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Nonlinear Systems Techniques and Applications

Offered in conjunction with

IMAC: International Conference & Exposition on Structural Dynamics

Next scheduled course, Saturday, January 29, 2005 at the Rosen Plaza Hotel, Orlando, FL USA.

COURSE OBJECTIVE
This one-day short course discusses work contained in the publication by the instructor, Nonlinear Systems Techniques and Applications, published by Wiley and available through SEM. The main objectives in this new book and new course are to acquaint people with important features and engineering applications from practical nonlinear system techniques developed in the last eight years that were not previously published in the instructor's 1990 book, Nonlinear System Analysis and Identification from Random Data. These new nonlinear system single-frequency spectral techniques can solve important nonlinear system problems in many engineering fields. Single-input/single-output (SI/SO) nonlinear models are replaced by equivalent multiple-input/single-output (MI/SO) linear models, where the measured physical data can have arbitrary probability, correlation and spectral properties. Nonlinear system amplitude and frequency-domain results can be identified by these new techniques that are easy to compute and interpret. Nonlinear system response effects can be ranked at each frequency with cumulative coherence functions. The correct nonlinear results are obtained that replace wrong results by conventional linear modal analysis techniques. This course will discuss computed results from recent practical solutions of nonlinear problems in automotive and oceanographic fields.

INSTRUCTOR

Dr. Julius S. Bendat is an internationally recognized authority in the field of random data analysis and engineering applications. He is a mathematical consultant for a wide range of organizations in both industry and government, and has presented many short courses in the United States and other countries on the topics discussed in seven previously published works. His recent 1998 publication, Nonlinear Systems Techniques and Applications, is the textbook for this course.

COURSE SCHEDULE

Saturday

8:30 am to 10:00 am

Linear Systems, Random Data

10:30 am to 12:00 Noon

Zero-Memory Nonlinear Systems

1:30 pm to 3:00 pm

Direct and Reverse MI/SO Techniques

3:30 pm to 5:00 pm

Determination of Nonlinear System Properties

COURSE CONTENT
Linear Systems, Random Data reviews some basic ideas about linear systems and random data, including probability density functions, correlation functions and spectral density functions. Procedures are explained to solve SI/SO linear system problems and MI/SO linear system problems.

Zero-memory Nonlinear Systems discusses established techniques for analyzing random data through zero-memory nonlinear systems. Probability results are shown for engineering applications to detect and identify properties of nonlinear systems from measured input/output data.

Direct and Reverse MI/SO Techniques describes how these new practical techniques can analyze nonlinear systems by replacing SI/SO nonlinear models, with and without feedback, with equivalent MI/SO linear models. The book has four chapters devoted to applications of these techniques.

Determination of Nonlinear System Properties demonstrates how the new practical direct and reverse MI/SO techniques are used to determine desired nonlinear system response properties from simulated data and from measured laboratory test data in recent automotive and oceanographic projects.

For further information about the course program, contact Julius Bendat, telephone (310) 476-6696.  For more information contact SEM, 7 School Street, Bethel, CT 06801, (203) 790-6373, fax (203) 790-4472, Email:  meetings@sem1.com.

CANCELLATION LIABILITY
If the course is cancelled for any reason, the Society for Experimental Mechanics' liability is limited to the return of the course fees.

COURSE FEE
The course fee includes a copy of the publication, Nonlinear Systems Techniques and Applications, plus a set of special course notes prepared by the instructor and refreshment breaks.

For more information contact SEM, 7 School Street, Bethel, CT 06801, (203) 790-6373, fax (203) 790-4472, Email:  meetings@sem1.com.

Nonlinear Systems Techniques and Applications

Julius S. Bendat

Table of Contents

Preface, xi

  1. Linear Systems, Random Data, 1
    • Linear Systems, 1
    • Random Data, 7
    • Spectral Density Functions, 12
    • Input/Output Spectral Relations, 18
  2. Zero-Memory Nonlinear Systems, 21
    • Nonlinear Material in Book, 21
    • Zero-Memory Nonlinear Systems, 22
    • Output Probability Density Function, 28
    • Output Autocorrelation Function, 31
    • Input/Output Cross-Correlation Function, 34
    • Examples with Discontinuous Derivatives, 37
    • Square-Law and Cubic Systems, 51
    • Hardening and Softening Spring Systems, 60
    • Third-Order Polynomial Least-Squares Approximation, 71
  3. Direct and Reverse MI/SO Techniques for Analysis and Identification of Nonlinear Systems, 77
  4. Parallel Linear and Nonlinear Systems, 97
    • Analysis Methodology, 97
    • Two-Input/Single-Output Linear Models, 102
    • Statistical Errors in Estimates, 105
    • Nonlinear Wave Force Models, 108
    • Nonlinear Drift Force Models, 110
    • Case 1 and Case 2 Nonlinear Models, 112
    • Nonlinear Automotive Application, 116
    • Nonlinear Biomedical Study, 129
    • Nonlinear Differential Equations of Motion, 132
  5. Determination of Physical Parameters with Memory in Nonlinear Systems, 139
    • Reverse MI/SO Technique, 139
    • Physical Parameters with Memory, 140
    • Computer Simulation Studies, 148
    • Discussion of Simulation Results, 151
    • Conclusions from Simulation Work, 195
    • Six-DOF Nonlinear Models for Ocean Engineering Applications, 196
  6. Nonlinear System Response Properties of a Naval Frigate from Measured Ocean Engineering Data, 213
    • Test Program in June 1994, 214
    • Test Objectives, 215
    • Test Description, 217
    • Equations of Motion for a Naval Frigate, 218
    • Results from Analysis of Frigate Date, 226
    • Conclusions from Frigate Tests, 256
    • MAC/RAN System Programs, 256
  7. Nonlinear System Response Properties of a Naval Barge from Measured Ocean Engineering Data, 269
    • Test Program in July 1995, 270
    • Test Objectives, 271
    • Test Description, 272
    • Equations of Motion for a Free Barge, 274
    • Results from Analysis of Barge Date, 285
    • Conclusions from Barge Tests, 367
  8. Bilinear and Trilinear Systems, 369
    • Functional Representation of Nonlinear Systems, 369
    • Examples, 386
    • Synthesis of Time-Varying Linear Systems, 400
    • Higher-Order Correlation and Spectra, 402
  9. Input/Output Relations for Bilinear and Trilinear Systems, 411
    • Linear, Bilinear, and Trilinear Systems, 411
    • General Third-Order Nonlinear Models, 430
    • Optimum Linear and Nonlinear Systems, 444
    • Case 1 and Case 2 Nonlinear Models, 449

References, 461
Index, 465
Glossary of Symbols, 473

Order # W-057; ISBN: 0-471-16576-X
Hardbound; 474 pages; pub. 1998
  
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