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# Example12Resonance of Metal Bars

General

• The resonance of three metal bars is analyzed.

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

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

### Analysis Space

 Item Settings Analysis Space 3D Model unit m

### 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 6 Approximated frequency 0[Hz]

### Model

Three metal bars and two support rods are created as box-shape solid body.

The bottom faces of support rods are fixed with the displacement boundary condition.

### Body Attributes and Materials

 Body Number/Type Body Attribute Name Material Name 0/Solid RESONANT 001_Al * 1/Solid RESONANT 001_Al * 2/Solid RESONANT 001_Al * 8/Solid BASE M_BASE 9/Solid BASE M_BASE

* Available from the Material DB

The material properties are set up as follows:

 Material Name Tab Properties M_BASE Elasticity Young’s modulus: 2×10^9[Pa] Poisson’s ratio: 0.3 Density Density: 0.1×10^3[Kg/m3]

### Boundary Conditions

The bottom faces of support rods are fixed with the displacement boundary condition.

 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.

 <> Eigenvalue (resonant frequency):[Hz] Mode[ 0] = 8.61552809e+002 Mode[ 1] = 1.06874655e+003 Mode[ 2] = 1.21598202e+003 Mode[ 3] = 1.24695787e+003 Mode[ 4] = 1.56876049e+003 Mode[ 5] = 1.69339225e+003

The resonant frequencies can be checked on Table.

The displacement diagrams of Mode[0] to Mode[ 2] are shown below.

The contour are the Z displacement.

The minimum and maximum values are manually set to

-4.000e+000 and 4.000e+000 respectively.

Mode[0]:8.615528e+002[Hz]

Mode[1]:1.068747e+003[Hz]

Mode[2]: 1.215982e+003[Hz]

The shorter bar exhibits the higher resonant frequency.

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