Sur les opérateurs différentiels symétrisants relatifs aux systèmes non-conservatifs

1998 ◽  
Vol 76 (5) ◽  
pp. 403-420
Author(s):  
R El Abdi ◽  
G Gambart
Keyword(s):  
Exact Solutions ◽  
Critical Load ◽  
General Expression ◽  
Critical Frequency ◽  
Differential Operators ◽  
Adjoint Problem ◽  
New Method ◽  
Numerical Comparison ◽  
Nonconservative Systems

For nonconservative systems, which we call systems with follower loads, a study is proposed concerning the differential operators which lead to a self-adjoint problem for a generalization of the Rayleigh quotient.In the case of punctual loads, we give the general expression for the identification of these operators. For some systems under follower loads, a new method is developed for the identification of the eigenvalues (critical load and critical frequency) when these operators do not exist. A numerical comparison is presented when the exact solutions do exist. PACS Nos. : 02.00 et 03.00

scholarly journals Exact solutions of compressible plane potential flows—a new method

2001 ◽  
Vol 59 (1) ◽  
pp. 175-191
Author(s):  
O. P. Chandna ◽  
I. Husain
Keyword(s):  
Exact Solutions ◽  
New Method ◽  
Potential Flows

Follower forces: Leipholz's early researches in elastic stability

1990 ◽  
Vol 17 (3) ◽  
pp. 277-286 ◽  
Author(s):  
G. M. L. Gladwell
Keyword(s):  
Critical Load ◽  
Key Words ◽  
Lower Bounds ◽  
Critical Loads ◽  
Elastic Stability ◽  
Follower Force ◽  
Historical Account ◽  
Nonconservative Systems ◽  
Flutter Instability ◽  
Force Systems

This paper provides an historical account of Leipholz's research into elastic stability. Emphasis is placed on divergence and flutter instability of follower force systems, the derivation of lower bounds for the critical load for divergence, and estimates for critical loads for flutter. Key words: elastic stability, divergence, flutter, lower bounds, nonconservative systems, symmetrisable matrix.

Three-Dimensional Exact Analysis of Laminated Piezoelectric Plates and Shells

2013 ◽  
Vol 745 ◽  
pp. 1-12
Author(s):  
Gennady M. Kulikov ◽  
S.V. Plotnikova
Keyword(s):  
Exact Solutions ◽  
Chebyshev Polynomial ◽  
Three Dimensional ◽  
Middle Surface ◽  
New Method ◽  
Efficient Approach ◽  
Exact Analysis ◽  
Anisotropic Structures ◽  
Plates And Shells ◽  
Piezoelectric Plates

A paper focuses on the use of the efficient approach to three-dimensional (3D) exact solutions of electroelasticity for laminated piezoelectric plates and shells. This approach is based on the new method of sampling surfaces (SaS). We introduce inside the nth layer Ιn not equally spaced SaS parallel to the middle surface of the shell and choose displacements of these surfaces as basic shell variables. This permits the derivation of 3D exact solutions of electroelasticity for thick and thin laminated piezoelectric anisotropic structures with a specified accuracy using a sufficient number of SaS, which are located at interfaces and Chebyshev polynomial nodes.

On the Approximate Solution of Viscous-Flow Problems

1963 ◽  
Vol 30 (2) ◽  
pp. 263-268 ◽  
Author(s):  
J. A. Schetz
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Viscous Flow ◽  
Closed Form ◽  
New Method ◽  
Two Dimensional ◽  
General Technique ◽  
Closed Form Solutions ◽  
Flow Problems

The need for a general technique for the approximate solution of viscous-flow problems is discussed. Existing methods are considered and a new method is presented which results in simple closed-form solutions. The accuracy of the method is demonstrated by comparisons with the results of known exact solutions, and finally the general technique is employed to determine a new solution for the fully expanded two-dimensional laminar nozzle problem.

Closed-Form Exact Solution to H∞ Optimization of Dynamic Vibration Absorbers (Application to Different Transfer Functions and Damping Systems)

2003 ◽  
Vol 125 (3) ◽  
pp. 398-405 ◽  
Author(s):  
Toshihiko Asami ◽  
Osamu Nishihara
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Optimization Problem ◽  
Vibration Suppression ◽  
Transfer Functions ◽  
New Method ◽  
Algebraic Solution ◽  
Vibration Absorbers ◽  
Dynamic Vibration ◽  
Dynamic Vibration Absorbers

H ∞ optimization of the dynamic vibration absorbers is a classical optimization problem, and has been already solved more than 50 years ago. It is a well-known solution, but we know this solution is only an approximate one. Recently, one of the authors has proposed a new method for attaining the H∞ optimization of the absorber in linear systems. The new method enables us to obtain the exact algebraic solution of the H∞ optimization problem of the absorber. In this paper, we first apply this method to the design optimization of a viscous damped (Voigt type) absorber and a hysteretic damped absorber attached to undamped primary systems. For each absorber, six different transfer functions are taken here as performance indices to vibration suppression or isolation. As a result, we found the closed-form exact solutions to all transfer functions. The solutions obtained here are then compared with those of the approximate ones. Finally, we present the closed-form exact solutions to the hysteretic damped absorber attached to damped primary systems.

A New Method for the Investigation of Cellular Dielectrophoresis

1989 ◽  
Vol 44 (9-10) ◽  
pp. 845-848 ◽  
Author(s):  
Jerzy J. Zieliński ◽  
Piotr Marszałek ◽  
Magdalena Fikus
Keyword(s):  
Single Cell ◽  
Cell Size ◽  
Electric Fields ◽  
Critical Frequency ◽  
Cell Types ◽  
New Method ◽  
New Type ◽  
Positive Dielectrophoresis ◽  
Different Cell Types ◽  
Medium Conductivity

A new method and a new type of measuring-microchamber for the investigation of cellular dielectrophoresis is presented. The method is based on the observation of the trajectory of a single cell in gravitational and electric fields being crossed and orientated perpendicularly to the observation direction. By means of this method the whole dielectrophoretic spectrum ranging from negative to positive dielectrophoresis may be easily and quickly obtained. The experiments carried out on different cell types showed that the dielectrophoretic spectra, as well as the dependence of the critical frequency upon medium conductivity and cell size agree well with the predictions of a new model of the dielectrophoretic mechanism proposed by Sauer.

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