An efficient numerical method for examining the stability of linear time varying systems modeled by finite element (FE) methods is presented in this paper. Parametric instability of pipes conveying pulsating fluid flow is studied using multivariable Floquet-Lyapunov theory. In order to solve large size problems, the system matrices are reduced to a smaller size by transforming to modal coordinates using modal vectors. This transformation preserves the stability information and the reduced matrix is used for the evaluation of the monodromy matrix. For dealing with large systems with parametric excitations, it is found that proposed method is numerically efficient. © 2003 Elsevier B.V. All rights reserved.

Chandramouli Padmanabhan

Department of Mechanical Engineering

Natrajan Ganesan

Approximation theory

Computational complexity

Computer simulation

Degrees of freedom (mechanics)

Mathematical models

Parameter estimation

Problem solving

PIPE DYNAMICS

Pulsating flow

Flow of fluids

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IIT Madras

Finite Elements in Analysis and Design

Dynamic response of spinning tapered Timoshenko beams using modal reduction

International Journal for Numerical Methods in Engineering

A modal and damping analysis of viscoelastic Timoshenko tubes conveying fluid

LAPACK Users' Guide

Chaotic motions of a simply supported nonlinear pipe conveying fluid with harmonic velocity fluctuations are investigated. The motions are investigated in two flow velocity regimes, one below and above the critical velocity for divergence. Analyses are carried out taking into account single mode and two mode approximations in the neighbourhood of fundamental resonance. The amplitude of the harmonic velocity perturbation is considered as the control parameter. Both period doubling sequence and a sudden transition to chaos of an asymmetric period 2 motion are observed. Above the critical velocity chaos is explained in terms of periodic motion about the equilibrium point shifting to another equilibrium point through a saddle point. Phase plane trajectories, Poincaré maps and time histories are plotted giving the nature of motion. Both single and two mode approximations essentially give the same qualitative behaviour. The stability limits of trivial and nontrivial solutions are obtained by the multiple time scale method and harmonic balance method which are in very good agreement with the numerical results. © 1996 Kluwer Academic Publishers.

Nonlinear Dynamics

Chaotic oscillations in pipes conveying pulsating fluid

Computers & Structures

An arbitrary lagrangian-eulerian velocity potential formulation for fluid-structure interaction

Efficient computation of parametric instability regimes in systems with a large number of degrees-of-freedom

Journal	Finite Elements in Analysis and Design
ISSN	0168874X
Open Access	No