On Eigenfrequencies of an Anisotropic Sphere

2000 ◽  
Vol 67 (2) ◽  
pp. 422-424 ◽  
Author(s):  
W. Q. Chen, ◽  
J. B. Cai, ◽  
G. R. Ye, and ◽  
H. J. Ding
Keyword(s):  
Boundary Conditions ◽  
Solid Sphere ◽  
Numerical Calculations ◽  
Fixed Boundary ◽  
Isotropic Solid

This note presents exact frequency equations of two independent classes of vibrations of a spherically isotropic solid sphere with fixed boundary conditions. Numerical calculations are performed and comparison between two different materials is made. Some useful observations are obtained. [S0021-8936(00)00102-1]

Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1099-1110 ◽  
Author(s):  
Albert C. Reynolds
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Synthetic Seismograms ◽  
Neumann Boundary Conditions ◽  
Numerical Calculations ◽  
Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

Force at Point in the Interior of a Semi-Infinite Solid With Fixed Boundary

1955 ◽  
Vol 22 (4) ◽  
pp. 545-546
Author(s):  
Leif Rongved
Keyword(s):  
Plane Boundary ◽  
Fixed Boundary ◽  
Fixed Plane ◽  
Isotropic Solid ◽  
Normal Traction

Abstract The Papkovitch functions are determined for a force acting at a point in the interior of a semi-infinite isotropic solid with a fixed plane boundary. The normal traction on the boundary is then calculated.

On Stress-Focusing Effect in a Uniformly Heated Solid Sphere

2003 ◽  
Vol 70 (2) ◽  
pp. 304-309 ◽  
Author(s):  
H. J. Ding ◽  
H. M. Wang ◽  
W. Q. Chen
Keyword(s):  
Temperature Rise ◽  
Stress Responses ◽  
Constant Pressure ◽  
Integral Transform ◽  
External Surface ◽  
Separation Of Variables ◽  
Solid Sphere ◽  
Uniform Temperature ◽  
Focusing Effect ◽  
Isotropic Solid

By using the separation of variables technique, the dynamic thermal stress responses in an isotropic solid sphere subjected to uniform temperature rise all over the sphere and a sudden constant pressure at the external surface are performed successfully. The analytical solutions of the radial and hoop dynamic stresses at the center are also obtained. By means of the present method, integral transform can be avoided. Numerical results denote that a very high dynamic stress peak appears periodically at the center of the isotropic solid sphere subjected to uniform temperature rise all over the sphere and a sudden constant pressure at the external surface.

Investigation of the Complex Two Degrees of Freedom Systems for Force Limited Vibration

2004 ◽  
Author(s):  
Andre Cote ◽  
Ramin Sedaghati ◽  
Yvan Soucy
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Simple Approach ◽  
Conservative Estimate ◽  
Two Degrees Of Freedom ◽  
Jet Propulsion ◽  
Fixed Boundary ◽  
Free Boundary Conditions ◽  
Force Data

Force Limited Vibration (FLV) Testing developed at Jet Propulsion Laboratory offers many opportunities to decrease the overtesting problem associated with traditional vibration testing. Among the force limited vibration methods, the complex two degrees of freedom system (TDFS) appears to be the most complete and versatile model which gives reasonably conservative force limits, and does not require extrapolation of interface force data for similar mounting structures and test articles. However there are some limitations to the complex TDFS model. The model is well adapted for nicely separated modes but issues regarding the closely space modes have not been fully addressed in the literature. Also, the complex TDFS model is based on free boundary conditions for the mounting structure, which appear to be natural for many cases such as spacecraft mounted on a launch vehicle. However this is not necessarily true for some other cases such as an electronic component mounted on a spacecraft antenna, which requires fixed boundary conditions. The main objective of this paper is to give greater insights into the complex TDFS method and propose methodologies to overcome its limitations. It is shown that a simple approach can be used to assure conservative estimate of the force limits in situations regarding closely spaced modes. It is also demonstrated that although the complex TDFS method is not perfectly adapted to fixed boundary conditions of the mounting structure, given certain precautions, it still provides good estimates of the force limits.

Analysis and Design of Fixed–Fixed Bistable Arch-Profiles Using a Bilateral Relationship

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Safvan Palathingal ◽  
G. K. Ananthasuresh
Keyword(s):  
Boundary Conditions ◽  
Closed Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Single Variable ◽  
Fixed Boundary ◽  
Analysis And Design ◽  
Bilateral Relationship ◽  
Variable Equation ◽  
Necessary And Sufficient

Arch-profiles of bistable arches, in their two force-free equilibrium states, are related to each other. This bilateral relationship is derived for arches with fixed–fixed boundary conditions in two forms: a nonlinear single-variable equation for analysis and a closed-form analytical expression for design. Some symmetrical features of shape as well as necessary and sufficient conditions for bistability are presented as corollaries. Analysis and design of arch-profiles using the bilateral relationship are illustrated through examples.

scholarly journals Topological Catastrophe in Massive Current Sheets

1989 ◽  
Vol 104 (2) ◽  
pp. 285-288
Author(s):  
Ph. Peterle ◽  
J. Hoyvaerts
Keyword(s):  
Boundary Conditions ◽  
Mass Flux ◽  
Flux Ratio ◽  
Continuous Variation ◽  
Two Dimensional ◽  
Cusp Point ◽  
Fixed Boundary ◽  
Current Sheets ◽  
Solar Filaments

AbstractA two-dimensional sheet model for solar filaments (Kippenhahn and Schluter configuration) is considered. We investigate, the quasi-static evolution of gravito-magnetohydrostatic equlibria in exploring the response of massive current sheets to a slow continuous variation of the mass/flux ratio with fixed boundary conditions. A catastrophic behavior of the field topology is found to occur in the sequence following the formation of a cusp point (bifurcation).

Aeolian transport with collisional suspension

2005 ◽  
Vol 363 (1832) ◽  
pp. 1625-1646 ◽  
Author(s):  
José Miguel Pasini ◽  
James T Jenkins
Keyword(s):  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Numerical Calculations ◽  
Aeolian Transport ◽  
Improved Model

This paper considers the aeolian transport of sand by a wind so strong that the concentration of sand near the bed makes collisions between grains inevitable. It employs an improved model of such a collisional flow which includes turbulent suspension, viscous dissipation and new top boundary conditions that are validated by numerical calculations of collisionless trajectories.

Sign in / Sign up

Export Citation Format

Share Document