Vibration analysis of bi-layered FGM cylindrical shells

In the present study, a vibration frequency analysis of a bi-layered cylindrical shell composed of two independent functionally graded layers is presented. The thickness of the shell layers is assumed to be equal and constant. Material properties of the constituents of bi-layered functionally graded cylindrical shell are assumed to vary smoothly and continuously through the thickness of the layers of the shell and are controlled by volume fraction power law distribution. The expressions for strain–displacement and curvature–displacement relationships are utilized from Love’s first approximation linear thin shell theory. The versatile Rayleigh–Ritz approach is employed to formulate the frequency equations in the form of eigenvalue problem. Influence of material distribution in the two functionally graded layers of the cylindrical shells is investigated on shell natural frequencies for various shell parameters with simply supported end conditions. To check the validity, accuracy and efficiency of the present methodology, results obtained are compared with those available in the literature.     

Study of dynamic processes in a rigid cylindrical vessel with elastic bottom partially filled with a liquid

The paper reports on the results from an experimental study of the nonlinear deformation of the elastic bottom of and the free liquid surface in a rigid shell. The shell and liquid interact with each other and with a cluster of gas bubbles produced by vibrational excitation __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 114–120, November 2006.     

Penetration of an elastic circular cylindrical shell into an incompressible liquid

The plane unsteady problem of impact of a thin elastic cylindrical shell on the surface of an ideal incompressible liquid is considered. The initial stage of interaction between the body and the liquid when the stresses in the shell attain peak values is studied. The problem is treated in a linearized formulation and is solved numerically by the normal modes method within the framework of the Wagner approach. The numerical results agree with experimental data for various types of circular cylindrical shells made from mild steel. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 186–197, November–December, 1999.     

Model of bending of a hydrostatically compressed shell near its stability threshold

A simplified model of bending dynamics of a hydrostatically compressed thin shell near the threshold of stability of its form is constructed within the framework of the nonlinear theory of elasticity. Conditions of existence and explicit expressions for spatially localized perturbations and patterns composed of dents on the shell surface, which are “precursors” of subsequent changes in the shell form, are found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 124–134, November–December, 2007.     

Vibration effects of the dynamic interaction between a gas-liquid medium and elastic shells

The paper presents the results of experimental investigations of regimes of the nonlinear deformation of elastic shells filled with a liquid. These regimes are due to the interaction of local clusters of gas bubbles formed in a vibrating liquid with the vibration modes of an elastic shell excited in the circumferential and longitudinal directions. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 67–73, July, 2000.     

The effect of the reinforcement structure on the heat conductivity of shells of revolution with a system of tubes filled with a liquid heat-transfer agent

The initial boundary-value heat-conduction problem for shells reinforced by tubes filled with a flowing liquid heat-transfer agent is considered. The dependence of the coefficients in the heat-conduction equations on the thermophysical characteristics of the composition phases, reinforcement parameters, and shell geometry is studied. A comparative analysis of the stationary temperature fields in thin shells of revolution of different Gaussian curvature is performed for various reinforcement structures and heat-exchange regimes. It is shown that the temperature distribution in the shells depends strongly on the reinforcement structure and the shell geometry, which opens up new possibilities of designing optimal structures. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 168–177, July–August, 2000.     

Use of particle image velocimetry to study heterogeneous drag reduction

Large polymer filaments can form when drag reducing polymers are injected through wall slots. The presence of these structures enhances the performance of the drag reducing function by mechanisms which are not understood. This paper shows how particle image velocimetry (PIV) techniques can be used to study changes in the configuration of the injected polymer and in the structure of the velocity field with increasing drag reduction. The filaments are found to behave as solid bodies which break up in high shear regions close to a boundary. The breakup process provides an explanation of why the filaments are not observed close to a wall and offers the possibility of providing a heterogeneous distribution of small aggregates of polymers which could be more effective than uniformly distributed molecules as suggested by Hoyer and Gyr (J Non-Newton Fluid Mech 65:221–240, 1996; J Fluids Eng 120:818–823, 1998), Dunlop and Cox (Phys Fluids 20:203–213, 1977) and Vlachogiannis et al. (Phys Fluid 15:3786–3794, 2004). PIV measurements show dramatic qualitative changes in the velocity patterns at maximum drag reduction.     

Parametric vibrations of cylindrical shells subject to geometrically nonlinear deformation: multimode models

The nonlinear parametric vibrations of cylindrical shell are described by the Donnell–Mushtari–Vlasov equations. The motions are represented as a mode expansion. Discretization is performed using the Bubnov–Galerkin method. The describing-function method is used to study traveling waves and nonlinear normal modes in systems with and without dissipation     

An Analytical Model for Capillary Pressure–Saturation Relation for Gas–Liquid System in a Packed-Bed of Spherical Particles

Capillary pressure is considered in packed-beds of spherical particles. In the case of gas–liquid flows in packed-bed reactors, capillary pressure gradients can have a significant influence on liquid distribution and, consequently, on the overall reactor performance. In particular, capillary pressure is important for non-uniform liquid distribution, causing liquid spreading as it flows down the packing. An analytical model for capillary pressure–saturation relation is developed for the pendular and funicular regions and the factors affecting capillary pressure in the capillary region are discussed. The present model is compared to the capillary pressure models of Grosser et al. (AIChE J., 34:1850–1860, 1988) and Attou and Ferschneider (Chem. Eng. Sci., 55:491–511, 2000) and to the experiments of Dodds and Srivastava (Part Part Syst. Charact., 23:29–39, 2006) and Dullien et al. (J. Colloid Interface Sci., 127:362–372, 1989). The non-homogeneity of real packings is considered through particle size and porosity distributions. The model is based on the assumption that the particles are covered with a liquid film, which provides hydrodynamic continuity. This makes the model more suitable for porous or rough particles than for non-porous smooth particles. The main improvements of the present model are found in the pendular region, where the liquid dispersion due to capillary pressure gradients is most significant. The model can be used to improve the hydrodynamic models (e.g., CFD and cellular automata models) for packed-bed reactors, such as trickle-bed reactors, where gas, liquid, and solid phases are present. Models for such reactors have become quite common lately (Sáez and Carbonell, AIChE J., 31:52–62, 1985; Holub et al., Chem. Eng. Sci, 47, 2343–2348, 1992; Attou et al., Chem. Eng. Sci., 54:785–802, 1999; Iliuta and Larachi, Chem. Eng. Sci., 54:5039–5045, 1999, IJCRE 3:R4, 2005; Narasimhan et al., AIChE J., 48:2459–2474, 2002), but they still lack proper terms causing liquid dispersion.     

Nonlinear parametric vibrations of orthotropic cylindrical shells interacting with a pulsating fluid flow

The paper addresses the dynamic interaction of an orthotropic cylindrical shell with the fluid flowing inside. Its velocity has a constant component and low-amplitude pulsations. A method to calculate the characteristics of the parametric vibrations of the shell when the velocity of the fluid is close to critical is proposed. The amplitude–frequency characteristics of the shell–fluid system at fundamental parametric resonance are determined     

Filtration of a liquid with free boundaries in unbounded regions

The variational method is used to solve problems of filtration of a liquid in unbounded regions (inflow of a liquid to a drain, filtration of a liquid through a plain earth dam on a permeable base, etc.). Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 188–195, September–October, 2000.     

Dynamic behavior of liquids and gases in conical shells in a vibrational force field

An experimental study is made of specific features of the motion of the free surface of liquid in different conical shells, the formation, motion, and local accumulation of gas bubbles in the shells, and the character of random motion of the gas-liquid medium in a vibrational force field. It is established that the liquid moves along the horizontal as well as the vertical axes under certain conditions when axisymmetric modes of vibration of the free surface are excited. The main characteristics of the dynamic behavior of a gas-liquid medium in a compound conical shell having the form of a de Laval nozzle are examined for the case when the medium forms a nonlinear oscillatory “liquid-gas” system that is dynamically stable. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 23–29, February, 1999.     

Nonlinear problems of the dynamics of elastic shells partialiy filled with a liquid

Theoretical and experimental investigations of the nonlinear vibrations and dynamic stability of thin shells partially filled with a liquid are reviewed. The paper deals with the basic laws governing the dynamic high-deflection deformation of carrying shell structures and the considerable vibrations of the free liquid surface due to the natural, forced, and parametrically excited vibrations of the combined system and also due to impulse loads acting on the carrying object. The nonlinear dynamic interaction of shells with a liquid filler is analyzed with allowance for the wave motions of the free liquid surface. S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 4, pp. 3–34, April, 2000.     

Elastoplastic state of flexible spherical shells with a reinforced elliptic hole

The elastoplastic state of a thin spherical shell weakened by an elliptic hole is analyzed. Finite deflections are considered. The hole is reinforced with a thin ring. The shell is made of an isotropic homogeneous material. The load is internal pressure. A relevant problem is formulated and solved numerically with allowance for physical and geometrical nonlinearities. The distribution of stresses, strains, and displacements along the elliptic boundary and in the zone of their concentration is studied. The stress–strain state of the shell near the hole is analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 93–101, December 2008.     

Buckling behavior of an underwater storage vessel

Optimum design considerations for an underwater storage vessel to contain liquid gases and oils led to the assessment of an axisymmetric shell of revolution—the Echinodome or drop shape. Analytical treatment of the various types of loading to which the shell could be subjected indicated that buckling was the more critical design criteria. A small GRP spherical shell under hydrostatic pressure was investigated for its buckling behavior both experimentally and theoretically. In the experimental approach surface strains were measured using electric resistance strain-gage rosettes on the inner and outer surfaces. Predictions of critical buckling pressure were made from the experimental results using a Southwell technique and numerically by the finite-element method. The influence of the results on design procedures is discussed. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Solution of contact problems on the basis of a refined theory of plates and shells

Solutions of contact mixed boundary-value problems for a plate and for a cylindrical shell are given. These solutions are obtained with the use of equations for shells constructed by expanding solutions of elasticity theory equations with respect to the Legendre polynomials. Results of numerical simulations of the stress state in the vicinity of points with changing conditions on the frontal faces of the shell are presented. The results obtained are compared with analytical solutions of elasticity theory problems and with solutions obtained on the basis of the classical equations of the shell theory. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 169–176, September–October, 2008.     

Microstructure observation and mechanical behavior modeling for limnetic nacre

In the present research, microstructure of akind of limnetic shell （Hyriopsis cumingii） is observed and measured by using the scanning electron microscopy, and mechanical behavior experiments of the shell nacre are carried out by using bending and tensile tests. The dependence of mechanical properties of the shell nacre on its microstructure is analyzed by using a modified shear-lag model, and the overall stress-strain relation is obtained. The experimental results reveal that the mechanical properties of shell nacre strongly depend on the water contents of the limnetic shell. Dry nacre shows a brittle behavior, whereas wetting nacre displays a strong ductility. Compared to the tensile test, the bending test overestimates the strength and underestimates the Young＇s modulus. The modified shear-lag model can characterize the deformation features of nacre effectively.     

Contact holographic interferometer for studying the deformation of small-curvature shells of revolution

The strains of a curvilinear surface are determined using holographic interferometry. Equations are derived to interpret the interference fringes for a shell of revolution. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 176–182, May–June, 2006.     

Boundary-value problems of longitudinal vibrations of circular cylindrical shells

This paper presents a rigorous formulation of boundary-value problems of longitudinal-radial vibration: approximate equations of vibration, boundary conditions on ends with different types of support, and initial conditions. Formulas are presented to calculate the stress-strain state of a shell through the unknown functions. Results are obtained on the basis of a rigorous mathematical approach in which the shell is examined as a three-dimensional body. Translated from Prikladnaya Mekhanika, Vol. 34, No. 12, pp. 34–40, December, 1998.     

Nonlinear vibrations of viscoelastic cylindrical shells taking into account shear deformation and rotatory inertia

The vibration problem of a viscoelastic cylindrical shell is studied in a geometrically nonlinear formulation using the refined Timoshenko theory. The problem is solved by the Bubnov–Galerkin procedure combined with a numerical method based on quadrature formulas. The choice of relaxation kernels is substantiated for solving dynamic problems of viscoelastic systems. The numerical convergence of the Bubnov–Galerkin procedure is examined. The effect of viscoelastic properties of the material on the response of the cylindrical shell is discussed. The results obtained by various theories are compared.