Weakly rarefied gas flows between nonuniformly heated parallel plates

The aim of this research is to establish the validity of the predictions of the theory of slow nonisothermal flows, to study the limits of applicability (with respect to the Knudsen number) of the conclusions reached and to determine the effect of the Knudsen layers on these flows on the basis of a numerical investigation of slow nonisothermal weakly rarefied gas flow in a plane infinite channel with weakly nonequilibrium heating of the walls and a finite wall temperature difference. The gas flow is described by a relaxation transport equation. The results obtained show how quickly, as the Knudsen number decreases, the solutions of the transport equation outside the Knudsen layers tend to the solution of the equations of gas dynamics of slow nonisothermal flows (and not to the solution of the Navier-Stokes equations).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 115–121, January–February, 1988.     

Three-dimensional thermoelasticity problems for nonuniformly heated laminar transversally isotropic plates

Three-dimensional heat-conduction and thermoelasticity boundary-value problems are considered for laminar transversally isotropic rectilinear plates under the action of a nonuniform temperature field. Both ideal and nonideal thermal and mechanical contact conditions at the interfaces are fulfilled. Cases where the roots of the basic characteristic equation are different and include duplicate values are discussed for transversally isotropic bodies (rectangular anisotropy). In the numerical calculation of thermoelastic deformation for a two-layer plate, a sinusoidal face temperature is specified. Characteristic thermomechanical effects are discovered. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 7, pp. 95–103, July 1999.     

A contribution to the stability of circular plates

Archive of Applied Mechanics - The dynamical response of thin circular plates and their stability, resulting from the action of an arbitrary load which is a spacetime function, has been examined....     

Static and dynamic non-linear behaviour of heated orthotropic circular plates

The fundamental quasilinear, decoupled equations of equilibrium and motion of heated orthotropic circular plates are derived from the energy equation in the light of a generalised analysis of a Berger-type which is based on the assumption that the effect of second strain invariant in the expression for total energy may be neglected. Solutions are obtained by Poincare's method of successive approximation and numerical results are given in graphical form for both static and dynamic cases of orthotropic circular plates, simply supported or clamped throughout the edge.     

加热压电纤维复合材料圆板的横向自由振动

基于经典薄板理论和极正交各向异性材料的本构理论,建立了加热压电纤维复合材料圆板的线性振动控制微分方程。采用打靶法分别获得了加热压电纤维复合材料圆板在周边固支和简支情况下,无量纲固有频率随温度和电场强度变化的关系曲线,并分析了压电纤维体积分数、刚度参数、电场强度和温度变化对压电纤维复合材料圆板无量纲固有频率的影响。结果表明,一定体积分数或者电场强度下,压电纤维复合材料圆板的无量纲固有频率都随温度的升高而单调下降;同一温度下,刚度参数越小,无量纲固有频率越低;电场强度越大,无量纲固有频率越高。     

Surface geometry of a liquid explosive burning beyond the stability limit

After L. D. Landau's work [1] on the stability of normal burning of liquid explosives, many experimental studies of this phenomenon, e. g., [2, 3], were published. In this paper, on the basis of Landau's theory, we investigate the geometry of the perturbations which develop on the surface of the liquid explosive in a vessel of circular cross section and consider the influence of vessel diameter on burning stability. Results of an experimental observation of the geometry of the liquid surface are also presented for developed turbulent combustion in a circular cylindrical tube. The calculation was based on the usual assumptions that the chemical reaction of combustion proceeds in a thin layer of vapor over the plane (meniscus neglected) surface of the inviscid liquid explosive.     

Precritical state and stability of cylindrical shells beyond the proportionality limit

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 2, pp. 29–33, February, 1995.