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Nonlinear normal modes Frequency-energy plot T04 Nonlinear modal analysis Nonlinear Vibrations of Aerospace Structures
Nonlinear normal modes
Frequency-energy plot
T04 Nonlinear modal analysis
Nonlinear Vibrations of
Aerospace Structures
Tutorial 1: The First Mode of
the Nonlinear Beam
3
2.37.109 𝑥3
0.289𝑥 + 0.1357𝑥 + 11009𝑥 = 𝐹𝑠𝑖𝑛𝜔𝑡
Linear model identified at low level (31 Hz, 0.12%):
Nonlinearity identified at high level:
The Nonlinear Beam
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The Nonlinear Beam
No forcing, no damping
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The NNM Solver
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Set Appropriate Parameters
7
Compute The First Nonlinear Mode
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30 35 400
0.01
0.02
0.03
0.04
The Link Between Nonlinear Modes and FRFs
8 8
Frequency (Hz)
x
(m)
10-4
10-1
30
40
50
Energy (J)
Resonance
frequency (Hz)
Backbone
Nonlinear
FRFs
Nonlinear
modes
Tutorial 2: The Modes of a
Multi-DOF System
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Create a 2-DOF Model
2
0
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Modify the 2-DOF Model
7
Introduce a
linear spring
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The Final Model
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In-Phase Mode: Set Appropriate Parameters
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In-Phase Mode: The Resonance Frequencies
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In-Phase Mode: The Modal Shapes
CTRL + LEFT CLICK
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In-Phase Mode: The Time Series
Double click + A
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In-Phase Mode: Harmonics
Double click + A
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Out-of-Phase Mode: Set the Parameters
Right click
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Out-of-Phase Mode: Frequencies and Modal Shapes
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Let’s Go Back to the In-Phase Mode
Right click
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Two New Features
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