Nonlinear Vibrations of Partially Fluid-Filled Cylindrical Shells

2010 ◽  
Author(s):  
Paulo B. Gonc¸alves ◽  
Frederico M. A. da Silva ◽  
Zeno´n J. G. N. del Prado
Keyword(s):  
Nonlinear Vibration ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Hydrodynamic Pressure ◽  
Vibration Modes ◽  
Internal Fluid ◽  
Irrotational Motion ◽  
Low Dimensional ◽  
The Galerkin Method ◽  
Modal Solution

The present work investigates the nonlinear dynamic behavior and instabilities of partially fluid-filled cylindrical shell subjected to lateral pressure. Donnell shallow shell theory is employed to model the shell. The fluid is modeled as non-viscous and incompressible and its irrotational motion is described by a velocity potential which satisfies the Laplace equation. A discrete low-dimensional model for the nonlinear vibration analysis of thin cylindrical shells is derived to study the shell vibrations. First, a general expression for the nonlinear vibration modes that satisfy all the relevant boundary, continuity and symmetry conditions is derived using a perturbation procedure validated in previous studies and then the Galerkin method is used to discretize the equations of motion. The same modal solution is used to derive the hydrodynamic pressure on the shell wall. The influence played by the height of the internal fluid on the natural frequencies, nonlinear shell response and bifurcations is examined.

Nonlinear Dynamics of Functionally Graded Cylindrical Shells With Internal Fluid

2015 ◽  
Author(s):  
Frederico M. A. Silva ◽  
Roger Otávio P. Montes ◽  
Paulo B. Gonçalves ◽  
Zenón J. G. N. del Prado
Keyword(s):  
Cylindrical Shell ◽  
Lateral Displacement ◽  
Equations Of Motion ◽  
Axial Loading ◽  
Functionally Graded ◽  
Displacement Fields ◽  
Internal Fluid ◽  
Graded Material ◽  
Low Dimensional ◽  
The Galerkin Method

This work analyzes the nonlinear vibrations of a simply supported functionally graded cylindrical shell considering the effects of an internal fluid and static preloading. The cylindrical shell is subjected to a time dependent axial loading. The fluid is considered to be incompressible, non-viscous and irrotational and its effect on the shell wall is obtained using the potential flow theory. The shell is modeled by Donnell nonlinear shallow shell theory. The axial and circumferential displacement fields are described in terms of lateral displacement, thus generating a low-dimensional model, while the lateral displacement field is determined by a perturbation procedure which provides a general expression for the nonlinear vibration modes. These modal expansions satisfy the boundary and symmetry conditions of the problem. The discretized equations of motion are obtained by applying the Galerkin method. Various numerical techniques are employed to obtain the resonance curves and time responses of the cylindrical shell, showing the influence of the geometry, the internal fluid, static preloading and functionally graded material law on the shell dynamics and stability.

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.

Nonlinear Vibrations and Multiple Resonances of Fluid-Filled, Circular Shells, Part 1: Equations of Motion and Numerical Results

2000 ◽  
Vol 122 (4) ◽  
pp. 346-354 ◽  
Author(s):  
M. Amabili ◽  
F. Pellicano ◽  
A. F. Vakakis
Keyword(s):  
Present Model ◽  
Equations Of Motion ◽  
Travelling Wave ◽  
Internal Resonances ◽  
Internal Fluid ◽  
Circumferential Displacement ◽  
Circular Cylindrical Shells ◽  
Frequency Relationship ◽  
The Galerkin Method ◽  
First Time

The 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 four ordinary differential equations by means of the Galerkin method. The radial deflection of the shell is expanded by using a basis of four linear modes. The effect of internal fluid is also investigated. The equations of motion are studied by using a code based on the Collocation Method. The present model is validated by comparison of some results with others available. A water-filled shell presenting the phenomenon of 1:1:1:2 internal resonances is investigated for the first time; it shows intricate and interesting dynamics. [S0739-3717(00)01204-6]

scholarly journals A New Analytical Approach for Nonlinear Global Buckling of Spiral Corrugated FG-CNTRC Cylindrical Shells Subjected to Radial Loads

2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Global Buckling ◽  
Homogenization Model ◽  
Corrugated Structure ◽  
The Galerkin Method

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

A Method for Fatigue Analysis of Pipelines on Topsides of FPSO Systems

2005 ◽  
Author(s):  
Pol Spanos ◽  
Alba Sofi ◽  
Juan Wang ◽  
Berry Peng
Keyword(s):  
Fatigue Life ◽  
Random Vibration ◽  
Equations Of Motion ◽  
Plug Flow ◽  
Fatigue Curve ◽  
Sea Waves ◽  
Random Loading ◽  
Euler Beam ◽  
Stress Spectrum ◽  
The Galerkin Method

Pipelines located on the decks of FPSO systems are exposed to damage due to sea waves induced random loading. In this context, a methodology for estimating the fatigue life of conveying-fluid pipelines is presented. The pipeline is subjected to a random support motion which simulates the effect of the FPSO heaving. The equation of motion of the fluid-carrying pipeline is derived by assuming small amplitude displacements, modeling the empty pipeline as a Bernoulli-Euler beam, and adopting the so-called “plug-flow” approximation for the fluid (Pai¨doussis, 1998). Random vibration analysis is carried out by the Galerkin method selecting as basis functions the natural modes of a beam with the same boundary conditions as the pipeline. The discretized equations of motion are used in conjunction with linear random vibration theory to compute the stress spectrum for a generic section of the pipeline. For this purpose, the power spectrum of the acceleration at the deck level is determined by using the Response Amplitude Operator of the FPSO hull. Finally, the computed stress spectrum is used to estimate the pipeline fatigue life employing an appropriate S-N fatigue curve of the material. An illustrative example concerning a pipeline simply-supported at both ends is included in the paper.

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