A new method for solving the coupled equations in the adiabatic representation

1978 ◽  
Vol 69 (7) ◽  
pp. 3414-3421 ◽  
Author(s):  
Vasil K. Babamov
Keyword(s):  
New Method ◽  
Coupled Equations ◽  
Adiabatic Representation

scholarly journals On the direct determination of the eigenmodes of finite flow–structure systems

2008 ◽  
Vol 465 (2101) ◽  
pp. 257-281 ◽  
Author(s):  
Mark W Pitman ◽  
Anthony D Lucey
Keyword(s):  
Flow Structure ◽  
Travelling Waves ◽  
Computational Modelling ◽  
Classical Problem ◽  
Direct Determination ◽  
New Method ◽  
Spatial Inhomogeneity ◽  
Flexible Plate ◽  
Coupled Equations ◽  
The Stability

A new method for directly determining the eigenmodes of finite flow–structure systems is presented using the classical problem of the interaction of a uniform incompressible flow with a flexible panel, held at both ends, as an exemplar. The method is a hybrid of theoretical analysis and computational modelling. This method is contrasted with Galerkin and travelling-wave methods, which are most often used to study the hydroelasticity of such systems. The new method does not require an a priori approximation of perturbations via a finite sum of modes. Instead, the coupled equations for the wall–flow system are used to derive a single matrix equation for the system that is a second-order differential equation for the panel-displacement variable. This is achieved in this exemplar by applying a combination of boundary-element and finite-element methods to the discretized system. Standard state-space methods are then used to extract the eigenmodes of the system directly. We present the results for the stability of the case of an unsupported flexible plate, elucidating its divergence and flutter characteristics, and the effect of energy dissipation in the structure. We then present the results for the case of a spring-backed flexible plate, showing that its motion is dominated by travelling waves. Finally, we illustrate the versatility of the approach by extracting the stability diagrams and modes for a panel with spatially varying properties and a panel with non-standard boundary conditions. In doing so, we show how spatial inhomogeneity can modify the energy exchanges between flow and structure, thereby introducing a single-mode flutter instability at pre-divergence flow speeds.

A New Method for Determining the Eigenmodes of Finite Flow-Structure Systems

2006 ◽  
Author(s):  
Anthony D. Lucey ◽  
Mark W. Pitman
Keyword(s):  
Galerkin Method ◽  
Flow Structure ◽  
A Priori ◽  
Computational Modelling ◽  
Classical Problem ◽  
New Method ◽  
Flexible Plate ◽  
Coupled Equations ◽  
Standard Galerkin Method ◽  
Single Matrix

A new method for directly determining the eigenmodes of finite flow-structure systems is presented, using the classical problem of the interaction of a uniform flow with a flexible panel, held at both ends, as an exemplar. The method is a hybrid of theoretical analysis and computational modelling. This new approach is contrasted with the standard Galerkin method that is most often used to study the hydro-elasticity of finite systems. Unlike the Galerkin method, the new method does not require an a priori approximation of perturbations via a finite sum of modes. Instead, the coupled equations for the wall-flow system are cast, using computational methods that, in this exemplar, combine boundary-element and finite-element methods, to yield a single matrix equation for the system that is a second-order differential equation for the panel-displacement variable. Standard state-space methods are then used to extract the eigenmodes of the system directly. We present definitive results for the stability of the case of an unsupported flexible plate, elucidating its divergence and flutter characteristics, and the effect of energy dissipation in the structure. Finally, we present some results for the case of a spring-backed flexible plate that illustrate the complicated dynamics of this type of wall; these dynamics would be poorly modelled by a traditional Galerkin method.

A new method to approximate coupled equations for scattering

1980 ◽  
Vol 13 (5) ◽  
pp. 1665-1671
Author(s):  
B J Verhaar ◽  
W J G Thijssen ◽  
A M Schulte
Keyword(s):  
New Method ◽  
Coupled Equations

scholarly journals A New Method with a Different Auxiliary Equation to Obtain Solitary Wave Solutions for Nonlinear Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Bülent Kiliç ◽  
Hasan Bulut
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Riccati Equation ◽  
Nonlinear Partial Differential Equations ◽  
New Method ◽  
Auxiliary Equation ◽  
Partial Differential ◽  
Coupled Equations ◽  
Wave Solutions ◽  
Solitary Solutions

A new method with a different auxiliary equation from the Riccati equation is used for constructing exact travelling wave solutions of nonlinear partial differential equations. The main idea of this method is to take full advantage of a different auxilliary equation from the Riccati equation which has more new solutions. More new solitary solutions are obtained for the RLW Burgers and Hirota Satsuma coupled equations.

Selective Sampling and Orientation of Non-Homogeneous Tissues

1968 ◽  
Vol 26 ◽  
pp. 98-99
Author(s):  
C. C. Clawson ◽  
L. W. Anderson ◽  
R. A. Good
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Light Microscopy ◽  
Random Sampling ◽  
New Method ◽  
Microscope Examination ◽  
Small Areas ◽  
Selective Sampling ◽  
Large Numbers ◽  
Specific Orientation

Investigations which require electron microscope examination of a few specific areas of non-homogeneous tissues make random sampling of small blocks an inefficient and unrewarding procedure. Therefore, several investigators have devised methods which allow obtaining sample blocks for electron microscopy from region of tissue previously identified by light microscopy of present here techniques which make possible: 1) sampling tissue for electron microscopy from selected areas previously identified by light microscopy of relatively large pieces of tissue; 2) dehydration and embedding large numbers of individually identified blocks while keeping each one separate; 3) a new method of maintaining specific orientation of blocks during embedding; 4) special light microscopic staining or fluorescent procedures and electron microscopy on immediately adjacent small areas of tissue.

Towards quantitative simulations of inelastic electron diffraction patterns and images

1992 ◽  
Vol 50 (2) ◽  
pp. 1170-1171
Author(s):  
Z. L. Wang
Keyword(s):  
Phonon Scattering ◽  
Incident Beam ◽  
Dynamical Theory ◽  
Inelastic Electron ◽  
Additional Advantage ◽  
Coupled Equations ◽  
Atomic Vibrations ◽  
Diffraction Patterns ◽  
Primary Advantage ◽  
The One

A new dynamical theory has been developed based on Yoshioka's coupled equations for describing inelastic electron scattering in thin crystals. Compared to existing theories, the primary advantage of this theory is that the incoherent summation of the diffracted intensities contributed by electrons after exciting vast numbers of different excited states has been evaluated before any numerical calculation. An additional advantage is that the phase correlations of atomic vibrations are considered, so that full lattice dynamics can be combined in the phonon scattering calculation. The new theory has been proven to be equivalent to the inelastic multislice theory, and has been applied to calculate energy-filtered diffraction patterns and images formed by phonon, single electron and valence scattered electrons.A calculated diffraction pattern of elastic and phonon scattered electrons for a parallel incident beam case is in agreement with the one observed (Fig. 1), showing thermal diffuse scattering (TDS) streaks and Kikuchi pattern.

A new method for the determination of nitrates

1960 ◽  
Vol 23 ◽  
pp. 227-232 ◽  
Author(s):  
P WEST ◽  
G LYLES
Keyword(s):  
New Method
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