FUZZY SENSITIVITY ANALYSIS FOR THE IDENTIFICATION OF MATERIAL PROPERTIES OF ORTHOTROPIC PLATES FROM NATURAL FREQUENCIES

To enhance the identification of material properties of orthotropic plates, a special method of fuzzy sensitivity analysis is presented which allows the determination of the dependencies between the material properties and the natural frequencies of each mode. The procedure is based on the classical thin-plate theory in conjunction with a recently developed method for calculating the natural frequencies of completely free orthotropic plates using the exact series solution. After presenting the fundamentals of fuzzy sensitivity analysis which include the numerical implementation of uncertain parameters as well as the simulation and the analysis of the model, the results of the proposed method applied to vibrations of an orthotropic plate are given.

[1]  J. T. S. Wang,et al.  A Method for Exact Series Solutions in Structural Mechanics , 1999 .

[2]  S. M. Dickinson,et al.  Improved approximate expressions for the natural frequencies of isotropic and orthotropic rectangular plates , 1985 .

[3]  Michael Hanss,et al.  The transformation method for the simulation and analysis of systems with uncertain parameters , 2002, Fuzzy Sets Syst..

[4]  Michael Hanss,et al.  Simulation of the human glucose metabolism using fuzzy arithmetic , 2000, PeachFuzz 2000. 19th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.00TH8500).

[5]  Lothar Gaul,et al.  Determination of Material Properties of Plates from Modal ESPI Measurements #5 , 1999 .

[6]  John E. Mottershead,et al.  REGULARISATION METHODS FOR FINITE ELEMENT MODEL UPDATING , 1998 .

[7]  H. Zimmermann,et al.  Fuzzy Set Theory and Its Applications , 1993 .

[8]  D. Larsson,et al.  Using Modal Analysis for Estimation of Anisotropic Material Constants , 1997 .

[9]  G. Alefeld,et al.  Introduction to Interval Computation , 1983 .

[10]  Per S. Frederiksen,et al.  APPLICATION OF AN IMPROVED MODEL FOR THE IDENTIFICATION OF MATERIAL PARAMETERS , 1997 .

[11]  M. Hanss.  A nearly strict fuzzy arithmetic for solving problems with uncertainties , 2000, PeachFuzz 2000. 19th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.00TH8500).

[12]  S. M. Dickinson.  THE BUCKLING AND FREQUENCY OF FLEXURAL VIBRATION OF RECTANGULAR ISOTROPIC AND ORTHOTROPIC PLATES USING RAYLEIGH'S METHOD , 1978 .

[13]  W. Ames.  Mathematics in Science and Engineering , 1999 .

[14]  L. Rayleigh,et al.  The theory of sound , 1894 .

[15]  E. Ayorinde,et al.  On the use of diagonal modes in the elastic identification of thin plates , 1999 .

[16]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[17]  G. B. Warburton,et al.  The Vibration of Rectangular Plates , 1954 .

[18]  Arthur W. Leissa,et al.  The free vibration of rectangular plates , 1973 .

[19]  Per S. Frederiksen,et al.  Parameter uncertainty and design of optimal experiments for the estimation of elastic constants , 1998 .

[20]  Ronald F. Gibson,et al.  Determination of elastic constants of orthotropic plates by a modal analysis/Rayleigh-Ritz technique , 1988 .

[21]  M. Hanss.  On the implementation of fuzzy arithmetical operations for engineering problems , 1999, 18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.99TH8397).

[22]  W. Ritz.  Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. , 1909 .

[23]  C. Fritzen,et al.  DAMAGE DETECTION BASED ON MODEL UPDATING METHODS , 1998 .

[24]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[25]  H. G. Natke.  PROBLEMS OF MODEL UPDATING PROCEDURES: A PERSPECTIVE RESUMPTION , 1998 .

[26]  Madan M. Gupta,et al.  Introduction to Fuzzy Arithmetic , 1991 .

[27]  Michael Link,et al.  UPDATING ANALYTICAL MODELS BY USING LOCAL AND GLOBAL PARAMETERS AND RELAXED OPTIMISATION REQUIREMENTS , 1998 .

[28]  Stefan Hurlebaus,et al.  AN EXACT SERIES SOLUTION FOR CALCULATING THE EIGENFREQUENCIES OF ORTHOTROPIC PLATES WITH COMPLETELY FREE BOUNDARY , 2001 .