Adhesion of bio-inspired microfibre arrays to a rough surface is studied theoretically. The array consists of vertical elastic rods fixed on a rigid backing layer, and the surface is modeled by rigid steps with a normally distributed height. Analytical expressions are obtained for the adhesion forces in both the approach and retraction processes. It is shown that, with the increasing preload, the pull-off force increases at first and then attains a plateau value. The results agree with the previous experiments and are expected helpful in adhesion control of the array in practical applications.
In this paper, transverse vibration of an axially moving beam supported by a viscoelastic foundation is analyzed by a complex modal analysis method. The equation of motion is developed based on the generalized Hamilton's principle. Eigenvalues and eigenfunctions are semi-analytically obtained. The governing equation is represented in a canonical state space form, which is defined by two matrix differential operators. The orthogonality of the eigenfunctions and the adjoint eigenfunctions is used to decouple the system in the state space. The responses of the system to arbitrary external excitation and initial conditions are expressed in the modal expansion. Numerical examples are presented to illustrate the proposed approach. The effects of the foundation parameters on free and forced vibration are examined.
The dynamic behavior of a rectangular crack in a three-dimensional(3D) orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional(2D) Fourier transform is applied, and the mixedboundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.
In this paper, the nonlinear analysis of stability of functionally graded material(FGM) sandwich doubly curved shallow shells is studied under thermo-mechanical loads with material properties obeying the general sigmoid law and power law of four material models. Shells are reinforced by the FGM stiffeners and rest on elastic foundations. Theoretical formulations are derived by the third-order shear deformation theory(TSDT) with the von Kármán-type nonlinearity taking into account the initial geometrical imperfection and smeared stiffener technique. The explicit expressions for determining the critical buckling load and the post-buckling mechanical and thermal load-deflection curves are obtained by the Galerkin method. Two iterative algorithms are presented. The effects of the stiffeners, the thermal element, the distribution law of material, the initial imperfection, the foundation, and the geometrical parameters on buckling and post-buckling of shells are investigated.
This paper investigates surface energy effects, including the surface shear modulus, the surface stress, and the surface density, on the free torsional vibration of nanobeams with a circumferential crack and various boundary conditions. To formulate the problem, the surface elasticity theory is used. The cracked nanobeam is modeled by dividing it into two parts connected by a torsional linear spring in which its stiffness is related to the crack severity. Governing equations and corresponding boundary conditions are derived with the aid of Hamilton's principle. Then, natural frequencies are obtained analytically, and the influence of the crack severity and position, the surface energy, the boundary conditions, the mode number, and the dimensions of nanobeam on the free torsional vibration of nanobeams is studied in detail. Results of the present study reveal that the surface energy has completely different effects on the free torsional vibration of cracked nanobeams compared with its effects on the free transverse vibration of cracked nanobeams.
Interfacial dislocation may have a spreading core corresponding to a weak shear resistance of interfaces. In this paper, a conic model is proposed to mimic the spreading core of interfacial dislocation in anisotropic bimaterials. By the Stroh formalism and Green's function, the analytical expressions of the elastic fields are deduced for such a dislocation. Taking Cu/Nb bimaterial as an example, it is demonstrated that the accuracy and efficiency of the method are well validated by the interface conditions, a spreading core can greatly reduce the stress intensity near the interfacial dislocation compared with the compact core, and the elastic fields near the spreading core region are significantly different from the condensed core, while they are less sensitive to a field point that is 1.5 times the core width away from the center of the spreading core.
Variable geometry truss manipulator(VGTM) has potential to work in the future space applications, of which a dynamic model is important to dynamic analysis and control of the system. In this paper, an approach is presented to model the dynamic equations of a VGTM by independent variables, which consists of two double-octahedral truss units and a 3-revolute-prismatic-spherical(3-RPS) parallel manipulator. In this approach, the kinematic recursive relations of two adjacent bodies and geometric constrains are used to deduce the kinematic equations of the VGTM, and Jourdain's velocity variation principle is adopted to establish the dynamic equations of the system. The validity of the proposed dynamic model is verified by comparison of numerical simulations with the software ADAMS. Besides, an active controller for trajectory tracking of the system is designed by the computed torque method. The effectiveness of the controller is numerically proved.
The approximate but analytical solution of the viscous Rayleigh-Taylor instability(RTI) has been widely used recently in theoretical and numerical investigations due to its clarity. In this paper, a modified analytical solution of the growth rate for the viscous RTI of incompressible fluids is obtained based on an approximate method. Its accuracy is verified numerically to be significantly improved in comparison with the previous one in the whole wave number range for different viscosity ratios and Atwood numbers. Furthermore, this solution is expanded for viscous RTI including the concentration-diffusion effect.
This paper studies stratified magnetohydrodynamic(MHD) flow of tangent hyperbolic nanofluid past an inclined exponentially stretching surface. The flow is subjected to velocity, thermal, and solutal boundary conditions. The partial differential systems are reduced to ordinary differential systems using appropriate transformations. The reduced systems are solved for convergent series solutions. The velocity, temperature, and concentration fields are discussed for different physical parameters. The results indicate that the temperature and the thermal boundary layer thickness increase noticeably for large values of Brownian motion and thermophoresis effects. It is also observed that the buoyancy parameter strengthens the velocity field, showing a decreasing behavior of temperature and nanoparticle volume fraction profiles.
This paper is concerned with establishing a reduced-order extrapolating finite volume element(FVE) format based on proper orthogonal decomposition(POD) for two-dimensional(2D) hyperbolic equations. For this purpose, a semi discrete variational format relative time and a fully discrete FVE format for the 2D hyperbolic equations are built, and a set of snapshots from the very few FVE solutions are extracted on the first very short time interval. Then, the POD basis from the snapshots is formulated, and the reduced-order POD extrapolating FVE format containing very few degrees of freedom but holding sufficiently high accuracy is built. Next, the error estimates of the reduced-order solutions and the algorithm procedure for solving the reduced-order format are furnished. Finally, a numerical example is shown to confirm the correctness of theoretical conclusions. This means that the format is efficient and feasible to solve the 2D hyperbolic equations.