Thermomechanical vibration analysis of a functionally graded shell with flowing fluid

This paper reports the results of an investigation into the vibration of functionally graded cylindrical shells with flowing fluid, embedded in an elastic medium, under mechanical and thermal loads. By considering rotary inertia, the first-order shear deformation theory (FSDT) and the fluid velocity potential, the dynamic equation of functionally graded cylindrical shells with flowing fluid is derived. Here, heat conduction equation along the thickness of the shell is applied to determine the temperature distribution and material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The equations of eigenvalue problem are obtained by using a modal expansion method. In numerical examples, effects of material composition, thermal loading, static axial loading, flow velocity, medium stiffness and shell geometry parameters on the free vibration characteristics are described. The new features in this paper are helpful for the application and the design of functionally graded cylindrical shells containing fluid flow.     

CORRECTION FOR HOUSNER’S EQUATION OF BENDING VIBRATION OF A PIPE LINE CONTAINING FLOWING FLUID

This paper points out that Housner’s equation of bending vibration of a pipe linecontaining flowing fluid is approximate and makes correction to it.An exact form ofthe vibration equation is given.     

Rotating cylinder in a flowing viscous incompressible fluid

New results are obtained in the problem of flow of a viscous fluid past a rotating cylinder by numerical solution of the Navier—Stokes equations for Reynolds numbers 10 Re 100. The drag and lift have been calculated. The oscillatory flow regime in the wake behind a fixed cylinder is investigated for Re = 80. The Strouhal number for auto-oscillations is 0.16.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–21, January–February, 1982.I am grateful to G. I. Petrov and V. Ya. Shkadov for constant interest in the work and helpful discussions.     

Instability in a spherical fluid shell

Summary The model considered is a collapsing or expanding spherical shell of incompressible fluid with constant total energy. The stability of its surfaces is studied by the usual perturbation method. There is a non-uniform acceleration through the shell which satisfies Taylor's criterion for stability at both surfaces. The inner surface however fails to satisfy Birkhoff's condition during collapse and is in general algebraically unstable. The stability of the outer surfaces is found to depend on the ratio of shell thickness to radius. For a thin shell the ratio of the initial perturbation amplitudes on the two surfaces is found to govern the motion at each surface, while for a thick shell, and for harmonics of order higher than the second, the two surfaces are independent, the inner surface being unstable during collapse and the outer surface unstable during expansion.     

Uniqueness of solution and well-posedness of the problem of determining the fastening parameters of a pipe containing flowing fluid

The inverse problem of determining the type and parameters of fastening of the pipe ends from the natural frequencies of the pipe flexural vibrations is formulated and solved for the case of fluid flowing through the pipe. The uniqueness of the solution of the problem is proved, and the Tikhonov well-posedness of the problem is shown. A method for solving the inverse problem is proposed, and examples of the solution are given.     

Stress state of a cylindrical shell of variable thickness with a branch pipe

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 1, pp. 70–74, January, 1988.     

Development of a thixotropic fluid flow in a pipe

This paper deals with the interaction between the modifications of the internal structure of a thixotropic fluid and the flow development along a pipe. The experimental set-up consists of a pipe, where a flow of thixotropic fluid is provided from a large vessel. The axial velocity distribution was determined using particle image velocimetry technique and ultrasonic velocity profile monitor. At the entrance section, the fluid is assumed to be in a homogeneous structural state corresponding to a high shear rate. The experimental results show a progressive flatness of the velocity profiles due to the aggregation of the structural elements of the fluid. The flow evolution is governed essentially by the kinetics of aggregation and segregation since the associated time scales are longer than the relaxation time of the flow. Received: 23 November 2000/Accepted: 20 May 2001     

Hydroelastic stability of a rectangular plate interacting with a layer of ideal flowing fluid

The three-dimensional formulation of the problem on the natural vibrations and stability of an elastic plate which interacts with a quiescent or flowing fluid is represented and a finite element algorithm of its numerical implementation is proposed. The governing equations, which describe vortex-free ideal fluid dynamics in the case of small perturbations, are written in terms of the perturbation velocity potential and transformed using the Bubnov–Galerkin method. The plate strains are determined on the basis of the Timoshenko theory. The variational principle of virtual displacements which takes into account the work done by inertial forces and the hydrodynamic pressure is used for the mathematical formulation of the dynamic problem of elastic structure. The solution of the problem is reduced to calculations and an analysis of complex eigenvalues of a coupled system of two equations. The effect of the fluid layer height on the eigenfrequencies and the critical velocities of the loss of stability is estimated numerically. It is shown that there exist different types of instability determined by combinations of the kinematic boundary conditions prescribed at the plate edges.     

Stability of elastic cylindrical shells interacting with flowing fluid

The buckling modes of a finite cylindrical shell interacting with a moving fluid are studied. Two types of instability are analyzed: quasistatic (divergence) and dynamic (flutter)     

Behavior of a cylindrical shell with fluid under momentary loads

All-Union Correspondence Institute of the Food Industry, Moscow. Translated from Prikladnaya Mekhanika, Vol. 25, No. 7, pp. 50–57, July, 1989.     

Motion of a permeable shell in a spherical container filled with non-Newtonian fluid

This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied.Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components,the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.