Vibrations of viscoelastic orthotropic shells in various media

The equation of motion of an orthotropic viscoelastic cylindrical shell in various media is obtained and solved. A numerical example is given.     

Equations of state of viscoelastic isotropic media

The equations of state of viscoelastic isotropic media are investigated in the form of a sum of integrals of increasing multiplicity. An expression is given for the second- and third-order kernels for an isotropic medium in terms of the metric tensor. The corresponding resolvents are found from the given first- and second-order kernels, and a method of obtaining the third-order resolvents is described. By means of the isotropy postulate of Il'yushin, the equations of state are simplified, and it is shown that they cannot contain scalar powers of tensors higher than the second. The form of these equations is written out.Mekhanika Polimerov, Vol. 3, No. 4, pp. 645–651, 1967     

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 thin piezoelectric shallow shells: Two-dimensional approximation

In this paper we consider the eigenvalue problem for piezoelectric shallow shells and we show that, as the thickness of the shell goes to zero, the eigensolutions of the three-dimensional piezoelectric shells converge to the eigensolutions of a twodimensional eigenvalue problem.     

Vibrations of thin cylindrical shells with a periodic structure

Free vibrations of thin linear–elastic Kirchhoff–Love cylindrical shells, having a periodic structure along one direction tangent to the shell midsurface, is considered. In order to take into account the effect of the periodicity cell size in this problem, a new averaged non–asymptotic model of such shells, proposed by Tomczyk (2006), is applied. The new additional higher–order free vibration frequencies dependent on the microstructure size will be derived and discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Brief note creep-stability analysis of viscoelastic cylindrical shells

The paper presents the creep-stability analysis of viscoelastic cylindrical shells under axial compression. The mechanical properties of the material are described by the constitutive equations of the linear viscoelastic theory in terms of convolution integral operators. The approximate analytical solution to the problem is obtained by means of a modification of the quasi-elastic method. As a result, the instability condition for the shell is formulated. It is shown that for viscoelastic materials with limited creep, there is a safe load limit below which the structure is asymptotically stable. Any load above the safe load limit leads to buckling at the corresponding critical time.     

Stability of laminar shells having a viscoelastic binder

Conclusions 1. In loading with a force whose value lies between the long-term and instantaneous critical values, a loss of shell stability by rupture takes place at a certain time after loading. This time is naturally taken as the critical one.2. Numerical estimates show that the level of the initial irregularities has a very great effect on the magnitude of the critical time. Therefore, in a theoretical estimate of the critical time it is necessary to take account of them as accurately as possible.Moscow Power Institute. Translated from Mekhanika Polimerov, No. 2, pp. 277–282, March–April, 1978.     

Vibrations of a shock-absorbing device on a nonlinear viscoelastic base

A method of calculating a viscoelastic shock-absorbing device or structure by the method of averaging systems of integro-differential equations is considered. The principal quadratic theory of hereditary viscoelasticity is used as the physical relationship between forces and displacements of the shock-absorbing base or structure.Moscow Institute of Electronic Machine Construction. Translated from Mekhanika Polimerov, No. 4, pp. 730–737, July–August, 1972.     

Stress concentrations around openings in transversely isotropic shells

A method of investigating stress concentrations around openings in shells made of a transversely isotropic material (oriented glass-reinforced plastic [5]) is described. The use of a Timoshenko-type theory makes it possible to take into account the effect of tangential shearing stresses and the anisotropy of the elastic properties of the shell in a direction normal to the middle surface. A complex form of the resolvents of this theory, constructed in [6], is employed.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. L'vov Franko State University. Translated from Mekhanika Polimerov, No. 6, pp. 1076–1081, November–December, 1970.     

Deformation of viscoelastic thick-walled shells in the post-critical stage

The progressive buckling of a viscoelastic cyclindrical shell with initial imperfections in axial compression is investigated in the geometrically nonlinear formulation. As distinct from previous research, shell deformation curves in the post-critical stage (after snap-through) are obtained for various load levels. The results obtained are in agreement with the experimental data. The experiments show that in the case of thick glass-reinforced plastic shells in the post-critical stage of deformation the material fails by debonding.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 96–99, January–February, 1976.     

Buckling shapes and hypercritical stressed state of viscoelastic shells

The buckling of shells of various thicknesses made from materials subject to nonlinear creep was studied experimentally. The distribution of the characteristic buckling shapes was established by spectral [harmonic] analysis. On the basis of the fundamental cubic theory of viscoelasticity [7], relationships are derived for determining the stress tensor components from the experimental deflection functions, with due allowance for various time factors. The stressed state of the test shells is analyzed. In approximating the deflection and stress functions use is made of a Fourier series in complex form.     

Parametric vibrations of cylindrical shells with a viscoelastic core

The method of calculating the axisymmetric and nonaxisymmetric parametric vibrations of a cylindrical shell bonded to an elastic core [2] is extended to the case of hollow and solid viscoelastic cores by substituting for the material moduli in the equations of motion of the core integral operators with kernels in the form of an exponential and a sum of exponentials. Expressions are given for the reaction of the viscoelastic core, together with the equation of the boundaries of the spectrum of principal regions of dynamic instability. The effect of relaxation time and the long-term modulus of elasticity of the core on the shape and location of the regions of dynamic instability is analyzed.     

Stability of transversally isotropic shells coupled with an elastic foundation

The stability of shells coupled with an elastic Winkler foundation is investigated. It is assumed that the shell is made of a material (glass-reinforced plastic) with low resistance to shear, as a result of which generalized theories that take transverse shear strains into account [1–4] must be used in the stability calculations. The solution obtained is compared with the corresponding solution obtained on the basis of the classical Kirchhoff-Love theory [8].Lvov Polytechnic Institute. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 669–673, July–August, 1969.     

Stability loss of reinforced cylindrical shells under isotropic external pressure

Conclusions 1. Upon the loading of a composite shell having a metallic matrix the shear effects are insignificant even in the case of comparatively large volume reinforcement contents and wall thicknesses.2. The principal modulus of a material which determines the stability of a reinforced shell upon isotropic external pressure is the secant modulus in the circumferential direction.3. In the case of complex reinforcement schemes some decrease in the stability of the shell is possible, probably due to an imperfection in reinforcement technology.Institute of Solid State Physics, Academy of Sciences of the USSR, Moscow Region. Translated from Mekhanika Polimerov, No. 1, pp. 90–95, January–February, 1977.