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.

The Nuclear Repulsive-Core Effect as a Possible Consequence of Matter in Interaction with a Classical Relativistic Scalar Field: A New Approach to the Question

1972 ◽  
Vol 50 (7) ◽  
pp. 636-645 ◽  
Author(s):  
D. Leiter ◽  
J. Huschilt ◽  
G. Szamosi
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Hard Core ◽  
Repulsive Core ◽  
Lagrangian Formalism ◽  
Field Equations ◽  
New Formalism ◽  
N Body Problem ◽  
Scalar Field Equations

The N-body problem is analyzed within the framework of a new formalism for relativistic point masses interacting via a scalar field, in which the problems of infinite self-energies are absent. A Lagrangian formalism is exhibited which yields the particle equations of motion in the form of a parameterized class of equations. The parameter determines the choice of boundary conditions which is chosen on the scalar-field equations. The existence or nonexistence of the relativistic nuclear hard-core effect, associated with the scalar-field interactions, is shown to depend critically on the particular set of boundary conditions which are imposed on the scalar-field equations. In particular, time-symmetric boundary conditions yield no hard-core repulsion, while retarded boundary conditions are shown to yield a hard-core repulsion at very short range.

Nonlinear Dynamics Analysis of a Printed Wiring Board With Simple and Clamped Boundary Conditions

2001 ◽  
Author(s):  
Xiaoling He
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Nonlinear Resonance ◽  
Failure Criteria ◽  
Dynamics Analysis ◽  
Printed Wiring Board ◽  
Resonance Behavior ◽  
Condition Effect ◽  
Wiring Board

Abstract Dynamic response of a printed wiring board (PWB) is analyzed in nonlinear dynamics approach. Equations of motion for the simply supported PWB and the clamped PWB are obtained by the Galerkin’s method. A 2-layer plastic PWB made of isotropic laminates is studied for its boundary condition effect on the vibratory behavior in deflection and stresses. Failure due to plane stress interaction is estimated based on the composite failure criteria. It is found that nonlinear resonance occurs almost periodically in both frequency and temporal domain. Load frequency and magnitude affect the deflection response under different boundary conditions. Resonance behavior is critical in PWB failure prediction based on the stress analysis. The analytical results can be extended to the nonlinear dynamics analysis of the thin laminated plate.

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.

Nonlinear Dynamics of Stockbridge Dampers

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
O. Barry ◽  
J. W. Zu ◽  
D. C. D. Oguamanam
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Nonlinear Frequency ◽  
Modulation Equations ◽  
Proposed Model ◽  
Cantilevered Beams ◽  
Stockbridge Damper

The present paper deals with the nonlinear dynamics of a Stockbridge damper. The nonlinearity is from damping and the geometric stretching of the messenger. The Stockbridge damper is modeled as two cantilevered beams with tip masses. The equations of motion and boundary conditions are derived using Hamilton’s principle. The model is valid for both symmetric and asymmetric Stockbridge dampers. Explicit expressions are presented for the frequency equation, mode shapes, nonlinear frequency, and modulation equations. Experiments are conducted to validate the proposed model.

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.

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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