Modeling of an inhomogeneous coating of an elastic cylinder with given sound-reflecting properties

This paper considers the inverse problem of determining the inhomogeneity laws of the coating of an elastic cylinder that provide minimum reflection of a plane acoustic wave in a particular angular sector and in a given frequency range. A functional that expresses the reflection intensity is constructed by direct solution of the direct problem, and an algorithm for minimizing this functional is proposed. Analytical expressions describing the mechanical parameters of the inhomogeneous coating are obtained.     

Generation of geostrophic motions of an inhomogeneous fluid by surface pressure

The conditions of generation of a geostrophic flow by a pressure zone applied to the free surface of an undisturbed continuously stratified fluid layer of constant depth are determined in the general linear formulation. At large times the spatial external pressure distribution is assumed to tend to the steady state. In the axisymmetric case the geostrophic vortex is qualitatively analyzed on the basis of a numerical calculation of integral representations of the hydrodynamic fields for a fluid with an exponential density stratification. Sevastopol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 51–59, January–February, 1999.     

Modeling of time-dependent motions of an axisymmetrical tank containing a liquid

Institute of Mathematics, National Academy of Sciences of Ukraine. Translated from Prikladnaya Mekhanika, Vol. 30, No. 5, pp. 63–68, May, 1994.     

On the theory of one-dimensional unsteady motions of an ideal compressible fluid

A transformation is constructed of the independent variables and the unknown functions for the momentum and continuity equations of which one-dimensional unsteady motions of a perfect gas, relative to which the governing system of equations is invariant.When this transformation is used, the governing equation of state of the gas is transformed into a new equation which contains arbitrary parameters. This may enable approximation of the complex equation of state of a given medium to be carried out by selection of the parameters (in particular, for gases with respect of the equilibrium reactions taking place therein), and the use of this transformation may make it possible to reduce the problem to one with a simpler equation of state, for which the corresponding problem is more easily solved.The transformations investigated do not have singularities and do not impose any significant limitations on the hydrodynamic quantitiesthey are applicable both for variable entropy and for flows with shock waves.     

Stability of certain one-dimensional unsteady gas motions

This paper studies the stability of the adiabatic unsteady motions of a perfect gas for which the velocity is proportional to the distance to the center of symmetry. The solutions of the gas dynamic equations of such a form and their physical interpretation are considered in [1]. The stability of one of the solutions, which corresponds to the pulsations of uniform gravitating spheres, was studied in paper [2]. The stability of the other solutions (gas motions in the absence of Newtonian gravitation, nonperiodic motions of gravitating gas) has not previously been investigated. The stability of such solutions is investigated in this paper and it is shown that the motions in which gas compression occurs are, as a rule, unstable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 120–127, November–December, 1985.     

Solution with a linear velocity field for a submodel of one-dimensional gas motions

A method for finding exact solutions of the equations of gas dynamics with a linear velocity field is proposed. This method was used to find exact solutions for one submodel of the evolutionary type which was fully integrated for the case of a polytropic gas. Examples of particle motion for the obtain exact solutions are given.     

一维连续体释放和回收过程的构形计算

一维连续体的释放和回收过程由时变的动力学方程描述。将一维连续体离散为有限单元,建立其时变自由度的高维离散动力学模型。通过重新划分单元,重置系统质量、阻尼和刚度矩阵,以及位移和荷载向量,并基于改进的有限差分法,提出了一维连续体释放和回收过程的一种构形计算方法。以柔性索的面内运动为例,计算了其释放和回收过程的动力学构形,实...     

Transformation-induced plasticity in high-temperature shape memory alloys: a one-dimensional continuum model

A constitutive model based on isotropic plasticity consideration ispresented in this work to model the thermo-mechanical behavior ofhigh-temperature shape memory alloys. In high-temperature shapememory alloys (HTSMAs), both martensitic transformation andrate-dependent plasticity (creep) occur simultaneously at hightemperatures. Furthermore, transformation-induced plasticity isanother deformation mechanism during martensitic transformation. Allthese phenomena are considered as dissipative processes to model themechanical behavior of HTSMAs in this study. The constitutive modelwas implemented for one-dimensional cases, and the results have beencompared with experimental data from thermal cycling test foractuator applications.     

A continuum analysis of charge induced ferroelectric domain wall motions

A continuum model is presented for the motion of a domain wall in a plane 90°-domain configuration subjected to an isolated extrinsic charge near the surface of a ferroelectric single crystal. Local pinning is postulated for the kinetic law. Before the appearance of the extrinsic charge, all polarization surface charges are taken to be neutralized by environmental charges. The domain wall motion after the appearance of the extrinsic charge is assumed to proceed sufficiently fast without any significant conductive currents on the surface or in the interior of the crystal such that new surface and interface polarization charges remain unscreened and contribute to the ferroelectric anisotropy energy. A non-admissible divergence of the electric field and consequently of the local thermodynamic driving force and of the domain wall velocity appears in the model if the domain wall charged by interface polarization charges intersects the crystal surface charged by surface polarization charges under an arbitrary angle. The physically possible domain wall angle is identified using the condition of a non-divergent driving force. The ferroelectric anisotropy energy and an intrinsic surface energy of the domain wall, however, do not provide stability of the domain wall trajectory against an unlimited increase of its curvature at the surface. The problem has been solved conceptually by proper account of the domain wall bending energy. Numerical and dimensional analysis explain also why domain walls driven by extrinsic charges remain almost straight in soft ferroelectrics.     

Statics and kinematics of discrete Cosserat-type granular materials

A theoretical framework is presented for the statics and kinematics of discrete Cosserat-type granular materials. In analogy to the force and moment equilibrium equations for particles, compatibility equations for closed loops are formulated in the two-dimensional case for relative displacements and relative rotations at contacts. By taking moments of the equilibrium equations, micromechanical expressions are obtained for the static quantities average Cauchy stress tensor and average couple stress tensor. In analogy, by taking moments of the compatibility equations, micromechanical expressions are obtained for the (infinitesimal) kinematic quantities average rotation gradient tensor and average Cosserat strain tensor in the two-dimensional case. Alternatively, these expressions for the average Cauchy stress tensor and the average couple stress tensor are obtained from considerations of the equivalence of the continuum force and couple traction vectors acting on a plane and the resultant of the discrete forces and couples acting on this plane. In analogy, the expressions for the average rotation gradient tensor and the average Cosserat strain tensor are obtained from considerations of the change of length and change of rotation of a line element in the two-dimensional case. It is shown that the average particle stress tensor is always symmetrical, contrary to the average stress tensor of an equivalent homogenized continuum. Finally, discrete analogues of the virtual work and complementary virtual work principles from continuum mechanics are derived.     

Vibration localization in one-dimensional linear and nonlinear lattices: discrete and continuum models

The phenomenon of vibration localization plays an important role in the dynamics of inhomogeneous and nonlinear materials and structures. The vibration localization can occur in the case of inhomogeneity under the following conditions: (i) the frequency spectrum of the periodic structure includes stopbands, (ii) a perturbation of periodicity is present, and (iii) the eigenfrequency of the perturbed element falls into a stopband. Under these conditions, the energy can be spatially localized in the vicinity of the defect with an exponential decay in the infinity. The influence of nonlinearity can shift frequency into the stopband zone. In the present paper, the localization of vibrations in one-dimensional linear and nonlinear lattices is investigated. The localization frequencies are determined and the attenuation factors are calculated. Discrete and continuum models are developed and compared. The limits of the applicability of the continuum models are established. Analysis of the linear problem has allowed a better understanding of specifics of the nonlinear problem and has led to developing a new approach for the analysis of nonlinear lattices alternative to the method of continualization.