L. Belenkaya. Numerical investigation of the stability of viscoelastic orthotropic cylindrical shell under the axial time-periodic load (original) (raw)
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In this paper a sufficient condition for stability and instability of rectilinear shape of orthotropic viscoelastic reinforced cylindrical shell under the axial time-periodic load by analytical methods are obtained. In addition, the upper and lower estimations of the critical loads corresponding to P-and 2P-periodic regimes are presented. The edges of the shell are pinned. The constitutive relations are described by a Volterra equations. The motion equations of mid-surface of the shell that are derived on basis the Timoshenko shell theory and the classical Kirchhoff–Love theory as well are considered. Having extended the conical methodology, originally developed for the differential equations (see Krasnosel'sky), to integro-differential equations we state the conditions for positive solution of the systems under consideration and the condition for instability of the shell.
Journal of Reinforced Plastics and Composites, 2006
In this study, the dynamic stability problem of a cylindrical shell composed of non-homogeneous orthotropic materials with Young’s moduli and density varying continuously in the thickness direction under the effect of an axial compressive load varying with a parabolic function of time is considered. At first, the fundamental relations and the modified Donnell type dynamic stability equations of a non-homogeneous orthotropic cylindrical shell are set up. Applying the Galerkin method, first, and then the Ritz-type variational method, the closed-form solutions have been derived for the dynamic critical axial load and dynamic factor. Finally, carrying out some computations, the effects of the non-homogeneity of the orthotropy ratio and the axial loading parameter on the critical parameters have been studied. Comparing results with those in the literature validates the present analysis.
In this study, the dynamic stability problem of a cylindrical shell composed of non-homogeneous orthotropic materials with Young's moduli and density varying continuously in the thickness direction under the effect of an axial compressive load varying with a parabolic function of time is considered. At first, the fundamental relations and the modified Donnell type dynamic stability equations of a non-homogeneous orthotropic cylindrical shell are set up. Applying the Galerkin method, first, and then the Ritz-type variational method, the closed-form solutions have been derived for the dynamic critical axial load and dynamic factor. Finally, carrying out some computations, the effects of the non-homogeneity of the orthotropy ratio and the axial loading parameter on the critical parameters have been studied. Comparing results with those in the literature validates the present analysis.
International Journal of Non-Linear Mechanics, 2014
The extensive use of circular cylindrical shells in modern industrial applications has made their analysis an important research area in applied mechanics. In spite of a large number of papers on cylindrical shells, just a small number of these works is related to the analysis of orthotropic shells. However several modern and natural materials display orthotropic properties and also densely stiffened cylindrical shells can be treated as equivalent uniform orthotropic shells. In this work, the influence of both material properties and geometry on the non-linear vibrations and dynamic instability of an empty simply supported orthotropic circular cylindrical shell subjected to lateral time-dependent load is studied. Donnell's non-linear shallow shell theory is used to model the shell and a modal solution with six degrees of freedom is used to describe the lateral displacements of the shell. The Galerkin method is applied to derive the set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge-Kutta method. The obtained results show that the material properties and geometric relations have a significant influence on the instability loads and resonance curves of the orthotropic shell.
In the present study, the dynamic stability of simply supported, circular cylindrical shells subjected to dynamic axial loads is analysed. Geometric nonlinearities due to finite-amplitude shell motion are considered by using the DonnellÕs nonlinear shallow-shell theory. The effect of structural damping is taken into account. A discretization method based on a series expansion involving a relatively large number of linear modes, including axisymmetric and asymmetric modes, and on the Galerkin procedure is developed. Axisymmetric modes are included; indeed, they are essential in simulating the inward deflection of the mean oscillation with respect to the equilibrium position and in describing the axisymmetric deflection due to axial loads. A finite length, simply supported shell is considered; the boundary conditions are satisfied, including the contribution of external axial loads acting at the shell edges. The effect of a contained liquid is investigated. The linear dynamic stability and nonlinear response are analysed by using continuation techniques and direct simulations. analysed the buckling of circular shells subjected to a suddenly applied load, using the DonnellÕs nonlinear shallow-shell theory. They noted that the presence of initial geometric imperfections largely reduce the critical load. A similar problem was analysed by using the same theory; in this work it is shown that, in the case of step loading, the effect of in-plane inertia can reduce the critical load.
Geometry Effects on the Nonlinear Oscillations of Viscoelastic Cylindrical Shells
2016
In this work the influence of geometry, load and material properties on the nonlinear vibrations of a simply supported viscoelastic circular cylindrical shell subjected to lateral harmonic load is studied. Donnell's non-linear shallow shell theory is used to model the shell, assumed to be made of a Kelvin-Voigt material type, and a modal solution with six degrees of freedom is used to describe the lateral displacements. The Galerkin method is applied to derive a set of coupled non-linear ordinary differential equations of motion. Obtained results show that the viscoelastic dissipation parameter has significant influence on the instability loads and resonance curves.
Journal of Sound and Vibration, 2006
In the present paper the dynamic stability of circular cylindrical shells subjected to static and dynamic axial loads is investigated. Both Donnell's nonlinear shallow shell and Sanders-Koiter shell theories have been applied to model finiteamplitude static and dynamic deformations. Results are compared in order to evaluate the accuracy of these theories in predicting instability onset and post-critical nonlinear response. The effect of a contained fluid on the stability and the post-critical behaviour is analyzed in detail. Geometric imperfections are considered and their influence on the dynamic instability and post-critical behaviour is investigated. Chaotic dynamics of pre-compressed shells is investigated by means of nonlinear time-series techniques, extracting correlation dimension and Lyapunov exponents. r (M. Amabili).
In the present paper the dynamic stability of circular cylindrical shells subjected to static and dynamic axial loads is investigated. Both Donnell's nonlinear shallow shell and Sanders-Koiter shell theories have been applied to model finiteamplitude static and dynamic deformations. Results are compared in order to evaluate the accuracy of these theories in predicting instability onset and post-critical nonlinear response. The effect of a contained fluid on the stability and the post-critical behaviour is analyzed in detail. Geometric imperfections are considered and their influence on the dynamic instability and post-critical behaviour is investigated. Chaotic dynamics of pre-compressed shells is investigated by means of nonlinear time-series techniques, extracting correlation dimension and Lyapunov exponents. r (M. Amabili).
Communications in Nonlinear Science and Numerical Simulation, 2009
In the present paper, the dynamic stability of circular cylindrical shells is investigated; the combined effect of compressive static and periodic axial loads is considered. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration; Lagrange equations are used to reduce the nonlinear partial differential equations to a set of ordinary differential equations. The dynamic stability is investigated using direct numerical simulation and a dichotomic algorithm to find the instability boundaries as the excitation frequency is varied; the effect of geometric imperfections is investigated in detail. The accuracy of the approach is checked by means of comparisons with the literature. Khoroshun [7] presented results obtained at the S.P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine over 20 years of research; the authors focused the attention on the variational-difference methods; more than 100 papers were cited. Kubenko and Koval'chuck [8] analyzed the stability and nonlinear dynamics of shells, following the historical advancements in this field, about 190 papers were deeply commented; they suggested, among the others, the effect of imperfections as an important issue to be further investigated.
In the present paper, the dynamic stability of circular cylindrical shells is investigated; the combined effect of compressive static and periodic axial loads is considered. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration; Lagrange equations are used to reduce the nonlinear partial differential equations to a set of ordinary differential equations. The dynamic stability is investigated using direct numerical simulation and a dichotomic algorithm to find the instability boundaries as the excitation frequency is varied; the effect of geometric imperfections is investigated in detail. The accuracy of the approach is checked by means of comparisons with the literature. Khoroshun [7] presented results obtained at the S.P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine over 20 years of research; the authors focused the attention on the variational-difference methods; more than 100 papers were cited. Kubenko and Koval'chuck [8] analyzed the stability and nonlinear dynamics of shells, following the historical advancements in this field, about 190 papers were deeply commented; they suggested, among the others, the effect of imperfections as an important issue to be further investigated.