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# Example14Resonance 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.

### Analysis Space

 Item Settings Analysis Space 3D Model unit mm

### Analysis Conditions

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.

 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 (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.

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