Acta Mechanica

The discussions of constitutive equations and their use in related studies by a number of writers for interacting continua, which is based on the form of theory given byGreen andNaghdi [1], is shown to be satisfactory for many purposes even though the expressions given for the partial stresses are incomplete. Complete constitutive equations are given in this paper, and a uniqueness theorem is stated, for the slow flow of a linear viscous fluid through an anisotropic linear elastic solid.

This paper analyzes a multilayer structure with a superconducting layer in the center and strengthening layers in the outer part. This represents a generalized structural form of multilayered high-temperature superconducting cable structures for space solar power station application. An analytical model for considering the influences of thermal–mechanical–electrical–magnetic coupling and the temperature on the stress distribution will be developed. The superposition method is used to solve the temperature distribution problem. After the temperature field is calculated, the magnetic field using a critical state model that considers the temperature effect will be developed. Finally, we analyzed the influence of material properties on the thermal and magnetically induced stress intensity factors in trapped field, zero field cooling and field cooling. Results show that the stress intensity factors induced either by thermal stress or by the Lorentz force must not be neglected. If the elastic module or the thickness of substrate layer increases, the stress intensity factor induced by thermal stress increases, while the one induced by the Lorentz force declines. Importantly, when reducing the thickness of the substrate layer, the total stress intensity factor will decrease at the early stage of heat conduction but increase at the late stage of heat conduction. This fact indicates that that thicker substrate layer is not always good from the reliability point of view.

The steady nonsimilar compressible laminar boundary-layer flow over a yawed infinite circular cylinder with nonuniform slot injection (suction) has been studied up to the point of separation. The finite discontinuities arising at the leading and trailing edges of the slot for the uniform slot injection (suction) are removed by choosing appropriate nonuniform mass transfer distributions in the slot. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme with an appropriate selection of finer step size along the streamwise direction. It is found that the nonuniform slot injection moves the point of separation downstream but the nonuniform slot suction has the reverse effect. The increase of Mach number shifts the point of separation upstream due to the adverse pressure gradient. The increase of total enthalpy at the wall causes the separation to occur earlier while cooling delays it. The yaw angle has very little effect on the location of the point of separation.

Diabatic processes dominate compressible flows with phase change where the heat of condensation or vaporization causes changes of enthalpy in the flow. The equations of motion for condensing flows are given in analogy to those of reacting flows and discontinuities are discussed. The nonequilibrium process of condensation by homogeneous nucleation in the supersaturated state is singled out by examples for steady and unsteady nozzle flows, Prandtl-Meyer flow, unsteady expansions and shock waves. A selective guide to the widely dispersed literature is provided and the early history of the discovery of condensation in supersonic wind tunnels is recounted.

The paper presents an analysis of functionally graded material doubly curved panels with rectangular planform under the action of thermal and mechanical loads. Based on the first-order shear deformation theory of modified Sanders assumptions, five coupled partially differential equations (PDEs) are established as equations of motion. Each thermo-mechanical property of the shell follows the power law distribution across the thickness, except Poisson’s ratio, which is kept constant through the panel. Assuming that four edges of the shell-panel are simply supported, a Navier-based solution is adopted to reduce the PDEs into time-dependent ODEs. Applying the Laplace transformation, the equations of motion are transformed into the Laplace domain. With the aid of analytical Laplace inverse method, solutions of stresses, strains, and displacements are obtained in time domain and expressed in explicit phrases. Dynamic, free vibration, and thermo-mechanical bending analysis of the panel is carried out for various geometries. Obtained results are validated with the well-known available data reported in the literature.

The present work uses integral equation method to develop a procedure for computing approximately steady inviscid transonic supercritical profile flow with shock past a thin unsymmetrical airfoil at small incidence. Starting from the shock-free solution at non-zero incidence of Chakraborty [9] and adopting a procedure similar to that of Hosokawa [12], the present work extends the work of Mitra [13] to the general case of lifting flow. Supercritical flow past NACA 0012 profile at different Mach numbers have been computed and compared with theoretical results of Garabedian and Korn [14], [15]. The agreements are satisfactory.

A solution is given for the problem of an infinite soft ferromagnetic solid containing a central crack subjected to normal impact load. The solid is permeated by a uniform magnetostatic field normal to the crack surface. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of integral equations in the Laplace transformed plane. A numerical Laplace inversion technique is used to compute the values of the dynamic stress-intensity factor, and the results are compared with the corresponding elastodynamic values to reveal the influence of magnetic field on the dynamic stress-intensity factor. The dynamic stress intensity factor is found to increase with increasing values of the magnetic field.

The free surface flow between two concentric cylinders with vertical axes is investigated using numerical and experimental approaches. The bottom end wall of the cylinders and the outer cylinder are stationary and fixed, and the inner cylinder is allowed to rotate. In such a case, an odd number of Taylor vortices is usually formed (normal mode). However, we found that anomalous modes with outer flow near the bottom end wall or inner flow at the free surface appear in some conditions. Further, we determined bifurcation diagrams between the normal three-cell mode and normal one-cell mode and between the normal five-cell mode and the normal three-cell mode.

High-order subharmonic parametric resonance of coupled microbeams is studied based on a model of multiple nonlinearly coupled micromechanical nonlinear oscillators. Of particular interest are the effects of nonlinear coupling between adjacent oscillators and elastic nonlinearity of individual oscillators. First, we analyze parametric resonance of a nonlinearly coupled nonlinear oscillator, and conduct instability analysis of steady-state solutions. Then we study parametric resonance of three nonlinearly coupled nonlinear oscillators. It is found that the nonlinear coupling between adjacent oscillators leads to the appearance of high-order subharmonic parametric resonance which, to the best of our knowledge, has received little attention in previous related works. In the present analysis, the effects of elastic nonlinearity of individual oscillators, damping and some loading parameters (such as dc and ac voltages) on high-order subharmonics are also examined in detail. Our results suggest that the range of excitation frequency for parametric resonance of coupled oscillators can be much larger than what the previous studies predicted, due to the appearance of high-order subharmonic parametric resonance. These results are believed to offer new and interesting insights into the ongoing research on nonlinear dynamics of coupled microbeams or nanobeams in MEMS or NEMS.