Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

Ordinary differential equations of the first order linear differential equations complex numbers and linear algebra simultaneous linear differential equations numerical methods the descriptive theory of nonlinear differential equations mechanical systems and electric circuits Fourier series Fourier integrals and Fourier transforms the Laplace transformation partial differential equations Bessel functions and Legendre polynomials applications and further properties of matrices vector analysis the calculus of variations analytic functions of a complex variable infinite series in the complex plane the theory of residues conformal mapping.

Advanced Engineering Mathematics. By C. R. Wylie. Pp. xiv, 813. 1966. (McGraw-Hill.)

FSI research in pipeline systems – A review of the literature

Carbon nanotubes will have extensive application in all areas of nano-technology, and in particular in the field of nano-fluidics, wherein they can be used for molecular separation, nano-scale filtering and as nano-pipes for conveying fluids. In the field of nano-medicine, nanotubes can be functionalized with various types of receptors to act as bio-sensors for the detection and elimination of cancer cells, or be used as bypasses and even neural connections. Modelling fluid flow inside nanotubes is a very challenging problem, since there is a complex interplay between the motion of the fluid and the stability of the walls. A critical issue in the design of nano-fluidic devices is the induced vibration of the walls, due to the fluid flow, which can promote structural instability. It has been established that the resonant frequencies depend on the flow velocity. We have studied, for the first time, the flow of viscous fluids through multi-walled carbon nanotubes, using the Euler–Bernoulli classical beam theory to model the nanotube as a continuum structure. Our aim has been to compute the effect of the fluid flow on the structural stability of the nanotubes, without having to consider the details of the fluid–walls interaction. The variations of the resonant frequencies with the flow velocity are obtained for both unembedded nanotubes, and when they are embedded in an elastic medium. It is found that a nanotube conveying a viscous fluid is more stable against vibration-induced buckling than a nanotube conveying a non-viscous fluid, and that the aspect ratio plays the same role in both cases.

https://iopscience.iop.org/article/10.1088/0022-3727/40/22/027/pdf

Computational modelling of the flow of viscous fluids in carbon nanotubes

Initially tensioned orthotropic cylindrical shells conveying fluid: a vibration analysis

A general approach to modelling the vibration of prestressed thin cylindrical shells conveying fluid is presented. The steady flow of fluid is described by the classical potential flow theory, and the motion of the shell is represented by Sanders' theory of thin shells. A strain-displacement relationship is deployed to derive the geometric stiffness matrix due to the initial stresses caused by hydrostatic pressure. Hydrodynamic pressure acting on the shell is developed through dynamic interfacial coupling conditions. The resulting equations governing the motion of the shell and fluid are solved by a finite element method. This model is subsequently used to investigate the small-vibration dynamic behaviour of prestressed thin cylindrical shells conveying fluid. It is validated by comparing the computed natural frequencies, within the linear region, with existing reported experimental results. The influence of initial tension, internal pressure, fluid flow velocity and the various geometric properties is also examined.

Vibration of prestressed thin cylindrical shells conveying fluid

Finite element analysis of the vibratory characteristics of cylindrical shells conveying fluid

A comparative study of the relative performance of several different axisymmetric finite elements, when applied to the dynamic problem of thin cylindrical shells conveying fluid, is presented. The methods used are based on (1) the Sanders' theory of thin shells and the potential flow theory, and (2) the theory of elasticity and the Euler equations. The elements studied are: linear, paralinear, parabolic and cubilinear. Extensive comparison with experiment is carried out for the free vibration of cylindrical shells in the absence of, and containing, quiescent and flowing fluid. The analysis of the relative competence of these elements is presented for shell length-to-radius ratios 1.95≤L/R≤32, shell radius-to-thickness ratios 10≤R/h≤375 and boundary conditions: clamped–clamped, clamped–free and simply supported. We show that natural frequencies of thin cylindrical shells in the absence of, and containing, quiescent and flowing fluid can be assessed accurately when using two- and eight-noded elements, and the latter are also applicable to the dynamic problem of thick cylindrical shells. Copyright © 2002 John Wiley & Sons, Ltd.

Y.L. Zhang

Papers

Initially tensioned orthotropic cylindrical shells conveying fluid: a vibration analysis

Vibration of prestressed thin cylindrical shells conveying fluid

Finite element analysis of the vibratory characteristics of cylindrical shells conveying fluid

A comparative study of axisymmetric finite elements for the vibration of thin cylindrical shells conveying fluid

An experimental study of the effects of pulsating and steady internal fluid flow on an elastic tube subjected to external vibration