Vast literature is available for modeling the coupled fluid structure interaction involving the flow of a pulsatile fluid through pipes/shells under ambient temperature. In contrast it is found that there is no literature on such problems under the influence of temperature. This paper considers the evaluation of dynamic instability regions due to a flow of pulsating hot fluid through an insulated composite cylindrical shell. A coupled fluid structure interaction model in conjunction with uncoupled thermomechanical model is used for analysis. The system's equations of motion containing periodic coefficients are expressed in modal domain considering linear transformation. Fourth order Runge-Kutta method using Gill's coefficient is adopted to compute the state transition matrix which provides the stability information of the periodic system following the Floquet-Liapunov theory. Pulsatile flow of water at various magnitude of steady state temperature is considered and hence the effect of water temperature on the instability regions is analyzed. The influence of lamina fibre angle on the instability regions is also examined. © 2004 Elsevier Ltd. All rights reserved.

Natrajan Ganesan

Fluid structure interaction

Mathematical models

Matrix algebra

Parameter estimation

Resonance

Runge Kutta methods

Shells (structures)

stability

Thermomechanical treatment

LINEAR TRANSFORMATION

PULSATILE FLUIDS

Composite materials

FIBER REINFORCED COMPOSITE

Fluid flow

Mathematical model

Water

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Composite Structures

A coupled fluid structure interaction problem is analyzed using semi-analytical finite element method involving composite cylindrical shells conveying hot fluid for free vibration and buckling behavior. The system under study is assumed to have a steady flow of hot fluid and the temperature variation is axi-symmetric. First order shear deformation theory is used to model the elastic shells of revolution. Geometric stiffness matrix is evaluated to consider the effects of axi-symmetric temperature variation through the shell continuum due to flow of hot fluid. The fluid domain is modeled using the wave equation. Numerical results of the studies on composite cylindrical shells made of HS-Graphite/Epoxy with two different length to radius ratios and clamped-clamped boundary condition conveying hot fluid are presented. The variation of the natural frequency of the coupled system is evaluated with the steady flow of the hot fluid. The influence of the temperature on the mean axial flow velocity through the shell is critically examined. The critical velocity of the hot fluid and cold fluid which leads to shell instability is compared thus establishing the fact that the lowest critical velocity of the hot fluid coincides with the mode corresponding to the lowest critical thermal buckling temperature. Various fibre angles are also considered in the study and its influence is also examined. © 2003 Elsevier Science Ltd. All rights reserved.

Free vibration and buckling analysis of composite cylindrical shells conveying hot fluid

Flexible pipes conveying fluid are often subjected to parametric excitation due to time-periodic flow fluctuations. Such systems are known to exhibit complex instability phenomena such as divergence and coupled-mode flutter. Investigators have typically used weighted residual techniques, to reduce the continuous system model into a discrete model, based on approximation functions with global support, for carrying out stability analysis. While this approach is useful for straight pipes, modelling based on FEM is needed for the study of complicated piping systems, where the approximation functions used are local in support. However, the size of the problem is now significantly larger and for computationally efficient stability analysis, model reduction is necessary. In this paper, model reduction techniques are developed for the analysis of parametric instability in flexible pipes conveying fluids under a mean pressure. It is shown that only those linear transformations which leave the original eigenvalues of the linear time invariant system unchanged are admissible. The numerical technique developed by Friedmann and Hammond (Int. J. Numer. Methods Eng. Efficient 11 (1997) 1117) is used for the stability analysis. One of the key research issues is to establish criteria for deciding the basis vectors essential for an accurate stability analysis. This paper examines this issue in detail and proposes new guidelines for their selection. © 2003 Elsevier Science Ltd. All rights reserved.

Journal of Sound and Vibration

Model reduction for parametric instability analysis in shells conveying fluid

A new formulation, based on the semi-analytical finite element method, is proposed for elastic shells conveying fluids. The structural equations are based on the shell element proposed by Ramasamy and Ganesan [Comput Struct 70 (1998) 363] while the fluid model is based on velocity potential. Dynamic pressure acting on the walls is derived from Bernoulli's equation. Imposing the requirement that the normal components of velocity of the solid and fluid be equal, introduces fluid-structure coupling. The proposed technique has been validated using results available in the literature. This study shows that instability occurs at a critical fluid velocity corresponding to the shell circumferential mode with the lowest natural frequency and this phenomenon is also independent of the type of structural boundary conditions imposed. © 2002 Elsevier Science Ltd. All rights reserved.

Computers and Structures

A semi-analytical coupled finite element formulation for shells conveying fluids

A coupled formulation based on the semi-analytical finite element technique is developed for composite shells conveying fluid. The structural finite element formulation is from Ramasamy and Ganesan (1998 Computers and Structures 70, 363-376), while the fluid part is modelled by the characteristic wave equation. The fluid part is modelled using a velocity potential formulation and the dynamic pressure acting on the walls is derived from Bernoulli's equation. Impermeability and dynamic condition are imposed on the fluidstructure interface. The finite element equations for the composite shell conveying fluid are validated using available results in the literature. A detailed parametric study is carried out for various boundary conditions as well as for different length-to-radius and radius-to-thickness ratios. © 2002 Elsevier Science Ltd. All rights reserved.

A semi-analytical coupled finite element formulation for composite shells conveying fluids

The finite element code is developed based on the displacement field proposed by Wilkins et al. to find out the natural frequencies and loss factors of fluid filled cylindrical shells with a constrained viscoelastic layer in between two facings made of composite material. The fluid effect on the natural frequencies and loss factors are taken care of by the added mass of the fluid on the structure. Effects of the fluid height, ratio of core to facing thickness and facing fibre orientation on the natural frequencies and loss factors of cylindrical shells are presented.

Journal	Composite Structures
ISSN	02638223
Open Access	No