Home / Examples / Stress Analysis [Galileo] / Example 36: Damping Vibration of Cantilever

Example 36: Damping Vibration of Cantilever

General

A cantilever is mechanically loaded. After it is unloaded, it starts to vibrate. The vibrations decay over time.
The displacement and the stress are solved for each timestep.
Unless specified in the list below, the default conditions will be applied.

The stress transient analysis is available in an optional package.

Analysis Space

Item	Settings
Analysis Space	3D
Model Unit	mm

Analysis Conditions

Item	Settings
Solver	Stress Analysis [Galileo]
Analysis Type	Transient Analysis

The transient analysis is set up as follows.

Tab

Setting Item

Settings

Transient Analysis Tab

Table

Calculation Steps	Output Interval	Timestep [s]
5	1	0.002
100	1	0.0002

Rayleigh Damping Coefficients

Beta=0.0002

The load gradually increases in the first 5 steps. In the next 100 steps,

it is unloaded, and the damping vibration occurs.

0 to 0.01 [sec]: Loading Period

0.01 to 0.03 [sec]: Vibration Period

Model

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Sheet	Body_Attribute_001	002_Polycarbonate(PC)

Boundary Conditions

Boundary Condition Name/Topology

Tab

Boundary Condition Type

Settings

Fix/Face

Mechanical

Displacement

Select all X/Y/Z components.

UX=0, UY=0, UZ=0

Force/Face

Mechanical

Distributed Face Load

X=0, Y=0, Z=-0.5x105

Time Dependency: Yes

Time	Weight
0	0
0.01	1
0.101	0
10	0

The loading is removed instantaneously at 0.01 [sec].

Tips on Analysis Conditions and Boundary Conditions

Perform a static analysis and obtain the adequate loading condition for the target displacement beforehand.

Perform a resonant analysis and obtain the adequate timestep for the expected vibration period.

If a timestep is large, it may degrade the analysis accuracy.

Results

The displacement diagram below shows the displacement at the time of 0.01 [sec] (mode number of 5). The color gradation contour indicates the Z displacement.

Plotted below is the Z displacement of the cantilever tip in 0.01 to 0.03 [sec] (Mode numbers 5 through 105)

The vibration decays as time passes.

The figure below shows the vibration when Beta, Rayleigh Damping Coefficients, is set to zero for no damping loss.

There is no decay.