Effect of non-linear modal interaction on the dynamic instability of axially excited cylindrical shells

2004 ◽  
Vol 82 (31-32) ◽  
pp. 2621-2634 ◽  
Author(s):  
P.B. Gonçalves ◽  
Z.G. del Prado
Keyword(s):  
Dynamic Instability ◽  
Cylindrical Shells ◽  
Modal Interaction ◽  
Non Linear

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.

The Effect of Internal Flowing Fluid on the Non-Linear Behavior of Orthotropic Circular Cylindrical Shells

2014 ◽  
Vol 706 ◽  
pp. 54-68 ◽  
Author(s):  
Z.J.G.N. del Prado ◽  
A.L.D.P. Argenta ◽  
F.M.A. da Silva ◽  
Paulo Batista Gonçalves
Keyword(s):  
Dynamic Instability ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Great Influence ◽  
Industrial Applications ◽  
Flowing Fluid ◽  
Non Linear ◽  
Circular Cylindrical Shells ◽  
Lateral Displacements ◽  
Orthotropic Shells

The great use of circular cylindrical shells for conveying fluid in modern industrial applications has made of them an important research area in applied mechanics. Many researchers have studied this problem, however just a reduced number of these works have as object the analysis of orthotropic shells. Although most investigations deal with the analysis of elastic isotropic shells in contact with internal and external quiescent or flowing fluid, several modern and natural materials display orthotropic properties and also stiffened cylindrical shells can be treated as equivalent uniform orthotropic shells. In this work, the influence of internal flowing fluid on the dynamic instability and non-linear vibrations of a simply supported orthotropic circular cylindrical shell subjected to axial and lateral time-dependent loads is studied. To model the shell, the Donnell’s non-linear shallow shell theory without considering the effect of shear deformations is used. A model with eight degrees of freedom is used to describe the lateral displacements of the shell. The fluid is assumed to be incompressible and non-viscous and the flow to be isentropic and irrotational. 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 presence of the internal fluid and material properties have a great influence on the vibration characteristics of the shell.

Sign in / Sign up

Export Citation Format

Share Document