Forced vibrations of a cylindrical shell affected by a pulsed perturbing load

Forced vibrations of a cylindrical shell affected by a local pulsed load of varying duration is considered. Collision resonance is treated as a special case. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 48–52, June, 1999.     

Experimental investigation of the dynamics of shells of revolution (review)

The results of experimental investigations carried out at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine are analyzed in this review. The analysis suggests that experimental investigations of shell dynamics must be contained and developed if the method used to calculate the stressed-strained state and stability of dynamically loaded shells is to be developed further and made more precise. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, 35, No. 7, pp. 3–11, March, 1999.     

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.     

Transition process of cylindrical-shell vibrations under a local disturbing load

Methods for study of the transition process of induced vibrations in a cylindrical shell under a local disturbing load whose amplitude and frequency vary in accordance with given laws are developed. The amplitudes of certain vibration modes are compared with those in the transition process under a disturbing load with a constant frequency and amplitude as well as under steady vibrations. It is confirmed that, to determine the maximum amplitudes of total shell deflection, it is sufficient to consider only the vibration modes whose natural frequencies are lower than the frequencies of the disturbing load. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 67–72, April, 1999.     

Transient process of the vibrations of a cylindrical shell as a system with many degrees of freedom

A procedure is developed for investigating the transient process associated with the forced vibrations of a cylindrical shell as a system with many degrees of freedom. The amplitudes of the bending deflections of circular modes induced by a driving load of variable frequency and amplitude are compared with the same amplitudes for a uniform driving load and steady-state vibrations. The total maximum deflections of all the investigated cases are found to differ substantially. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 57–63, March, 1999.     

Determination of the axisymmetric geometrically nonlinear thermoviscoelastoplastic stress-strain state of shells of revolution

A method is developed for determining the axisymmetric thermoviscoelastoplastic stress-strain state of shells subjected to bending and torsion. The problem is solved in a geometrically nonlinear formulation with allowance for transverse shear. The geometrically nonlinear deformation of an annular plate, the thermoviscoelastoplastic deformation of a cylindrical shell, and the limiting state of a corrugated shell are studied as examples. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 40–48, December, 1999.     

Elastoplastic state of nonshallow flexible ellipsoidal shells under concentric loading

The elastoplastic stress-strain state of flexible ellipsoidal shells under concentric loading is investigated by the solution of nonlinear boundary-value problems. Numerical results are presented for open shells in the case of a free (unsupported) edge and a shell with a central opening (the periphery of the opening is supported by a thin ring). Solutions of the problems in linear and nonlinear statements are analyzed. Numerical results for ellipsoidal and spherical shells are compared. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 54–60, April, 1999.     

Interaction of boundaries of opening and rigid inclusion under unsteady convective heat exchange on external surfaces of cylindrical shell

The stressed state of a thin cylindrical shallow shell containing a circular opening and a circular undeformable inclusion is investigated using a thermoelasticity equation in complex forces. The boundaries of the opening and inclusion are thermally insulated. The unsteady convective heat exchange between the environment and the shell surfaces is described by Newton's law. Numerical studies of thermal stresses are carried out for various times and reduced distances between the boundaries of the opening and inclusion. Simferopol University. Donetsk University, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 61–66, April, 1999.     

Shock loading of a cylindrical shell filled with viscous compressible liquid

The effect of a uniformly distributed shock load on a thin-walled cylindrical shell filled with viscous compressible liquid is considered. An analytical method of inverse Laplace transformation of the general solution of the linearized Navier-Stokes equations is proposed. A numerical example is presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 11, pp. 55–61, November, 1999.     

Analysis of the stress-strain state of noncircular cylindrical shells subject to thickness viration and weight retention

The stress-strain state of noncircular shells has been analyzed based upon solution of boundary value static problems of variable shell thickness using the methods of spline-collocation and discrete orthogonization. Shell weight was preserved depending on the degree of change in the thickness and the value of the eccentricity. Three classes of problems were considered in which the thickness varied along the generatrix, the guide, and in two coordinate directions; data are presented about the deflection and tangential force in the cross section under different values of the parameters. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine, Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 39–47, June, 1999.     

Study of the stability of composite shells with allowance for the cracked state of components of the material

An approximate method is described for determining the effective strain characteristics of composite materials with allowance for the presence of plane microcracks in the components. The character of the effect of such defects on the critical loads is illustrated by examining the problem of the stability of a conical shell. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 11, pp. 46–54, November, 1999.     

One approach to the construction of the basic equations of the theory of nonthin shells with variable thickness

A method for determining the principal curvatures of medium-thickness shells through the vector representation of local bases is proposed based on the parametrization of the base median surface of a shell and its front surfaces. Repeated partial derivatives of vector functions with respect to variable Gaussian coordinates, which is a standard practice in theory of shells when calculating the curvatures as coefficients of the second quadratic form, are not used. Such an approach allows us to accurately account for the geometry of the front surfaces of the shell in determining its stress-strain state. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 58–65, September, 1998.     

Dynamic behavior of liquids and gases in conical shells in a vibrational force field

An experimental study is made of specific features of the motion of the free surface of liquid in different conical shells, the formation, motion, and local accumulation of gas bubbles in the shells, and the character of random motion of the gas-liquid medium in a vibrational force field. It is established that the liquid moves along the horizontal as well as the vertical axes under certain conditions when axisymmetric modes of vibration of the free surface are excited. The main characteristics of the dynamic behavior of a gas-liquid medium in a compound conical shell having the form of a de Laval nozzle are examined for the case when the medium forms a nonlinear oscillatory “liquid-gas” system that is dynamically stable. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 23–29, February, 1999.     

Vibrations of shallow shells that are circular in plan and have local supports

The paper deals with vibrations of doubly curved shallow shells that are circular in plan and are reinforced by local rod-type supporting elements or cylindrical shells. The coefficients of the frequency equation are found by using numerical-analytical methods to solve boundary-value problems for fixed values of frequency. The natural frequencies and modes of vibration of a system composed of a shell and elastic supports are determined in the course of solving the problem. It is shown that it is possible to also account for reactive moments and shearing forces, in addition to the normal reactions of an elastic support. The potential of the approach which is developed is illustrated by the solution of specific problems. Special Design Office of the S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 69–75, March, 1999.     

Transient dynamic behavior of a closed gas-filled shell subjected to internal blast loading

The paper concerns the numerical solution of a problem on the forced vibration of a shell system under a blast load. The mathematical model of the transient dynamic process in the given multicomponent system is based on the use of a system of hydrodynamic equations to describe the motion of the detonation products and air and equations from shell theory to determine the stress-strain state of the shell system. The hydrodynamic equations are integrated in moving grids by the method developed by S. K. Godunov. The shell-theory equations are integrated by the integro-interpolation method. The distribution of the loads on the shells, the distribution of the maximum strains along the generatrix of the shell system, and the transformations of the detonation products at characteristic points are presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 34, No. 3, pp. 76–82, March, 1999.     

On solution of problems of dynamics of plates and shells with local structure heterogeneities

A general approach to the solution of nonstationary problems of the theory of shells with local structure heterogeneities is proposed. The approach is based on representation of solutions for the systems of differential motion equations of shell theory in the form of expansions in terms of free forms of vibrations (FFV). Two implementations of the approach, involving FFV expansions of certain members and FFV expansions of the system as a whole, are considered. The capabilities of the approach are illustrated by results for specific problems. In the first implementation, we determine the dynamic stress-strain state of a square plate with three rod supports. A round plate connected to a coaxial circular cylindrical shell is considered as an example of FFV expansion of the system as a whole. Special Design and Engineering Office, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 46–53, October, 1999     

On the theory and solution of dynamic problems of the nonstationary behavior of cylindrical shells with discrete variable stiffeners

The formulation and development of a numerical algorithm for solving shell theory problems concerning cylindrical shells with variable-stiffness reinforcements are considered. The Hamilton-Ostrogradskii variational principle is used to obtain the equation of motion. The algorithm is based on finite-difference approximation of the initial variational functional. A numerical example is presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 34, No. 6, pp. 53–59, June, 1999.     

Calculation of spatial vibrations of plates of complex shape

We consider problem of the spatial vibrations of plates with complex shape within Timoshenko's theory of plates. We write the constitutive equations in a local oblique coordinate system where all the bounding contours coincide with coordinate lines. We have demonstrated the effectiveness of the proposed method using as an example the vibration of a rectangular plate weakened by a regular hexagonal hole under the action of an impulsive surface load. We analyze the effect of nonlinear terms on the frequency and amplitude of normal displacements of the shell as a function of the load amplitude. S. P. Timoshenko Institute of Mechanics. National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 8, pp. 44–53, August, 1999.     

The stress state of a laminated nonlinearly elastic thick-walled spherical shell

This paper deals with spatial axisymmetric boundary-value problems of the physically nonlinear theory of elasticity for piecewise-homogeneous spherical bodies. The passage to dimensionless characteristics of the stress-strain state allows us to extract a physical dimensionless small parameter in the nonlinear state equations. The solution of nonlinear equilibrium equations and boundary-value problems is searched for in the form of series in positive degrees of the small parameter. This approach allows reducing the stated physically nonlinear boundary-value problem to a sequence of corresponding linear nonhomogeneous problems. A specific analytical solution and numerical results are obtained for a two-layer nonlinearly elastic spherical shell under bilateral pressure. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 26–32, December, 1999.     

Errors in determination of coordinates and velocities of objects in a navigational system

We consider the problem of constructing the covariance matrix for errors in coordinate and velocity determination in satellite navigation systems. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 98–102, June 1999.