Home / Examples / Stress Analysis [Galileo] / Example 14: Resonance of Cantilever

Example 14: Resonance of Cantilever

General

• The resonance of a cantilever is analyzed. One end is set with the fixed displacement boundary condition.
  
   

• The deformation, the displacement and the stress are solved.
  

• The vibration sensitivity in a certain direction can be examined by the excitation factor and effective mass of the generated modes.
   

• Unless specified in the list below, the default conditions will be applied.
   

• Obtain this session's project file. (Right-click and choose 'Save link as')




• Results will vary depending on Femtet version and the PC environment.

 

Analysis Space

Item	Settings
Analysis Space	3D
Model Unit	mm

 

Analysis Conditions

The analysis type is the harmonic analysis.

Item	Settings
Solver	Stress Analysis [Galileo]
Analysis Type	Resonant Analysis
Options	N/A

 

The resonant analysis tab is set up as follows.

Tab	Setting Item	Settings
Resonant analysis	Number of Modes	3
	Approximated Frequency	0 [Hz]

Model

The cantilever is created as a box-shape solid body.

The material is silicon. One end is fixed with the displacement boundary condition.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Solid	LEVER	301_Silicon(single-crystal) *

* Available from the material DB

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

 

Results

The following will be output on the output window or the log file.

<<Eigenvalue analysis>> Eigenvalue (resonant frequency):[Hz] Mode[ 0] = 2.50953498e+004 Mode[ 1] = 1.65669006e+005 Mode[ 2] = 3.22935422e+005

 

The resonant frequencies can be checked on Table.

 

 

The displacement of the fundamental mode, Mode[0] , is shown below. The contours are the Z displacement.

 

The displacement of the higher-order mode, Mode[1], is shown below. The contours are the Z displacement.

The fundamental mode and the higher-order mode show different displacements.

 

The effective mass ratio graph can be output from [Table].

 

 

UZ component (the effective mass ratio in Z direction) is 62.0 [%] at Mode 0, 18.4 [%] at Mode 1, and 0 [%] at Mode 2.

Mode 0 is the main mode for the vibration in the Z direction.

The accumulated value up to mode 2 is 80.4 [%].

If more modes are calculated, the accumulated value will approach 100 [%].

 

UX and UY components are nearly zero. As for vibrations in the X and Y directions, the main modes are not obtained yet.

You need to calculate more modes.