Complex dynamics of circular cylindrical shells

Complex dynamics of circular cylindrical shells subjected to inertial axial loads are investigated. The shell is vertically mounted on a shaker, i.e. its base is clamped to the shaker fixture, which induces a vertical motion along the shell axis. On the top of the shell a rigid disk is mounted, the vertical motion induced by the shaker induces huge inertial forces due to the rigid body motion. A complicating effect is due to the base actuator, which is an electro-dynamic shaking table; the interaction between the shell and shaker dynamics changes dramatically the system behaviour. The non-linear Sanders–Koiter theory is considered for the structural dynamics: the resulting set of non-linear partial differential equations is coupled with the linear ordinary differential equations that govern the shaker dynamics. A deep analysis of the non-stationary response of the shell is carried out in order to clarify the transition from stationary to non-stationary response. The model is validated by means of experimental results

Dynamics and Stability of Carbon Nanotubes

The low-frequency oscillations and energy localization of Single-Walled Carbon Nanotubes (SWNTs) are studied in the framework of the Sanders-Koiter shell theory. The circumferential flexure modes (CFMs) are analysed. Simply supported, clamped and free boundary conditions are considered. Two different approaches are proposed, based on numerical and analytical models. The numerical model uses in the linear analysis a double mixed series expansion for the displacement fields based on Chebyshev polynomials and harmonic functions. The Rayleigh-Ritz method is applied to obtain approximate natural frequencies and mode shapes. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions. An energy approach based on Lagrange equations is considered in order to obtain a set of nonlinear ordinary differential equations, which is solved by the Runge-Kutta numerical method. The analytical model considers a reduced version of the Sanders-Koiter shell theory obtained by assuming small circumferential and tangential shear deformations. These two assumptions allow to condense the longitudinal and circumferential displacement fields into the radial one. A nonlinear fourth-order partial differential equation for the radial displacement field is derived, which allows to calculate the natural frequencies and to estimate the nonlinearity effect. An analytical solution of this equation is obtained by the multiple scales method. The previous models are validated in linear field by means of comparisons with experiments, molecular dynamics simulations and finite element analyses retrieved from the literature. The concept of energy localization in SWNTs is introduced, which is a strongly nonlinear phenomenon. The low-frequency nonlinear oscillations of the SWNTs become localized ones if the intensity of the initial excitation exceeds some threshold which depends on the SWNTs length. This localization results from the resonant interaction of the zone-boundary and nearest nonlinear normal modes leading to the confinement of the vibration energy in one part of the system. The value of the initial excitation corresponding to this energy confinement is referred to as energy localization threshold. The effect of the aspect ratio on the analytical and numerical values of the energy localization threshold is investigated; different boundary conditions are considered

Vibration Localization of Imperfect Circular Cylindrical Shells

none4noThe goal of the present paper is the analysis of the effect of geometric imperfections in circular cylindrical shells. Perfect circular shells are characterized by the presence of double shell-like modes, i.e., modes having the same frequency with modal shape shifted of a quarter of wavelength in the circumferential direction. In presence of geometric imperfections, the double natural frequencies split into a pair of distinct frequencies, the splitting is proportional to the level of imperfection. In some cases, the imperfections cause an interesting phenomenon on the modal shapes, which present a strong localization in the circumferential direction. This study is carried out by means of a semi-analytical approach compared with standard finite element analyses.openPellicano, Francesco; Zippo, Antonio; Barbieri, Marco; Strozzi, MatteoPellicano, Francesco; Zippo, Antonio; Barbieri, Marco; Strozzi, Matte

Linear and nonlinear dynamics of a circular cylindrical shell under static and periodic axial load

In this paper an experimental study on circular cylindrical shells subjected to axial compres- sive and periodic loads is presented. The setting of the experiment is explained and deeply described along with a complete analysis of the results. The linear and the nonlinear dynamic behaviour associated with a combined effect of compressive static and a periodic axial load has been considered and a chaotic response of the structure has been observed close to the resonance. The linear shell behaviour is also investigated by means of a theoretical and finite element model, in order to enhance the comprehension of experimental results, i.e. the natural frequencies of the system and their ratios