Identification of the dynamic characteristics of nonlinear structures

Chapter 
q
IDENTIFICATION OF NONLINEARITY USING
FIRST-ORDER FREQUENCY RESPONSE FUNCTIONS
2.1 
GENERAL INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
11
2.2
MEASUREMENT OF FIRST-ORDER FREQUENCY
RESPONSE FUNCTIONS.. 
2.2.1
Sinusoidal
Excitation Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2
Measurement Using Random Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.3
Measurement Using Transient Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.4
Comments and Practical Considerations of Nonlinearity Measurement 
19

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2.3
2.4
2.5
2.6
RECENT DEVELOPMENTS ON THE IDENTIFICATION OF NONLINEARITY
BASED ON FIRST-ORDER FREQUENCY RESPONSE FUNCTIONS ......... . 2
2.3.1
..................... 23
2.3.2 Isometric Damping Plot Technique .............................................. 26
2.3.3 Inverse Receptance Method ......................................................
29
2.3.4
Comments on Current Nonlinear Modal Analysis Methods.. ...............
OF VIBRATION MODES ............................................. 3 4
Theoretical Basis ..................................................................
34
2.4.2
Numerical Example of Complex Modes .......................................
2.4.3
Complex Modes from Measurements ...........................................
41
A NEW METHOD OF NONLINEAR MODAL ANALYSIS
OF COMPLEX MODES ..................................................................
4 2
2.5.1
2.5.2
2.5.3
2.5.4
2.5.5
2.5.6
Harmonic Balance Theory........................................................
42
Description of the Method ........................................................
47
Application of the New Method to the Analysis of
Nonlinear Systems Simulated Using Analogue Circuits.. ...................
Extension of the Method to Nonlinear MDOF Systems
Application of the Method to Practical Nonlinear Structures
Identification of Nonlinear Physical characteristics
CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 3
Chapter 
q
IDENTIFICATION OF NONLINEARITY USING
HIGHER-ORDER FREQUENCY RESPONSE FUNCTIONS
3.1
3.2
3.3
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 6
THE 
SERIES REPRESENTATION OF
NONLINEAR SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 
0
3.2.1
Basic Characteristics o f Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.2.2
The Volterra Series Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
HIGHER-ORDER FREQUENCY RESPONSE FUNCTIONS 
3
3.3.1
Theory of Higher-Order Frequency Response Functions.. 
3.3.2 Analytical Calculation of Higher-Order Frequency Response Functions. 
3.3.3
Measurement of Higher-Order Frequency Response Functions Using
Harmonic Probing Method.. 

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