The problem of finite, partially glued to a fixed rigid base rod longitudinal vibrations damping by optimizing adhesive structural topology is investigated. Vibrations of the rod are caused by external load, concentrated on free end of the rod, the other end of which is elastically clamped. The problem is mathematically formulated as a boundary-value problem for onedimensional wave equation with attenuation and variable controlled coefficient. The intensity of adhesion distribution function is taken as optimality criterion to be minimized. Structure of adhesion layer, optimal in that sense, is obtained as a piecewise-constant function. Using Fourier real generalized integral transform, the problem of unknown function determination is reduced to determination of certain switching points from a system of nonlinear, in general, complex equations. Some particular cases are considered.
Distribution optimization of elastic material under elastic isotropic rectangular thin plate subjected to concentrated moving load is investigated in the present paper. The aim of optimization is to damp its vibrations in finite (fixed) time. Accepting Kirchhoff hypothesis with respect to the plate and Winkler hypothesis with respect to the base, the mathematical model of the problem is constructed as two-dimensional bilinear equation, i.e. linear in state and control function. The maximal quantity of the base material is taken as optimality criterion to be minimized. The Fourier distributional transform and the Bubnov-Galerkin procedures are used to reduce the problem to integral equality type constraints. The explicit solution in terms of twodimensional Heaviside's function is obtained, describing piecewise-continuous distribution of the material. The determination of the switching points is reduced to a problem of nonlinear programming. Data from numerical analysis are presented.
Diffraction of waves in an elastic space is investigated, when a shear wave is incident in an arbitrary direction on a. semi-infinite inclusion in the form of elastic layer of a small thickness. The problem is to determine the wave field both in the contact region and in the space. In the both regions of shade and reflected wave and, naturally, in the contact region a wave part i s discovered ~ localized (surface) wave of Love (if only the. shear wave speed in the space is greater than that in the inclusion)+ As an extreme case solutions of problems of space with a semi-infinite crack and also a semi-infinite rigid inclusion are derived. Asymptotic presentations of displacements and st#resses in the far field and asymptotics of stresses near the inclusion's edge are dcrived.1. Consider an elastic space? in Cartesian coordinate system Ozyz, containing an elastic semi-infinite inclrision in the form of a semi-infinite strip of a sma.11 thickness 2 h , which occupies the region Ro (-m < 5 5 0, IyI 5 h, Irl < m).A plane shear wave with time harmonic factor e-iwt and amplitude(1) u,im) (z, y) = e -i k r c o s P -i h~s i n P is incident form infinite at an angle j ? (0 < , O < 7~/2), where k. = w/c is the wave number, c = is the shear watm speed, fi, p and D O , po are the elastic moduli and densities of the spacc and the inclusion. The space is in the state of an anti-plane deformamtion.The task is to determine the diffracted wave field both in the contact region and in t,he space.One can present uzm) ( (5, y) in tlie form of it sum of its even part and odd part Then the displacement; will dso bc represented i n t,he form 21, (w, = w (w) + w 2 (G?l) where w1 (x, y) is the even part and iu2 (2: y) is thc odd part of thc unknown displacement amplitude, which is i o he determincd.
Պիեզոէլեկտրական կիսատարածությունում սահքի հարթ ալիքի դիֆրակցիան դիէլեկտրիկ կիսատարածությունում առկա կիսաանվերջ մետաղական շերտի վրա Դիէլեկտրիկ կիսատարածությունում գտնվող կիսաանվերջ մետաղական շերտի վրա սահքի հարթ էլեկտրաառաձգական ալիքի դիֆրակցիայի խնդիրը բերվում է անալիտիկ ֆունկցիաների տեսության Ռիմանի տիպի խնդրի իրական առանցքի վրա: Դիֆրակցիայի խնդիրը լուծվում է օգտագործելով Ֆուրյեի ինտեգրալ ձևափոխությունների մեթոդը: Կիսաանվերջ մետաղական շերտի՝ էլեկտրոդի ,առկայությունը բերում է ալիքների դիֆրակցիայի՝ պիեզոէլեկտրական կիսատարածությունում տարածվում են ծավալային և երկու մակերևութային ալիքներ: Բացահայտվել են ալիքային դաշտի մի քանի առանձնահատկություններ: Jilavyan S.H., Ghazaryan H.A. Diffraction of Plane Shear Wave in Piezoelectric Semi-Space at a Semi-Infinite Metallic Layer in the Dielectric Medium The problem of diffraction of plane shear electro-elastic wave in a piezoelectric medium with a semi-infinite metallic layer in dielectric half-space is reduced to the solution to Riemann problem in analytic functions theory. The problem of diffraction is solved using Fourier transformation. The presence of the semi-infinite metallic layer leads to a diffraction of waves and some special features,a result of which two surface electroelastic waves occur in a piezoelectric medium. Задача дифракции плоской электроупругой волны сдвига в пьезоэлектрическом полупространстве при полубесконечном металлическом слое в диэлектрическом полупространстве сводится к решению задачи типа Римана на действительной оси в теории аналитических функций. Решается задача методом интегрального преобразования Фурье. Наличие полубесконечного металлического слоя (электрода) в диэлектрике приводит к распространению дифрагированных объёмных и двух поверхностных электроупругих волн в пьезоэлектрическом полупространстве. Выявлены некоторые особенности волнового поля. Введение. При исследовании волновых процессов в деформируемых средах некоторые характерные свойства существенно влияют на волновое поле, но важным
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