Invariant Imbedding Applied to Eigenvalue Problems in Mechanics

1965 ◽  
Vol 32 (1) ◽  
pp. 47-50 ◽  
Author(s):  
E. M. Shoemaker
Keyword(s):  
Wave Propagation ◽  
Eigenvalue Problem ◽  
Initial Value Problem ◽  
Present Method ◽  
Eigenvalue Problems ◽  
Transport Theory ◽  
Formal Method ◽  
Point Boundary ◽  
Invariant Imbedding ◽  
Initial Value

A formal method is presented for obtaining eigenvalues of ordinary differential equations associated with problems of buckling and vibration. The method utilizes the idea of invariant imbedding which has previously been applied to two point boundary value problems in transport theory and wave propagation. The present method reduces the eigenvalue problem to an initial value problem for a matrix of Riccati equations. The numerical solution of such formulations has proved to be generally more efficient than known methods.

Invariant Imbedding and Sequential Interpolating Filters for Nonlinear Processes

1969 ◽  
Vol 91 (2) ◽  
pp. 195-199 ◽  
Author(s):  
H. H. Kagiwada ◽  
R. E. Kalaba ◽  
A. Schumitzky ◽  
R. Sridhar
Keyword(s):  
Boundary Value Problem ◽  
Initial Value Problem ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Point Boundary ◽  
Invariant Imbedding ◽  
Nonlinear Processes ◽  
Initial Value ◽  
Imprecise Observations ◽  
Sequential Filter

Suppose imprecise observations are made on imprecisely defined nonlinear processes, and one wishes to estimate the state of the process at certain fixed instants of time lying within the interval of observation. Furthermore, assume that it is required to update these estimates as additional observations become available. This is precisely the problem of sequential interpolation. The equations of the sequential interpolating filter, when a least-squares estimation criterion is used, are obtained in this paper. The interpolation problem is first shown to be equivalent to a two-point boundary-value problem. The two-point boundary-value problem is converted to an initial-value problem using invariant imbedding. The initial-value problem leads directly to a sequential filter.

An initial value problem in the theory of nonlinear wave propagation

1980 ◽  
Vol 4 (4) ◽  
pp. 781-789
Author(s):  
M.N. Oğuztörel[doti] ◽  
E.S. Şuhubi ◽  
M. Teymur
Keyword(s):  
Wave Propagation ◽  
Nonlinear Wave ◽  
Initial Value Problem ◽  
Nonlinear Wave Propagation ◽  
Initial Value

Dual extremum principles for the heat equation

1977 ◽  
Vol 77 (3-4) ◽  
pp. 273-292 ◽  
Author(s):  
W. D. Collins
Keyword(s):  
Hilbert Space ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Initial Value Problem ◽  
General Class ◽  
Initial Value Problems ◽  
Linear Operators ◽  
Point Boundary ◽  
Initial Value ◽  
Quantities Of Interest

SynopsisDual extremum principles characterising the solution of initial value problems for the heat equation are obtained by imbedding the problem in a two-point boundary-value problem for a system in which the original equation is coupled with its adjoint. Bounds on quantities of interest in the original initial value problem are obtained. Such principles are examples of ones which can be obtained for a general class of linear operators on a Hilbert space.

Dynamic Instability in Ice-Lifting From a Flat Road Surface Through Penetration With a Sharp Blade

1982 ◽  
Vol 49 (1) ◽  
pp. 187-190 ◽  
Author(s):  
N. C. Huang
Keyword(s):  
Wave Propagation ◽  
Numerical Solution ◽  
Initial Value Problem ◽  
Initial Velocity ◽  
Flat Surface ◽  
Dynamic Instability ◽  
Inertia Force ◽  
Initial Value ◽  
Impulsive Load ◽  
Horizontal Thrust

This paper is concerned with the problem of dynamic instability during ice-lifting from a flat surface through penetration of the interface by means of a sharp blade. The blade is subjected to a horizontal impulsive load and a constant horizontal thrust, both applied suddenly and simultaneously. The principle of the balance of energy is used to analyze the deformation of the ice associated with the crack propagation along the interface. In our formulation, the effect of wave propagation in the ice is neglected. However, the inertia force due to the acceleration of the blade is included. The motion of the blade is investigated by the numerical solution of a complex, nonlinear, initial value problem. It is found that under a given horizontal thrust, if the initial velocity of the blade is sufficiently small, the motion of the blade may stop. However, if the initial velocity of the blade is sufficiently large, the motion of the blade is always forward and the crack can propagate indefinitely along the interface.

Wave propagation in a thin-walled liquid-filled initially stressed tube

1984 ◽  
Vol 141 ◽  
pp. 289-308 ◽  
Author(s):  
G. D. C. Kuiken
Keyword(s):  
Blood Pressure ◽  
Wave Propagation ◽  
Dispersion Equation ◽  
Newtonian Fluid ◽  
Initial Value Problem ◽  
Wave Mode ◽  
Initial Value ◽  
Thin Walled ◽  
Speed Of Propagation ◽  
Infinite Tube

Wave propagation through a thin-walled cylindrical orthotropic viscoelastic initially stressed tube filled with a Newtonian fluid is discussed. Special attention is drawn to the influence of the initial stretch on the wave propagation. It is shown that initial stretching of real arteries enhances the propagation of blood pressure pulses in mammalian arteries. The dispersion equation for the initial-value problem of a semi-infinite tube is also derived. It is shown that the speed of propagation and the attenuation vary with the distance from the support. The results obtained for the axial wave mode provide an explanation for the experimental observations, which is not possible with the results obtained for the infinite tube.

Instability growth rate of two-phase mixing layers from a linear eigenvalue problem and an initial-value problem

2010 ◽  
Vol 22 (9) ◽  
pp. 092104 ◽  
Author(s):  
Anne Bagué ◽  
Daniel Fuster ◽  
Stéphane Popinet ◽  
Ruben Scardovelli ◽  
Stéphane Zaleski
Keyword(s):  
Growth Rate ◽  
Eigenvalue Problem ◽  
Initial Value Problem ◽  
Instability Growth Rate ◽  
Mixing Layers ◽  
Initial Value ◽  
Two Phase ◽  
Phase Mixing ◽  
Linear Eigenvalue Problem ◽  
Instability Growth
Sign in / Sign up

Export Citation Format

Share Document