Interaction Between an Oscillating Sphere and a Thin Elastic Cylindrical Shell Filled with a Compressible Liquid. Internal Axisymmetric Problem

The problem on the interaction between a spherical body that oscillates in a prescribed manner and a thin elastic cylindrical shell filled with an ideal compressible liquid is formulated. It is assumed that the geometrical center of the sphere is located on the cylinder axis. The problem is solved based on the possibility of representing a partial solution of the Helmholtz equation written in cylindrical coordinates in terms of partial solutions in spherical coordinates, and vice versa. By satisfying the boundary conditions on the surfaces of the sphere and the shell, we obtain an infinite system of linear algebraic equations to determine the coefficients of expansion of the liquid-velocity potential into a Fourier series in terms of Legendre polynomials. The hydrodynamic characteristics of the liquid filling the cylindrical shell are determined and compared with the cases where a sphere oscillates in an infinite liquid and in a rigid cylindrical vessel     

Vibrations of a Cylindrical Shell Filled with a Liquid

The concurrent effect of a harmonic excitation and an airflow on the vibrations and vibroaccelerations of a thin-walled cylindrical shell filled with a liquid is studied     

Propagation of Normal Axisymmetric Waves in Compliant Elastic Cylinders Filled with and Immersed in a Fluid

The paper studies the relationship between the physical characteristics of a cylinder and the properties of normal axisymmetric waves in elastic–liquid waveguides. The cylinder is made of a compliant material in which the velocity of shear waves is less than the sonic velocity in a perfect compressible liquid. The complete system of dynamic elasticity equations and the wave equation are used to describe the wave fields in the elastic cylinder and fluid, respectively. This approach allows obtaining the dispersion characteristics of coupled normal waves in compound waveguides over wide ranges of frequencies and wavelengths. The curves of real, imaginary, and complex wave numbers versus frequency are plotted for specific pairs of waveguide materials. Computations are carried out for a thick-walled cylinder filled with a fluid and immersed in either vacuum or a fluid. It is found out that compliant and rigid materials of the cylinder affect differently the wave interaction process in elastic–liquid waveguides     

Vibrations of Cylindrical Shells Filled with a Liquid

The paper reports on experimental results for a dynamic system of two identical shells filled with a liquid and placed on a common elastic foundation. It is established that vibrations excited in one of the shells synchronize the vibrations of the whole system     

Equilibrium of an Elastic Spherical Shell Filled with a Heavy Fluid under Pressure

This paper considers the problem of equilibrium of a nonlinearly elastic spherical shell filled with a heavy fluid and resting on a smooth, absolutely rigid, flat surface. The weight of the shell is assumed to be negligible in comparison with the weight of the fluid filling it. The contact region with the supporting plane is one of the unknowns in the problem. Equilibrium equations for a membrane shell are obtained in an accurate nonlinear formulation. Stresses and strains of a shell made of a Mooney–Rivlin material are numerically investigated. The results are compared with calculation results for the case of inflation of a spherical shell ignoring the weight of the fluid filling. The effect of the fluid weight on shell strains and stresses is estimated.     

轴对称层合圆柱壳混合状态方程的弱形式及其边值问题

从Ｈｅｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ变分原理出发，在柱坐标系中，导出圆柱壳轴对称问题的弱形式混合状态方程和边界条件，联用状态空间法给出强厚度叠层柱壳的解析解，此法使得求解该类问题的形式得以扩大和统一。     

The Problem of Forced Nonlinear Vibrations of Cylindrical Shells Completely Filled with Liquid

The forced nonlinear vibrations of a thin cylindrical shell completely filled with a liquid are studied. A refined mathematical model is used. The model takes into account the nonlinear terms up to the fifth power of the generalized displacement of the shell. The Bogolyubov’Mitropolsky averaging method is used to plot amplitude’frequency response curves for steady-state vibrations. The steady-state vibrations at the frequency of principal harmonic resonance are analyzed for stability__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 52–59, February 2005.     

Forced Nonlinear Vibrations of Cylindrical Shells Filled with a Liquid

Forced nonlinear vibrations of cylindrical shells partially filled with a liquid are studied. The wave motions of the free liquid surface are taken into account. Regular periodic deformation modes of the shell are studied, and frequency ranges where these modes do not occur are determined     

Nonlinear Elastic State of a Composite Cylindrical Shell with a Rectangular Hole

International Applied Mechanics - Physically nonlinear boundary-value problems for an orthotropic cylindrical shell with a rectangular hole under static loads are formulated. The system of...     

圆柱形弹性贮液容器的自振特性分析

贮液容器,无论是由钢材制成的或是由钢筋混凝土建造的。在工业或工程上都有着广泛的应用,如石油化工工业中的储油罐,给水工程中的水即为典型例子。在核动力工程中的压水堆或快增残堆,所用的主容器都可看成为一种特殊的贮液容器。它与一般容器很大的区别在于除贮液外,在堆内还设置一些构件。这对结构分析计算速写为不小的困难。本文根据剪切悬壁梁理论且考虑液动压力效应,建立了弹性圆柱形贮液容器的自振方程及相关特征值矩阵,     

Stability of an Elastic System Consisting of a Ribbed Cylindrical Shell and Noncrossing Longitudinal Plates

The paper presents a method for stability analysis of an elastic system consisting of a ribbed cylindrical shell and noncrossing plates. The influence of the width and thickness of the plate on the buckling stresses and modes is analyzed     

Nonstationary Displacements in an Axisymmetric Problem for an Elastic Half-Space Under Mixed Boundary Conditions*

International Applied Mechanics - The strain state of an elastic half-space under a non-stationary normal load acting on its boundary is determined. A mixed boundary-value problem is stated. Its...     

An Axisymmetric Electrothermoviscoelastic Problem for a Partially Depolarized Piezoceramic Sphere Under Quasistatic Harmonic Loading

The analytical solution is obtained for the vibrations and dissipative heating of a hollow piezoceramic sphere polarized across the thickness, with thermal depolarization taken into account. The sphere is subjected to a quasistatic potential difference varying harmonically with time. The inside surface is heat-insulated and the outside surface is involved in convective heat exchange with the environment. A numerical analysis is made and the depolarization conditions and the effect of the depolarized region on the stress–strain state and heating temperature are analyzed.     

Study of the Nonlinearly Elastic State of an Orthotropic Cylindrical Shell with a Hole, Using Mixed Functionals

An analogy is established between some terms of the functionals under consideration and the formulas of the theory of random processes. On this basis, the efficiency of mixed functionals is attributed to a deeper minimum they help to reach by taking the energy of so-called false strains into consideration. We perform a numerical stress—strain analysis of an organoplastic cylindrical shell with a side circular hole and study how the orthotropy and nonlinear properties of the composite affect the stress distribution near the hole. The case is discovered where the orientation of the composite about the cylindrical shell changes so that a larger nonlinear effect corresponds to a smaller initial stress     

Shell-Core Method for the Analysis of a Long Circular Cylindrical Sandwich Shell Subjected to Axisymmetric Loading

The analysis of a sandwich shell having a thick core and thin outer and inner layers (facings) and subjected to axisymmetric loads is considered. The problem is solved by applying the three-dimensional theory of elasticity to the core and the classical thin shell theory for the outer and inner facings. The displacement and stress continuity conditions are satisfied along the junctions of the facings and core. The results obtained from this solution have been compared with the results obtained from the sandwich shell theory of Fulton.     

Dynamics of a Semi-Infinite Cylindrical Shell with a Liquid Containing a Vibrating Spherical Segment

A semi-infinite cylindrical shell filled with a perfect incompressible liquid is considered. A vibrating rigid spherical segment placed on the shell axis excites the shell. The Laplace equation is solved under appropriate boundary conditions on the spherical, cylindrical, and flat surfaces bounding the liquid. Possibility is used to reexpand a spherical harmonic function in terms of a system of cylindrical harmonic functions and vice versa. The potential constructed is used to compute the shell deflections and the liquid pressure and velocity.