Influence of Geometry on the Non-Linear Vibrations of Cylindrical Shells With Internal Flowing Fluid

2010 ◽  
Author(s):  
Zenon J. del Prado ◽  
Paulo B. Gonc¸alves ◽  
Michael P. Pai¨doussis
Keyword(s):  
Cylindrical Shell ◽  
Degrees Of Freedom ◽  
Lateral Displacement ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Dynamic Environment ◽  
Geometric Parameters ◽  
Flowing Fluid ◽  
Non Linear ◽  
Linear Vibrations

In this work, the influence of the characteristic geometric parameters of a cylindrical shell, such as radius-to-thickness and radius-to-length ratios, on both the linear and non-linear vibrations of a fluid-filled cylindrical shell with internal flowing fluid is studied. The Donnell non-linear shallow shell equations are used to study a simply supported cylindrical shell subjected to both lateral and axial time-dependent loads with internal flowing fluid. The fluid is assumed to be inviscid and incompressible and the flow isentropic and irrotational. An expansion with eight degrees of freedom, containing the fundamental, companion, gyroscopic and five axisymmetric modes is used to describe the lateral displacement of the shell. The Galerkin method is used to obtain the nonlinear equations of motion which are, in turn, solved by the Runge-Kutta method. First, the parametric linear equations are used to study the influence of geometry and physical properties on the natural frequencies, critical flow and critical circumferential wavenumber. Secondly, numerical methods are used to describe the influence of geometric characteristics on the non-linear frequency-amplitude relations of the shell. The results obtained show the influence of the geometric parameters on the vibration characteristics of the shell and can be used as a basic tool for design of cylindrical shells in a dynamic environment.

scholarly journals Non-linear Vibrations of Deep Cylindrical Shells by thep-Version Finite Element Method

2010 ◽  
Vol 17 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Pedro Ribeiro ◽  
Bruno Cochelin ◽  
Sergio Bellizzi
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Cylindrical Shells ◽  
Element Formulation ◽  
Fe Model ◽  
Various Boundary Conditions ◽  
Non Linear ◽  
Linear Vibrations

Ap-version shell finite element based on the so-called shallow shell theory is for the first time employed to study vibrations of deep cylindrical shells. The finite element formulation for deep shells is presented and the linear natural frequencies of different shells, with various boundary conditions, are computed. These linear natural frequencies are compared with published results and with results obtained using a commercial software finite element package; good agreement is found. External forces are applied and the displacements in the geometrically non-linear regime computed with thep-model are found to be close to the ones computed using a commercial FE package. In all numerical tests thep-FE model requires far fewer degrees of freedom than the regular FE models. A numerical study on the dynamic behaviour of deep shells is finally carried out.

Non-Linear Vibrations of Plates Under Thermal and Mechanical Loads

2005 ◽  
Author(s):  
P. Ribeiro
Keyword(s):  
Equations Of Motion ◽  
Time Integration ◽  
Implicit Time ◽  
Linear Elastic ◽  
Time Integration Method ◽  
Thermal Fields ◽  
Non Linear ◽  
Linear Vibrations ◽  
The Time Domain ◽  
Constitutive Material

The geometrically non-linear vibrations of plates under the combined effect of thermal fields and mechanical excitations are analyzed. With this purpose, an accurate model based on a p-version, hierarchical, first-order shear deformation finite element is employed. The constitutive material of the plates is linear elastic and isotropic. The equations of motion are solved in the time domain by an implicit time integration method. The temperature and the amplitude of the mechanical excitation are varied, and transitions from periodic to non-periodic motions are found.

The Role of Modal Coupling on the Non-Linear Response of Cylindrical Shells Subjected to Dynamic Axial Loads

2000 ◽  
Author(s):  
Paulo B. Gonçalves ◽  
Zenón J. G. N. Del Prado
Keyword(s):  
Dynamic Instability ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Parametric Instability ◽  
Compressive Load ◽  
Basins Of Attraction ◽  
Dynamic Component ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Low Dimensional

Abstract This paper discusses the dynamic instability of circular cylindrical shells subjected to time-dependent axial edge loads of the form P(t) = P0+P1(t), where the dynamic component p1(t) is periodic in time and P0 is a uniform compressive load. In the present paper a low dimensional model, which retains the essential non-linear terms, is used to study the non-linear oscillations and instabilities of the shell. For this, Donnell’s shallow shell equations are used together with the Galerkin method to derive a set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge-Kutta method. To study the non-linear behavior of the shell, several numerical strategies were used to obtain Poincaré maps, stable and unstable fixed points, bifurcation diagrams and basins of attraction. Particular attention is paid to two dynamic instability phenomena that may arise under these loading conditions: parametric instability and escape from the pre-buckling potential well. The numerical results obtained from this investigation clarify the conditions, which control whether or not instability may occur. This may help in establishing proper design criteria for these shells under dynamic loads, a topic practically unexplored in literature.

On the Non-Linear Dynamics of a Traveling Cable With Small Sag

1995 ◽  
Author(s):  
Christoph G. Reuter ◽  
Peter Hagedorn
Keyword(s):  
Equations Of Motion ◽  
Steady State Solution ◽  
Extended Model ◽  
Transport Velocity ◽  
Non Linear ◽  
Mechanical Models ◽  
Linear Vibrations ◽  
Technical Systems ◽  
Inertia Forces ◽  
Made In

Abstract Traveling cables or threadlines appear in a number of technical applications such as textile machinery, V-belts, ski lifts, funiculars and also in simple models of traveling webs in paper machinery. The mechanical models used so far, most often neglect the effect of sag due to the weight of the cable, although it is well known that in some cases it may be quite important. In this paper, the authors develop a particularly simple model for translating cables using the assumption that the longitudinal inertia forces are negligible in comparison to the transversal inertia forces if the sag of the cable is sufficiently small. This assumption has already been made in a study of linear vibrations of stationary cables in 1970 by Irvine & Caughey. This lead to surprising results which have also been verified experimentally in the laboratory. The extended model presented in this paper includes gyroscopic and nonlinear terms in the equations of motion, related to the cable transport velocity and geometric nonlinearities. As a particular case (zero longitudinal speed and linear theory) the model of Irvine & Caughey is again contained in the present analysis. The linear and non-linear vibrations about a steady state solution are studied. The results show some interesting features which may also be relevant to technical systems if the transport speed is sufficiently high.

Hunting stability analysis of a railway vehicle system using a novel non-linear creep model

2012 ◽  
Vol 226 (6) ◽  
pp. 612-629 ◽  
Author(s):  
Yung-Chang Cheng
Keyword(s):  
Degrees Of Freedom ◽  
Lateral Displacement ◽  
Creep Model ◽  
Railway Vehicle ◽  
Vehicle Speed ◽  
System Parameters ◽  
Proposed Model ◽  
Linear Creep ◽  
Non Linear ◽  
Six Dof

A non-linear creep model that considers non-constant creep coefficients that vary as a function of vehicle speed is derived using Hertz contact theory, Kalker’s linear theory and a heuristic non-linear creep model. The proposed model is created by modifying the heuristic non-linear creep model by adding a linear creep moment and the semi-axis lengths in the non-linearity of the saturation constant. In this paper, the vehicle is modeled by a system with 28 degrees of freedom, taking into consideration the lateral displacement, vertical displacement, roll angle and yaw angle of each wheelset, the truck frames and car body. To analyze the respective effects of the major system parameters on the vehicle dynamics, the 28 degree-of-freedom (DOF) system is reduced to a 25-DOF model, by excluding designated subsets of the system parameters. The accuracy of the present analysis is verified by comparing a six-DOF system and the current numerical results with results in the literature. The effects of suspension parameters of a vehicle on the critical hunting speeds evaluated by the currently proposed model, the traditional non-linear creep model and the linear creep model are illustrated. In most cases, the obtained results show that the critical hunting speed evaluated using the new non-linear creep model is greater than that derived using the traditional non-linear creep model. Additionally, the critical hunting speed evaluated using the linear creep model is higher than that evaluated using the currently proposed non-linear creep model.

Effect of a Dent of Different Sizes and Angles of Inclination on Buckling Strength of a Short Stainless Steel Cylindrical Shell Subjected to Uniform Axial Compression

2007 ◽  
Vol 10 (5) ◽  
pp. 581-591 ◽  
Author(s):  
B. Prabu ◽  
N. Bujjibabu ◽  
S. Saravanan ◽  
A. Venkatraman
Keyword(s):  
Stainless Steel ◽  
Cylindrical Shell ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
Buckling Analysis ◽  
Buckling Strength ◽  
Non Linear ◽  
Geometrical Imperfections ◽  
Steel Cylindrical Shell

Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells, but in this paper only effect of a dent on strength of a short (L / D ∼1 and R/t = 280) stainless steel cylindrical shell is considered for analysis. The dent is modeled on the FE surface of perfect cylindrical shell for different angles of inclination and sizes at half the height of cylindrical shell. The cylindrical shells with a dent are analyzed using non-linear static buckling analysis. From the results it is found that in case of shorter dents, size and angle of inclination dents do not have much effect on static buckling strength of thin cylindrical shells, where as in the case of long dents, size and angle of inclination of dents have significant effect. But both short and long dents reduce the static buckling strength drastically.

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