Solution of the problem of interaction of Rayleigh waves with the edge of a wedgewith a small apex angle

The problem of interaction of Rayleigh waves with the edge of a wedge with a small apex angle was solved using classical methods. This solution describes surface waves whose characteristics agree with well-known experimental data and bulk waves which have a significant effect on energy distribution. New features of surface wave propagation in wedge-shaped bodies are revealed.     

Natural vibrations of a conical orthotropic shell with small curvatures of the generatrix

The Ostrogradskii-Hamilton principle is used with the variational-difference approach to solving eigenvalue problems as the basis for analyzing the influence of small distortions of the generatrix on the natural frequencies of vibration of free conical shells and conical shells precompressed in the axial direction. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 64–68, March 1999.     

To the solution of the thermoelasticity problem for conical shells

We consider the stress-strain state of thin conical shells in the case of arbitary distribution of the temperature field over the shell. We obtain equations of the general theory based on the classical Kirchhoff-Love hypotheses alone. But since these equations are very complicated, attempts to construct exact solutions by analytic methods encounter considerable or insurmountable difficulties. Therefore, the present paper deals with boundary value problems posed for simplified differential equations. The total stress-strain state is constructed by “gluing” together the solutions of these equations. Such an approach (the asymptotic synthesis method) turns out to be efficient in studying not only shells of positive and zero curvature [1, 2] and cylindrical shells [3] but also conical shells [4, 5]. Here we illustrate it by an example of an arbitrary temperature field, and the problem is reduced to solving differential equations with polynomial coefficients and with right-hand side containing the Heaviside function, the delta function, and their derivatives.     

To the problem of stability of a cylindrical shell under axial compression

The classical problem of stability of a thin elastic cylindrical shell loaded by axial compressions forces is considered. The axially symmetric and non-axisymmetric buckling modes of isotropic and orthotropic shells are studied. In contrast to the traditional approach, the well-known expressions for the critical load are obtained by analyzing the equations for the shell behavior and are independent of the boundary conditions.     

Numerical analysis of the flutter of a shallow shell

The stability of vibrations of a shallow shell that is rectangular in plant in a gas flow is studied for an arbitrary vector of flow velocity. Mathematically, the problem is shown to reduce to an ill-conditioned computational problem. To solve this problem, we propose a numerical saturation-free algorithm that allows one to obtain a sufficiently accurate solution for a grid containing 169 (13×13) nodes. In calculations for cylindrical and spherical shallow shells, new mechanical effects concerning the vibration modes and the dependence of the critical flutter velocity on the direction of the flow-velocity vector were found. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 97–102, November–December, 1999.     

Stress-strain analysis of a composite truncated conical shell

The stress-strain state of a nonshallow truncated conical shell made of a composite material and subjected to axial forces at the ends is studied. A variational difference method is used. Calculations are carried out for an orthotropic shell with low shear stiffness __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 66–72, July 2007.     

Elastoplastic state of a conical shell with a circular hole on the lateral surface

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 1, pp. 74–79, January, 1988.     

Asymptotic method for analysis of a conical shell under local loading

Differential equations of the general theory describing the stress-strain state of conical shells are very complicated, and when computing the exact solution of the problem by analytic methods one encounters severe or even so far insurmountable difficulties. Therefore, in the present paper we develop an approach based on the method of asymptotic synthesis of the stressed state, which has already proved efficient when solving similar problems for cylindrical shells [1, 2]. We essentially use the fourth-order differential equations obtained by Kan [3], which describe the ground state and the boundary effect. Earlier, such equations have already been used to solve problems concerning force and thermal actions on weakly conical shells [4–6]. By applying the asymptotic synthesis method to these equations, we manage to obtain sufficiently accurate closed-form solutions.     

截锥型薄壁结构声振耦合动力特性分析

采用大型通用软件ANSYS,建立截锥型薄壁结构的实体有限元动力学模型,通过与相关实验数据的对比验证了模型合理性。据此,利用无限元模拟自由声场边界,建立声场-截锥型薄壁结构的直接耦合有限元动力学模型。通过数值仿真分析研究了声场中截锥壳结构的振动特性,并讨论了声振动对结构动力特性的影响。研究结果表明:数值仿真结果和截锥壳声振实验数据比较一致。在考虑声场影响后发现:结构位移共振频率值大多有所降低,结构位移共振频率数量显著增多;在低频下,结构位移响应峰值在声场的影响下明显增大;在高频下则明显减小。     

Stress-strain state of a ribbed conical shell at resonance

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 4, pp. 25–28, April, 1991.     

Non-linear stability problem of an open conical sandwich shell under external pressure and compression

The stability problem of a shallow sandwich shell of conical segment shape, subjected to uniform external pressure and compression along generators is analysed based on the finitedeformation theory. With the help of the Ritz method the system of five non-linear, heterogeneous equations is obtained. They are the basic equations of elastic stability of the shell under consideration. The results of numerical calculations are presented in diagrams, which show the influence of basic mechanical properties and geometric parameters of the shell on the value of the upper and lower critical load.     

Magnetoelastic nonlinear deformation of a conical shell of variable stiffness

A complete system of equations of nonlinear magnetoelasticity of shells is presented. A resolving system of equations of a conical shell of variable thickness is constructed for the axisymmetric case. A numerical example of a flexible shell illustrates the possibility of using the proposed technique to solve this class of problems. T. G. Shevchenko National University, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 11, pp. 34–39, November, 1999.