nonlinear vibrations of aerospace structures · nnm (nonlinear normal modes) continuation global...

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

4

The Nonlinear Beam

No forcing, no damping

5

The NNM Solver

6

Set Appropriate Parameters

7

Compute The First Nonlinear Mode

8

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

10

Create a 2-DOF Model

2

0

11

Modify the 2-DOF Model

7

Introduce a

linear spring

12

The Final Model

13

In-Phase Mode: Set Appropriate Parameters

13

14

In-Phase Mode: The Resonance Frequencies

15

In-Phase Mode: The Modal Shapes

CTRL + LEFT CLICK

16

In-Phase Mode: The Time Series

Double click + A

17

In-Phase Mode: Harmonics

Double click + A

18

Out-of-Phase Mode: Set the Parameters

Right click

19

Out-of-Phase Mode: Frequencies and Modal Shapes

20

Let’s Go Back to the In-Phase Mode

Right click

21

Two New Features

?

?