Axial Impact of Twisted Wire Cables

1977 ◽  
Vol 44 (1) ◽  
pp. 127-131 ◽  
Author(s):  
J. W. Phillips ◽  
G. A. Costello
Keyword(s):  
Boundary Conditions ◽  
Finite Length ◽  
Equations Of Motion ◽  
Laplace Transforms ◽  
Numerical Results ◽  
Longitudinal Impact ◽  
Axial Impact ◽  
Coupled Equations ◽  
Initial And Boundary Conditions ◽  
Twisted Wire

The nonlinear, coupled equations of motion governing the axial and rotational displacements of a straight, single lay, twisted wire cable are presented. Linearization of the equations of motion allows a solution by Laplace transforms which is valid for arbitrary initial and boundary conditions. The longitudinal impact of a finite-length cable fixed at one end is considered in detail, and numerical results for this case are presented.

Free-Edge Plastic Buckling of Axially Compressed Cylindrical Shells

1968 ◽  
Vol 35 (1) ◽  
pp. 73-79 ◽  
Author(s):  
S. C. Batterman
Keyword(s):  
Boundary Conditions ◽  
Finite Length ◽  
Cylindrical Shells ◽  
Free Edge ◽  
Numerical Results ◽  
Negligible Effect ◽  
Tangent Modulus ◽  
Plastic Buckling ◽  
Simple Support ◽  
Axisymmetric Plastic

Axisymmetric plastic buckling of axially compressed cylindrical shells is studied for semi-infinite shells and shells of finite length subject to free-edge boundary conditions. It is shown that the length of the cylinder has a negligible effect on the buckling load. Reductions in buckling stresses from the classical simple-support value are significant, with the amount of reduction dependent on the details of the variation of tangent modulus with stress. Numerical results are presented for cylinders composed of 2024-T4 aluminum and 3003-0 aluminum.

Accounting Viscous Dissipation at Round Tubes Filling

2016 ◽  
Vol 685 ◽  
pp. 191-194
Author(s):  
E.I. Borzenko ◽  
O.Yu. Frolov ◽  
G.R. Shrager
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Dissipative Heating ◽  
Mathematical Basis ◽  
One Dimensional ◽  
Parametric Studies ◽  
Initial And Boundary Conditions ◽  
Formulation Of Problems

The fountain nonisothermal flow of a viscous fluid realized during circular pipe filling is investigated. The mathematical basis of the process is formed by equations of motion, continuity and energy with respective initial and boundary conditions with due account of the temperature dependence of viscosity, the presence of a free boundary and dissipation of mechanical energy. To solve the problem numerically a finite difference method is required. Depending on the values defining the dimensionless parameters the results of parametric studies in temperature, viscosity, dynamic and kinematic characteristics of the flow are shown. Flow patterns for the formulation of problems with different initial and boundary conditions are given. The separation of flow into the zone of spatial flow in the vicinity of the free surface and one dimensional flow away from it, and changing the shape of the free boundary, depending on the level of dissipative heating are demonstrated.

scholarly journals Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 429 ◽  
Author(s):  
Krzysztof Żur ◽  
Piotr Jankowski
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Special Functions ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Coupled Equations

Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as a linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the neglected effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported.

Nonlinear Shell Dynamics—Intrinsic and Semi-Intrinsic Approaches

1983 ◽  
Vol 50 (3) ◽  
pp. 531-536 ◽  
Author(s):  
A. Libai
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Field Equations ◽  
Nonlinear Shell ◽  
Initial And Boundary Conditions ◽  
Shell Dynamics

The intrinsic approach to the nonlinear dynamics of shells, which was introduced in [6], is reviewed and extended by the addition of appropriate initial and boundary conditions of the dynamic and kinematic types to the field equations. The alternative semi-intrinsic velocity approaches (where the velocity components supply the connection between the equations of motion and the time rates of the metric and curvature) are also presented. Both linear and rotational velocity forms are included. The relative merits of these approaches to shell dynamics are discussed and compared with extrinsic approaches.

scholarly journals An Analytical Closed-Form Solution for Free Vibration of Functionally Graded Circular Plates with Even and Uneven Porosity Distributions

2018 ◽  
Author(s):  
Krzysztof Kamil Żur
Keyword(s):  
General Solution ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Numerical Results ◽  
Axisymmetric Vibration ◽  
Gradient Index ◽  
Circular Plates ◽  
Coupled Equations

Free axisymmetric and non-axisymmetric vibration analysis of the unsaturated porous functionally graded circular plates has been presented on the basis of classical plate theory. The defined coupled equations of motion for the porous functionally graded circular plate were decoupled based on the properties of the physical neutral surface. The one general solution of the decoupled equation of motion was obtained as linear combinations of the multiparametric special Bessel functions for the functionally graded circular plate with even and uneven porosity distributions. The influences of the even and uneven distributions of porosity, gradient index, diverse boundary conditions and the negligible effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied. The obtained numerical results show the differences and significant effect of considered types of distributions of porosities, values of the gradient index and the porosity volume fraction on the distribution of eigenfrequencies of the circular plates. Additionally, the obtained multiparametric general solution of the defined differential equation will allow to study the influences of diverse additional complicating effects such as stepped thickness, cracks, additional mounted elements expressed by only additional boundary conditions on the dynamic behavior of the porous functionally graded circular/annular plates. The formulated boundary value problem, the method of solution and the obtained numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported. The present paper fills this void in the literature.

DETERMINISTIC APPROACH TO WATERSHED MODELING

1971 ◽  
Vol 2 (3) ◽  
pp. 146-166 ◽  
Author(s):  
DAVID A. WOOLHISER
Keyword(s):  
Boundary Conditions ◽  
Watershed Modeling ◽  
Deterministic Approach ◽  
Mass Energy ◽  
Deterministic Models ◽  
Conservation Of Mass ◽  
Hydrologic Process ◽  
Theoretical Structure ◽  
Physically Based ◽  
Initial And Boundary Conditions

Physically-based, deterministic models, are considered in this paper. Physically-based, in that the models have a theoretical structure based primarily on the laws of conservation of mass, energy, or momentum; deterministic in the sense that when initial and boundary conditions and inputs are specified, the output is known with certainty. This type of model attempts to describe the structure of a particular hydrologic process and is therefore helpful in predicting what will happen when some change occurs in the system.

Model of vortex flow of charge in a vessel with turbine impeller

1987 ◽  
Vol 52 (8) ◽  
pp. 1888-1904
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Theoretical Data ◽  
Eddy Diffusion ◽  
Quantitative Agreement ◽  
Creeping Flow ◽  
Model Parameters ◽  
Mean Flow ◽  
Two Dimensional Flow ◽  
Vorticity Transport

A theoretical model is described of the mean two-dimensional flow of homogeneous charge in a flat-bottomed cylindrical tank with radial baffles and six-blade turbine disc impeller. The model starts from the concept of vorticity transport in the bulk of vortex liquid flow through the mechanism of eddy diffusion characterized by a constant value of turbulent (eddy) viscosity. The result of solution of the equation which is analogous to the Stokes simplification of equations of motion for creeping flow is the description of field of the stream function and of the axial and radial velocity components of mean flow in the whole charge. The results of modelling are compared with the experimental and theoretical data published by different authors, a good qualitative and quantitative agreement being stated. Advantage of the model proposed is a very simple schematization of the system volume necessary to introduce the boundary conditions (only the parts above the impeller plane of symmetry and below it are distinguished), the explicit character of the model with respect to the model parameters (model lucidity, low demands on the capacity of computer), and, in the end, the possibility to modify the given model by changing boundary conditions even for another agitating set-up with radially-axial character of flow.

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