by the stiffness of the two clips and bracket. The harmonic balance method (HBM) is used to study the responses in the adjacent natural frequency region. The results show that the vibration energy transmits from the active pipe to the passive pipe swimmingly via the clips together with a flexible bracket, while the locations of them are not node points. The adjacent natural frequencies may arouse wide resonance curves with two peaks for both pipes. The stiffness of the clip and bracket can release the vibration coupling. It is suggested that the stiffness of the clip on the passive pipe should be weak and the bracket should be strong enough. In this way, the vibration energy is reflected by the almost rigid bracket, and is hard to transfer to the passive pipe via a soft clip. The best choice is to set the clips at the pipe node points. The current work gives some suggestions for weakening the coupled vibration during the dynamic design of a coupled hydraulic pipe system.

The present study aims to perform computational simulations of two-dimensional (2D) hemodynamics of unsteady blood flow via an inclined overlapping stenosed artery employing the Casson fluid model to discuss the hemorheological properties in the arterial region. A uniform magnetic field is applied to the blood flow in the radial direction as the magneto-hemodynamics effect is considered. The entropy generation is discussed using the second law of thermodynamics. The influence of different shape parameters is explored, which are assumed to have varied shapes (spherical, brick, cylindrical, platelet, and blade). The Crank-Nicolson scheme solves the equations and boundary conditions governing the flow. For a given critical height of the stenosis, the key hemodynamic variables such as velocity, wall shear stress (WSS), temperature, flow rate, and heat transfer coefficient are computed.