Applied Mathematics and Mechanics-English Edition最新文献

The weakly ionized plasma flows in aerospace are commonly simulated by the single-fluid model, which cannot describe certain nonequilibrium phenomena by finite collisions of particles, decreasing the fidelity of the solution. Based on an alternative formulation of the targeted essentially non-oscillatory (TENO) scheme, a novel high-order numerical scheme is proposed to simulate the two-fluid plasmas problems. The numerical flux is constructed by the TENO interpolation of the solution and its derivatives, instead of being reconstructed from the physical flux. The present scheme is used to solve the two sets of Euler equations coupled with Maxwell’s equations. The numerical methods are verified by several classical plasma problems. The results show that compared with the original TENO scheme, the present scheme can suppress the non-physical oscillations and reduce the numerical dissipation.

The boiling heat transfer technology with cavity surfaces can provide higher heat flux under lower wall superheat, which is of great significance for the cooling of electronic chips and microelectromechanical devices. In this paper, the boiling characteristics of the cavity surfaces are investigated based on the lattice Boltzmann (LB) method, focusing on the effects of cavity shapes, sizes, and heater thermal conductivity on the heat transfer performance. The results show that the triangular cavity has the best boiling performance since it has less residual vapor and higher bubble departure frequency than those of the trapezoidal and rectangular cavities. As the cavity size increases, the enhancement of heat transfer by the cavity mouth is suppressed by the heat accumulation effect at the heater bottom. The liquid rewetting process during bubble departure is the reason for the fluctuation of the space-averaged heat flux, and the heater thermal conductivity determines the fluctuation amplitude. The evaporation of liquid in the cavity with high thermal conductivity walls is more intense, resulting in shorter waiting time and higher bubble departure frequency.

This study investigates the vibration and acoustic properties of porous foam functionally graded (FG) plates under the influence of the temperature field. The dynamics equations of the system are established based on Hamilton’s principle by using the higher-order shear deformation theory under the linear displacement-strain assumption. The displacement shape function is assumed according to the four-sided simply-supported (SSSS) boundary condition, and the characteristic equations of the system are derived by combining the motion control equations. The theoretical model of vibro-acoustic coupling is established by using the acoustic theory and fluid-structure coupling solution method under the simple harmonic acoustic wave. The system’s natural frequency and sound transmission loss (STL) are obtained through programming calculations and compared with the literature and COMSOL simulation to verify the validity and reliability of the theoretical model. The effects of various factors, such as temperature, porosity coefficients, gradient index, core thickness, width-to-thickness ratio on the vibration, and STL characteristics of the system, are discussed. The results provide a theoretical basis for the application of porous foam FG plates in engineering to optimize vibration and sound transmission properties.

The flow field induced by internal solitary waves (ISWs) is peculiar wherein water motion occurs in the whole water depth, and the strong shear near the pycnocline can be generated due to the opposite flow direction between the upper and lower layers, which is a potential threat to marine risers. In this paper, the flow field of ISWs is obtained with the Korteweg-de Vries (KdV) equation for a two-layer fluid system. Then, a linear analysis is performed for the dynamic response of a riser with its two ends simply supported under the action of ISWs. The explicit expressions of the deflection and the moment of the riser are deduced based on the modal superposition method. The applicable conditions of the theoretical expressions are discussed. Through comparisons with the finite element simulations for nonlinear dynamic responses, it is proved that the theoretical expressions can roughly reveal the nonlinear dynamic response of risers under ISWs when the approximation for the linear analysis is relaxed to some extent.

Wetting of a liquid droplet on another liquid substrate is governed by the well-known Neumann equations. The present work aims to develop an explicit modified version of the Neumann equations for axisymmetric wetting of a liquid droplet on a highly stretched elastic membrane of non-zero bending rigidity. An explicit modified form of the Neumann equations is derived to determine the two contact angles, which is reduced to Young’s equation for a liquid droplet on a rigid membrane or to the Neumann equations for a liquid droplet on another liquid substrate. Further implications of the modified Neumann equations are examined by comparison with some previous results reported in the recent literature, particularly considering the ranges of material and geometrical parameters of the liquid droplet-membrane system which have not been recently addressed in the literature.

To achieve better anti-vibration performance in a low frequency region and expand the range of vibration isolation, a bilateral supported bio-inspired anti-vibration (BBAV) structure composed of purely linear elements is proposed, inspired by the motion form of bird legs and the nonlinear extension and compression of muscles and tendons. The kinematic relations and nonlinear dynamic model considering vertical and rotational vibrations are established. The loading capacity and equivalent stiffness are investigated with key parameters. The amplitude-frequency characteristics and force transmissibility are used to evaluate the stability and anti-vibration performance with the effects of the excitation amplitude, rod length, installation angle, and spring stiffness. The results show that the loading requirements and resonant characteristics of the BBAV structure are adjustable, and superior vibration isolation performance can be achieved readily by tuning the parameters. The X-shaped vibration structure is sensitive to the spring stiffness, which exhibits a wider vibration isolation bandwidth with smaller spring stiffness. Besides, depending on the parameters, the nonlinear behavior of the BBAV system can be interconverted between the softening type and the hardening type. The theoretical analysis in this study demonstrates the advantages and effectiveness of the vibration isolation structure.

The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed (APS) thermal barrier coatings (TBCs). As APS TBCs are typical multilayer porous ceramic materials, the direct applications of the traditional single edge notched beam (SENB) method that ignores those typical structural characters may cause errors. To measure the surface fracture toughness more accurately, the effects of multilayer and porous characters on the fracture toughness of APS TBCs should be considered. In this paper, a modified single edge V-notched beam (MSEVNB) method with typical structural characters is developed. According to the finite element analysis (FEA), the geometry factor of the multilayer structure is recalculated. Owing to the narrower V-notches, a more accurate critical fracture stress is obtained. Based on the Griffith energy balance, the reduction of the crack surface caused by micro-defects is corrected. The MSEVNB method can measure the surface fracture toughness more accurately than the SENB method.

An integral nonlocal stress gradient viscoelastic model is proposed on the basis of the integral nonlocal stress gradient model and the standard viscoelastic model, and is utilized to investigate the free damping vibration analysis of the viscoelastic Bernoulli-Euler microbeams in thermal environment. Hamilton’s principle is used to derive the differential governing equations and corresponding boundary conditions. The integral relations between the strain and the nonlocal stress are converted into a differential form with constitutive constraints. The size-dependent axial thermal stress due to the variation of the environmental temperature is derived explicitly. The Laplace transformation is utilized to obtain the explicit expression for the bending deflection and moment. Considering the boundary conditions and constitutive constraints, one can get a nonlinear equation with complex coefficients, from which the complex characteristic frequency can be determined. A two-step numerical method is proposed to solve the elastic vibration frequency and the damping ratio. The effects of length scale parameters, viscous coefficient, thermal stress, vibration order on the vibration frequencies, and critical viscous coefficient are investigated numerically for the viscoelastic Bernoulli-Euler microbeams under different boundary conditions.

The recently developed hard-magnetic soft (HMS) materials manufactured by embedding high-coercivity micro-particles into soft matrices have received considerable attention from researchers in diverse fields, e.g., soft robotics, flexible electronics, and biomedicine. Theoretical investigations on large deformations of HMS structures are significant foundations of their applications. This work is devoted to developing a powerful theoretical tool for modeling and computing the complicated nonplanar deformations of flexible beams. A so-called quaternion beam model is proposed to break the singularity limitation of the existing geometrically exact (GE) beam model. The singularity-free governing equations for the three-dimensional (3D) large deformations of an HMS beam are first derived, and then solved with the Galerkin discretization method and the trust-region-dogleg iterative algorithm. The correctness of this new model and the utilized algorithms is verified by comparing the present results with the previous ones. The superiority of a quaternion beam model in calculating the complicated large deformations of a flexible beam is shown through several benchmark examples. It is found that the purpose of the HMS beam deformation is to eliminate the direction deviation between the residual magnetization and the applied magnetic field. The proposed new model and the revealed mechanism are supposed to be useful for guiding the engineering applications of flexible structures.

The transient and static anti-plane problem of a rigid line inclusion pulled out from an elastic medium is studied. The singular integral equation method is used to solve the stress field. Under the static load, the stress intensity factor (SIF) at the inclusion tips increases with the medium length. The problem becomes equivalent to an inclusion in a medium with an infinite length when the length of the medium is 3.5 times longer than that of the inclusion. However, under the transient load, the maximum value of the SIF occurs when the medium length is about two times the inclusion length. Besides, the relation between the pull-out force and the anti-plane displacement is given. The conclusions are useful in guiding the design of fiber reinforced composite materials.