Forced vibrations of a viscoelastic damping layer

Forced vibrations of a viscoelastic damping layer are investigated. The equations obtained are reduced to normal modes, and the solutions are determined for nonresonance and resonance cases of vibrations.Moscow Institute of Electronic Machine Construction. Translated from Mekhanika Polimerov, No. 1, pp. 124–132, January–February, 1972.     

Stability of hinged viscoelastic rods under dynamic loading

Equations of Mathieu type describing the transverse vibrations of a straight viscoelastic rod compressed by a periodic longitudinal force are examined. The resonance regime is investigated by means of the method of averaging [2–4] in the case of a hinged viscoelastic rod acted upon by a periodic force.Institute of Cybernetics and Computer Center, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 6, pp. 1126–1129, November–December, 1973.     

Vibrations of a viscoelastic cylinder with an elastic shell

The nonlinear vibrations of a viscoelastic cylinder with an elastic shell subjected to two harmonic forces are investigated using the averaging scheme described in [3, 4]. Nonresonance, resonance, and subharmonic vibrations are examined. It is shown that the presence of viscosity in the system leads to a single stationary equilibrium position for which the stability conditions are given.V. I. Lenin Tashkent State University. Translated from Mekhanika Polimerov, No. 4, pp. 691–697, July–August, 1973.     

Vibrations of isotropic viscoelastic shells

It is shown that the boundary value problems for viscoelastic and elastic shells coincide. The natural and forced vibrations of shells are investigated by the averaging method.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 157–163, January–February, 1971.     

Dynamics of a Sea Platform Interacting with the Seabed and the Water Medium

Transient vibrations of the system {structure–seabed–water layer} are investigated. The schematic representation of the structure consists of a rigid circular foundation slab and a superstructure in the form of a vertical viscoelastic cylinder with lumped masses. The interaction of the foundation with a viscoelastic half-space (the seabed) is taken into account by using the method of orthogonal polynomials to solve the dynamical contact boundary-value problem. A procedure is developed for including in the analysis the interaction of a cylindrical foundation-supported structure with the water layer (to simulate the dynamics of an oil-drilling platform). The assumed load is seismic action specified by an analog accelerogram of the local area. A computational system is developed for numerical simulation of the vibrations and for determining the forces, displacements, accelerations, and contact stresses.     

Free vibrations of a viscoelastic beam

The method of averaging is used to investigate the free transverse vibrations of a viscoelastic beam supported at the ends. The material properties of the beam are described by a certain nonlinear integral equation of Volterra type.Institute of Mechanics and Seismic Stability of Structures, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 4, pp. 752–756, July–August, 1971.     

An asymptotic calculation of the vibrations of a viscoelastic cylinder with a slowly varying internal boundary

The vibrational problem is considered for a long hollow viscoelastic cylinder with a variable internal boundary, this being enclosed in an elastic shell. An asymptotic method based on averaging is used to find the resonant vibrations in response to a small uniformly distributed internal pressure that varies periodically with time. The calculation is carried through to quadrature working formulas.Moscow Institute of Electric Machine Construction. Translated from Mekhanika Polimerov, No. 5, pp. 935–939, September–October, 1973.     

Effect of ultrasonic vibrations on the flow of a viscoelastic liquid

The rheological characteristics of a viscoelastic liquid flow, on which finite-amplitude ultrasonic shear vibrations have been superimposed, are investigated. It is shown that at periodic deformation amplitudes of 5 µ or more there is a thixotropic reduction of the viscosity and elasticity of the system owing to the destruction of certain types of structural bonds. The experimental apparatus is described.Moscow Institute of Chemical Machine Building. Translated from Mekhanika Polimerov, No. 6, pp. 1097–1099, November–December, 1971.     

Investigation of the vibrations of relaxing systems by the averaging method

The method of averaging is used to investigate the damping of the vibrations of a one-dimensional, physically and geometrically linear viscoelastic system with one degree of freedom. The motion of this system under an external load is studied at resonance. The averaging principle is justified on both finite and infinite time intervals for nonlinear multidimensional systems.Institute of Cybernetics and Computer Center, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 5, pp. 806–813, September–October, 1969.     

Natural vibrations of composite viscoelastic cylinders

Free damping spatial and axisymmetrical vibrations of short cylinders consisting of elastic and viscoelastic layers are considered. A numerical study is made of the dependence of natural frequencies and damping coefficients on the ratio of geometric cylinders.Translated from Dinamicheskie Sistemy, No. 5, pp. 55–58, 1986.     

On the theory of the flexural vibrations of a rotating viscoelastic cantilever

A new solution is worked out for the problem of the flexural vibrations of a viscoelastic cantilever. The method is based on the use of Laplace contour integrals for integration in a complex domain. The dependence of the solutions of the problem on the parameters introduced is investigated. Asymptotic expansions of the integrals at large and small values of the argument are constructed for numerical calculations. Solutions in the form of polynomials are found for particular values of the elastic vibration frequencies and the properties of these solutions are established.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 2, pp. 305–311, March–April, 1973.     

Determination of the physicomechanical characteristics of viscoelastic materials in orthotropic and isotropic layers from the propagation velocities and damping constants of longitudinal and shear vibrations

The author examines the propagation of longitudinal and shear waves in viscoelastic orthotropic and isotropic layers. Relations are obtained for determining the elastic constants and the real and imaginary parts of the complex moduli and Poisson's ratios in orthotropic and isotropic layers from the propagation velocities and damping constants of longitudinal and shear vibrations.Mekhanika Polimerov, Vol. 3, No. 1, pp. 161–166, 1967     

Separation of variables as a means of solving the mixed boundary-value problem of viscoelasticity

The quasistatic mixed boundary-value problem is considered for a viscoelastic body with constant Poisson's ratio. A method of reducing viscoelastic problems to the solution of a series of uniform elastic problems is described. The convergence of the method is proved. The method is illustrated with reference to the solution of a specific viscoelastic problem. Tabulated influence functions of the Abel type are used in the solutions.Moscow M. V. Lomonosov State University. Translated from Mekhanika Polimerov, No. 4, pp. 588–596, July–August, 1969.     

Method of elastic solutions of problems of thermoviscoelasticity

The quasi-static mixed boundary value problem is considered for a viscoelastic body with time-dependent properties and a singular nondegenerate relaxation kernel. The existence of a time-temperature (or similar) analogy is not assumed. A method of reducing the viscoelastic problem to the solution of a series of uniform elastic problems is proposed and its convergence proved. The method is illustrated with reference to examples of solutions of specific viscoelastic problems.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 4, pp. 603–614, July–August, 1970.     

Effect of small additives of oligomer on the viscoelastic properties of carbon fiber plastics

The viscoelastic properties of carbon fiber composites whose phenol-formaldehyde matrix is modified by thermodynamically incompatible isocyanate derivatives have been investigated. Data are given on fiber wetting (Table 11), internal stress (Table 2), viscoelastic properties (Fig. 1), and tensile strength (Fig. 2). The modified composites are strengthened by the addition of 0.5–4% oligomer additive. This process involves the formation of a two-phase structure, in which the additive phase microparticles act as a polymer filler. Due to selective interactions, the intermediate layer formed at the fiber-binder interface leads to changes in the viscoelastic properties and tensile strength of the matrix and improved maintenance characteristics for the material as a whole.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 440–445, July–August, 1993.     

Investigation of the vibration of viscoelastic pipes in a viscoelastic soil

The vibration equation for a viscoelastic pipe laid in a viscoelastic soil is obtained and solved. A specific problem is examined using the results of an experimental investigation. The time dependence of the pipe displacements relative to the soil is constructed.M. T. Urazbaev Institute of Structural Mechanics and Seismic Stability, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 6, pp. 1112–1115, November–December, 1973.     

Method of solving equations of motion of viscoelastic media

A new method is proposed for solving dynamic problems for viscoelastic media based on the introduction of potential functions and transformation of equations of motion. The equations obtained for potential functions are used for constructing the general solution in the case of the effect of moving loads on viscoelastic media with plane-parallel interfaces. The problem of the propagation of Rayleigh surface waves is solved independently of the form of the kernels of the linear operators; a formula is obtained for determining the velocity of the Rayleigh surface wave with an arbitrary form of the viscoelastic operators. A method of experimental determination of the kernels determining the linear viscoelastic operators is proposed.V. V. Kuibyshev Moscow Civil Engineering Institute. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 429–435, May–June, 1973.     

Effect of Torsion and Warping on the Free Vibration of Sandwich Beams

The problem on free vibrations of wide sandwich beams is tackled in this paper. Torsional and warping effects in addition to flexure are included in the formulation of the dynamic problem. In order to show the effects of bending-torsion coupling and warping on the natural frequencies and the corresponding vibration modes, three cases are considered. First, the warping and torsion effects are neglected, second, the effect of warping on the coupling terms is neglected, and third, the effect of warping on the coupling terms is included. The viscoelastic core is modeled by elastic translational and rotational springs. The finite-difference method is used to solve the partial differential equations of motion with different boundary conditions for the top and bottom layers. Results for different materials, fiber orientations, depth-to-width ratios, and boundary conditions are found. The natural frequencies and the corresponding vibration modes obtained are in a good agreement with those cited in the literature. If the bending-torsion coupling is pronounced, the inclusion of warping affects the natural frequency considerably.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 163–176, April–May, 2005.     

An approximate method of solving dynamical problems of thermoviscoelasticity

A generalization of Whitham's asymptotic method is proposed for solving systems of integro-differential equations describing the dynamic behavior of bodies composed of nonlinear viscoelastic materials. The possibility of using this approach to solve coupled problems of thermoviscoelasticity is indicated. A number of examples are considered including the propagation of a harmonic disturbance in a rod of nonlinear viscoelastic material under isothermal conditions and the coupled problem of the high-frequency vibration of a rod of linear viscoelastic material, whose properties depend on temperature in accordance with the time-temperature superposition principle.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 1, pp. 58–65, January–February, 1973.     

Method of solving quasistatic boundary value problems of viscoelasticity for media with time-varying properties

It is shown that, if certain conditions are satisfied, the solution of a viscoelastic mixed boundary value problem can be obtained from the solution of the corresponding elastic problem by substituting time operators for the body and surface forces or given displacements. A similar assertion is also proved for media with time-varying properties. The applicability of the method to the theory of shallow flexible viscoelastic shells is demonstrated.Moscow Lomonosov State University. Translated from Mekhanika Polimerov, No. 6, pp. 987–993, November–December, 1969.