Example14 Resonance of Cantilever

General

The resonance of a cantilever is analyzed. Unlike Exercises 11 through 13,
one end is fixed with the displacement boundary condition.
The deformation, the displacement and the mechanical stress are solved.
The directional sensitivity due to the participation factor and the effective mass can be examined for obtained modes.
Unless specified in the list below, the default conditions will be applied.

The analysis type is the harmonic analysis.

Item	Settings
Solvers	Mechanical Stress Analysis [Galileo]
Analysis Type	Resonant analysis
Options	N/A

The resonant analysis tab is set up as follows.

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

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

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

* Available from the Material DB

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

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 diagram of Mode[0] is shown below. The contour is the Z displacement.

The displacement diagram of Mode[1] is shown below. The contour is the Z displacement.

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.

The accumulated value is 80.4[%].

If more modes are calculated, it will approach 100[%].

As for UX and UY components, the main modes are not obtained yet.

You need to calculate more modes.