Identification of the dynamic characteristics of nonlinear structures

3.4
3.5
3.6
3.7
CORRELATION ANALYSIS USING RANDOM INPUT .......................... 9 2
3.4.1 Theory of Wiener Series ..........................................................
92
3.4.2
Determination of Wiener Kernels by Cross-correlation.. ....................
MEASUREMENT 
OF 
WIENER 
KERNELS .......................................... 9 7
Measurement of Wiener Kernels Using
Correlation Analysis with Random Input.. ....................................
3.5.2
Removal o f Linear Contributions.. ............................................ .lOl
IDENTIFICATION OF NONLINEARITY USING HIGHER-ORDER
FREQUENCY RESPONSE FUNCTIONS
2
CONCLUSIONS ......................................................................... 104
Chapter 
q
IDENTIFICATION OF CHAOTIC VIBRATIONAL SYSTEMS
4.1
4.2
4.3
PRELIMINARIES .......................................................................
106
INTRODUCTION TO CHAOTIC VIBRATION ...................................
4.2.1 Dynamic System Theory ........................................................
109
4.2.2
Steady-state Behaviour of Dynamic Systems ................................. 112
4.3.3 Chaotic Attractors ................................................................
116
4.3.4 The 
Map ................................................................
118
4.3.5
Stability of Limit Sets and Lyapunov Exponents
4.2.6
The Dimension of an Attractor ..................................................
124
CHAOTIC VIBRATION OF MECHANICAL SYSTEM WITH BACKLASH . . 
12 6
4.3.1
Introduction .......................................................................
126
4.3.2
General System ...................................................................
127
4.3.3
Chaotic Motions and Strange Attracting Sets ................................. 129
4.3.4
Fractal Dimension of Strange Attractors ....................................... 132
4.3.5
Sensitivity on Initial Conditions and Lyaponov Exponents..
4.3.6
Forcing Parameter Field and Damping Effect on Chaos
4.3.7
Two-degree-of-freedom Backlash System .................................... 139
4.3.8
Experimental Investigation ......................................................
140
4.4
CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

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Chapter 
q
LOCATION OF STRUCTURAL NONLINEARITIES
5.1
5.2
5.3
5.4
5.5
5.6
5.7