1,721,104 research outputs found
Dynamic stability and sensitivity to geometric imperfections of strongly compressed circular cylindrical shells under dynamic axial loads
No full textIn the present paper, the dynamic stability of circular cylindrical shells is investigated; thecombined 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 finiteamplitude of vibration; Lagrange equations are used to reduce the nonlinear partial differentialequations to a set of ordinary differential equations. The dynamic stability is investigatedusing direct numerical simulation and a dichotomic algorithm to find the instabilityboundaries as the excitation frequency is varied; the effect of geometric imperfections isinvestigated in detail. The accuracy of the approach is checked by means of comparisonswith the literature
VIBRATIONS OF CIRCULAR CYLINDRICAL SHELLS: THEORY AND EXPERIMENTS
No full textIn the present paper, a method for analysing linear and nonlinear vibrations of circular cylindrical shells having differentboundary conditions is presented; the method is based on the Sanders–Koiter theory. Displacement fields are expanded ina mixed double series based on harmonic functions and Chebyshev polynomials. Simply supported and clamped–clampedboundary conditions are analysed, as well as connections with rigid bodies; in the latter case experiments are carried out.Comparisons with experiments and finite-element analyses show that the technique is computationally efficient andaccurate in modelling linear vibrations of shells with different boundary conditions.An application to large amplitude of vibration shows that the technique is effective also in the case of nonlinearvibration: comparisons with the literature confirm the accuracy of the approach.The method proposed is a general framework suitable for analysing vibration of circular cylindrical shells both in thecase of linear and nonlinear vibrations
On the dynamic properties of axially moving systems
No full textThe objective of the present paper is a deep analysis of some recent numerical and experimental results regarding the complex dynamics of axially moving systems. Such important mechanical systems exhibit interesting dynamic behaviors: homoclinic orbits; sub-harmonic responses; amplitude modulations; and chaos. These dynamics have been obtained numerically and in some cases have been experimentally observed. Using recent techniques of the non-linear time series analysis, the response of axially moving systems has been studied for a large variety of test cases. The correlation dimension of the time series, which is deeply related to the minimal dimension of a system able to reproduce the dynamics, is estimated. Lyapunov exponents are evaluated in order to quantify the response regularity. The present work gives a contribution towards understanding the complex dynamics observed both in conservative and dissipative systems. The dynamical phenomena are analyzed within the unified framework of the non-linear time series analysis. In the case of experimental data the new non-linear filtering techniques, based on the embedding techniques, have been applied to reduce high noise when classical techniques give bad results
Dynamic instability of a circular cylindrical shell carrying a top mass under base excitation: Experiments and theory
No full textThe present paper is focused on the experimental and theoretical analysis of circular cylindrical shells under base excitation. The shell axis is vertical, it is clamped at the base and connected to a rigid body on the top; the base provides a vertical seismic-like excitation. The goal is to investigate the shell response when a resonant harmonic forcing is applied: the first axisymmetric mode is excited around the resonance at relatively low frequency and low amplitude of excitation. A violent resonant phenom- enon is experimentally observed as well as an interesting saturation phenomenon close to the previously mentioned resonance. A theoretical model is developed to reproduce the experimental evidence and pro- vide an explanation of the complex dynamics observed experimentally; the model takes into account geometric shell nonlinearities, electrodynamic shaker equations and the shell shaker interaction
Boundary layers and non-linear vibrations in an axially moving beam
No full textThe non-linear oscillations of a one-dimensional axially moving beam with vanishing flexural stiffness and weak non-linearities are analysed. The solution of the initial-boundary value problem for the partial differential equation that describes the motion of the beam when two parameters related to the flexural stiffness and the non-linear terms vanish is expanded into a perturbative double series. Two singular perturbation effects due to the small flexural stiffness and to the weak non-linear terms arise: (i) a boundary layer effect when the flexural stiffness vanishes, (ii) a secular effect. Some tests are performed to compare the first order perturbative solution with an approximate solution obtained by a finite difference scheme. The effect of the oscillation amplitude combined with the presence of small bending stiffness and axial transport velocity is investigated enlighting some interesting aspects of axially moving systems. The value of the perturbative series as a computational tool is shown
Energy dissipation in EHL Film in Gear Lubrication
No full textA characterization of the energy dissipation of the lubricant film between mating teeth in gear pairs
is proposed. The film fluid is modeled using the fully flooded elastohydrodynamical point contact
and the solution is found by means of a numerical multilevel solver. Some comparison with other
solutions proposed in the literature for the line contact problem are drawn to validate the proposed
approach. In order to understand the effect of the lubricant film on the vibration of the gear pair, it is
important to describe both the stiffness of the film and the viscous energy dissipation: in the present
paper, some initial results about this problem are presented
Low-dimensional model for nonlinear vibrations of circular cylindrical shells
No full textThe response-frequency relationship in the vicinity of a resonant frequency, the occurrence of travelling wave response and the presence of internal resonances are investigated for simply supported, circular cylindrical shells. Donnell's nonlinear shallow-shell theory is used. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. The mode shape is expanded by using four degrees of freedom. The effect of internal dense fluid is studied. The solution is obtained by the Method of Normal Forms. Comparison of a three and a four degree-of-freedom model is performed. A water-filled shell presenting the phenomenon of 1:1:1:2 internal resonances is investigated; specific Normal Forms are developed for this study
Nonlinear vibrations of functionally graded circular cylindrical shells subjected to harmonic external load
No full textThe nonlinear vibrations of functionally graded (FGM) circular cylindrical shells are analysed. The Sanders-Koiter theory is applied in order to model the nonlinear dynamics of the system. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on Chebyshev polynomials for the longitudinal variable and harmonic functions for the circumferential variable. Both driven and companion modes are considered. Numerical analyses are carried out in order to characterize the nonlinear response when the shell is subjected to a harmonic external load. A convergence analysis is carried out to obtain the correct number of axisymmetric and asymmetric modes describing the actual nonlinear behaviour. The influence of the material distribution on the nonlinear response is analysed considering different configurations and volume fractions of the constituent materials. The effect of the companion mode participation on the nonlinear response of the shell is analysed
Nonlinear vibration of functionally graded cylindrical shells: effect of constituent volume fractions and configurations
No full textIn this paper, the nonlinear vibration of functionally graded (FGM) cylindrical shells under different constituent volume fractions and configurations is analyzed. The Sanders-Koiter theory is applied to model nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. Displacement fields are expanded by means of a double mixed series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. Both driven and companion modes are also considered, allowing for the travelling-wave response of the shell. The functionally graded material considered is made of stainless steel and nickel, properties are graded in the thickness direction according to a real volume fraction power-law distribution. In the nonlinear model, shells are subjected to an external radial excitation. Nonlinear vibrations due to large amplitude of excitation are considered. Specific modes are selected in the modal expansions; a dynamical nonlinear system is then obtained. Lagrange equations are used to reduce nonlinear partial differential equations to a set of ordinary differential equations, from the potential and kinetic energies, and the virtual work of the external forces. Different geometries are analyzed; amplitude-frequency curves are obtained. Convergence tests are carried out considering a different number of asymmetric and axisymmetric modes. The present model is validated in linear field (natural frequencies) by means of data present in the literature
Normal modes and boundary layers for a slender tensioned beam on a nonlinear foundation
No full textIn this paper, the nonlinear normal modes (NNMs) of a thin beam resting on a nonlinear spring bed subjected to an axial tension is studied. An energy-based method is used to obtain NNMs. In conjunction with a matched asymptotic expansion, we analyze, through simple formulas, the local effects that a small bending stiffness has on the dynamics, along with the secular effects caused by a symmetric nonlinearity. Nonlinear mode shapes are computed and compared with those of the unperturbed linear system. A double asymptotic expansion is employed to compute the boundary layers in the nonlinear mode shape due to the small bending stiffness. Satisfactory agreement between the theoretical and numerical backbone curves of the system in the frequency domain is observed
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