Applied Mathematics and Mechanics-English Edition最新文献

This paper proposes a distributed control method based on the differential flatness (DF) property of robot swarms. The swarm DF mapping is established for underactuated differentially flat dynamics, according to the control objective. The DF mapping refers to the fact that the system state and input of each robot can be derived algebraically from the flat outputs of the leaders and the cooperative errors and their finite order derivatives. Based on the proposed swarm DF mapping, a distributed controller is designed. The distributed implementation of swarm DF mapping is achieved through observer design. The effectiveness of the proposed method is validated through a numerical simulation of quadrotor swarm synchronization.

In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor (PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion (NLDD) model and the first-order shear deformation theory. The nonlinear constitutive relations are presented, and the strain energy, kinetic energy, and virtual work of the PS doubly-curved shell are derived. Based on Hamilton’s principle as well as the condition of charge continuity, the nonlinear governing equations are achieved, and then these equations are solved by means of an efficient iteration method. Several numerical examples are given to show the effect of the nonlinear drift current, elastic foundation parameters as well as geometric parameters on the nonlinear vibration frequency, and the damping characteristic of the PS doubly-curved shell. The main innovations of the manuscript are that the difference between the linearized drift-diffusion (LDD) model and the NLDD model is revealed, and an effective method is proposed to select a proper initial electron concentration for the LDD model.

By considering electromechanical coupling, a unified dynamic model of the cylindrical shell with the piezoelectric shunt damping patch (PSDP) is created. The model is universal and can simulate the vibration characteristic of the shell under different states including the states in which PSDP cannot be connected, partially connected, and completely connected to the shunt circuit. The equivalent loss factor and elastic modulus with frequency dependence are proposed to consider the electrical damping effect of resistance shunt circuits. Moreover, the semi-analytical dynamic equation of the cylindrical shell with PSDP is derived by the Lagrange equation. An experimental test is carried out on the cylindrical shell with PSDP to verify the vibration suppression ability of PSDP on the cylindrical shell and the correctness of the proposed model. Furthermore, the parameter analysis shows that determining the appropriate resistance value in the shunt circuit can achieve a good vibration suppression effect.

Cables composed of rare-earth barium copper oxide (REBCO) tapes have been extensively used in various superconducting devices. In recent years, conductor on round core (CORC) cable has drawn the attention of researchers with its outstanding current-carrying capacity and mechanical properties. The REBCO tapes are wound spirally on the surface of CORC cable. Under extreme loadings, the REBCO tapes with layered composite structures are vulnerable, which can lead to degradation of critical current and even quenching of superconducting devices. In this paper, we simulate the deformation of CORC cable under external loads, and analyze the damage inside the tape with the cohesive zone model (CZM). Firstly, the fabrication and cabling of CORC are simulated, and the stresses and strains generated in the tape are extracted as the initial condition of the next step. Then, the tension and bending loads are applied to CORC cable, and the damage distribution inside the tape is presented. In addition, the effects of some parameters on the damage are discussed during the bending simulations.

In this article, an investigation is conducted to study the precise role of zirconium nanoparticles that exist in a slime-like fluid subject to specific adjustments. Since gliding is a technique of mobility used by bacteria that lack motility components, bacteria travel on their own strength in gliding locomotion by secreting a layer of slime on the substrate. A model of an undulating sheet over a layer of slime of a Rabinowitsch fluid is investigated as a potential model of bacteria’s gliding motility. With the aid of long wavelength approximation, the equations governing the circulation of slime underneath the cells are established and analytically solved. The effects of pseudoplasticity, dilatation and non-Newtonian parameter on the behavior of zirconium concentration, speed of microorganism (bacteria), streamline patterns, and pressure rise for non-Newtonian and Newtonian fluids are compared. The power required for propulsion is also investigated. Physical interpretation for the pertinent variables has been graphically discussed against the parameters under consideration. It is found that with the increase in the concentration of zirconium nanoparticles, the bacterial flow is accelerated and attains its maximum near the rigid substrate wall while an opposite behavior is noticed in the rest region.

The present research focuses on the analysis of wave propagation on a rotating viscoelastic nanobeam supported on the viscoelastic foundation which is subject to thermal gradient effects. A comprehensive and accurate model of a viscoelastic nanobeam is constructed by using a novel nonclassical mechanical model. Based on the general nonlocal theory (GNT), Kelvin-Voigt model, and Timoshenko beam theory, the motion equations for the nanobeam are obtained. Through the GNT, material hardening and softening behaviors are simultaneously taken into account during wave propagation. An analytical solution is utilized to generate the results for torsional (TO), longitudinal (LA), and transverse (TA) types of wave dispersion. Moreover, the effects of nonlocal parameters, Kelvin-Voigt damping, foundation damping, Winkler-Pasternak coefficients, rotating speed, and thermal gradient are illustrated and discussed in detail.

The thermal properties and irreversibility of the Jeffrey nanofluid through an upright permeable microchannel are analyzed by means of the Buongiorno model. The effects of the Hall current, exponential space coefficient, nonlinear radiation, and convective and slip boundary conditions on the Jeffrey fluid flow are explored by deliberating the buoyant force and viscous dissipation. The non-dimensionalized equations are obtained by employing a non-dimensional system, and are further resolved by utilizing the shooting approach and the 4th- and 5th-order Runge-Kutta-Fehlberg approaches. The obtained upshots conclude that the amplified Hall parameter will enhance the secondary flow profile. The improvement in the temperature parameter directly affects the thermal profile, and hence the thermal field declines. A comparative analysis of the Newtonian fluid and non-Newtonian fluid (Jeffrey fluid) is carried out with the flow across a porous channel. In the Bejan number, thermal field, and entropy generation, the Jeffrey nanofluid is more highly supported than the Newtonian fluid.

Fluid-conveying pipes are widely used to transfer bulk fluids from one point to another in many engineering applications. They are subject to various excitations from the conveying fluids, the supporting structures, and the working environment, and thus are prone to vibrations such as flow-induced vibrations and acoustic-induced vibrations. Vibrations can generate variable dynamic stress and large deformation on fluid-conveying pipes, leading to vibration-induced fatigue and damage on the pipes, or even leading to failure of the entire piping system and catastrophic accidents. Therefore, the vibration control of fluid-conveying pipes is essential to ensure the integrity and safety of pipeline systems, and has attracted considerable attention from both researchers and engineers. The present paper aims to provide an extensive review of the state-of-the-art research on the vibration control of fluid-conveying pipes. The vibration analysis of fluid-conveying pipes is briefly discussed to show some key issues involved in the vibration analysis. Then, the research progress on the vibration control of fluid-conveying pipes is reviewed from four aspects in terms of passive control, active vibration control, semi-active vibration control, and structural optimization design for vibration reduction. Furthermore, the main results of existing research on the vibration control of fluid-conveying pipes are summarized, and future promising research directions are recommended to address the current research gaps. This paper contributes to the understanding of vibration control of fluid-conveying pipes, and will help the research work on the vibration control of fluid-conveying pipes attract more attention.

This paper proposes a three-dimensional (3D) Maltese cross metamaterial with negative Poisson’s ratio (NPR) and negative thermal expansion (NTE) adopted as the core layers in sandwich plates, and aims to explore the relations between the mechanical responses of sandwich composites and the NPR or NTE of the metamaterial. First, the NPR and NTE of the metamaterial are derived analytically based on energy conservation. The effective elastic modulus and mass density of the 3D metamaterial are obtained and validated by the finite element method (FEM). Subsequently, the general governing equation of the 3D sandwich plate under thermal environments is established based on Hamilton’s principle with the consideration of the von Kármán nonlinearity. The differential quadrature (DQ) FEM (DQFEM) is utilized to obtain the numerical solutions. It is shown that NPR and NTE can enhance the global stiffness of sandwich structures. The geometric parameters of the Maltese cross metamaterial significantly affect the responses of the thermal stress, natural frequency, and critical buckling load.

DNA-based biosensors have played a huge role in many areas, especially in current global coronavirus outbreak. However, there is a great difficulty in the characterization of piezoelectric and flexoelectric coefficients of the nanoscale DNA film, because the existing experimental methods for hard materials are almost invalid. In addition, the relevant theoretical models for DNA films only consider a single effect without clarifying the difference between the two electromechanical effects on device detection signals. This work aims to present multiscale models for DNA-microcantilever experiments to clarify the competitive mechanism in piezoelectric and flexoelectric effects of DNA films on detection signals. First, a Poisson-Boltzmann (PB) equation is used to predict the potential distribution due to the competition between fixed phosphate groups and mobile salt ions in DNA films. Second, a macroscopic piezoelectric/flexoelectric constitutive equation of the DNA film and a mesoscopic free energy model of the DNA solution are combined to analytically predict the electromechanical coefficients of the DNA film and the relevant microcantilever signals by the deformation equivalent method and Zhang’s two-variable method. Finally, the effects of detection conditions on microscopic interactions, electromechanical coupling coefficients, and deflection signals are studied. Numerical results not only agree well with the experimental observations, but also reveal that the piezoelectric and flexoelectric effects of the DNA film should be equivalently modeled when interpreting microcantilever detection signals. These insights might provide opportunities for the microcantilever biosensor with high sensitivity.