# Frequency Response Analysis

## Frequency Response Analysis

This analysis uses the data of tutorial/17_freq_beam.

### Analysis target

The analysis target is a cantilevered beam, and the geometry is shown in Figure 4.17.1 and the mesh data is shown in Figure 4.17.2.

Item Description Notes Reference
Type of analysis Frequency response analysis !SOLUTION,TYPE=EIGEN !SOLUTION,TYPE=DYNAMIC
Number of nodes 55
Number of elements 126
Element type Four node tetrahedral element !ELEMENT,TYPE=341
Material name Material-1 !MATERIAL,NAME=Material-1
Boundary conditions Restraint, Concentrated force, eigen value !EIGENREAD
Matrix solution CG/SSOR !SOLVER,METHOD=CG,PRECOND=1

Fig. 4.17.1 : Shape of the cantilever

Fig. 4.17.2 : Mesh data of the cantilever

### Analysis content

The end of a cantilevered beam to be analyzed is fully constrained, and a frequency response analysis is performed by applying concentrated loads to two nodes at the opposite end.

After analyzing eigenvalues up to the 10th order under the same boundary conditions, the analysis is performed using eigenvalues and eigenvectors up to the 5th order. The analysis control data for frequency response analysis is shown below.

#### Analysis control data beam_eigen.cnt.

#  Control File for FISTR
!VERSION
3
!WRITE,RESULT
!WRITE,VISUAL
!SOLUTION, TYPE=EIGEN
!EIGEN
10, 1.0E-8, 60
!BOUNDARY
_PickedSet4, 1, 3, 0.0
!SOLVER,METHOD=CG,PRECOND=1,ITERLOG=NO,TIMELOG=YES
10000, 1
1.0e-8, 1.0, 0.0
!VISUAL,metod=PSR
!surface_num=1
!surface 1
!output_type=VTK
!END


#### Analysis control data beam_freq.cnt.

#  Control File for FISTR
!VERSION
3
!WRITE,RESULT
!WRITE,VISUAL
!SOLUTION, TYPE=DYNAMIC
!DYNAMIC
11 , 2
14000, 16000, 20, 15000.0
0.0, 6.6e-5
1, 1, 0.0, 7.2E-7
10, 2, 1
1, 1, 1, 1, 1, 1
eigen_0.log
1, 5
!BOUNDARY
_PickedSet4, 1, 3, 0.0
_PickedSet5, 2, 1.
_PickedSet6, 2, 1.
!SOLVER,METHOD=CG,PRECOND=1,ITERLOG=NO,TIMELOG=YES
10000, 1
1.0e-8, 1.0, 0.0
!VISUAL,metod=PSR
!surface_num=1
!surface 1
!output_type=VTK
!END


### Analysis procedure

First, change hecmw_ctrl_eigen.dat to hecmw_ctrl.dat for eigenvalue analysis, and then run eigenvalue analysis.

Next, change hecmw_ctrl_freq.dat to hecmw_ctrl.dat and 0.log to eigen_0.log (which is specified in the control data for frequency response analysis), and then perform the frequency response analysis.

$cp hecmw_ctrl_eigen.dat hecmw_ctrl.dat$ fistr1 -t 4
$mv 0.log eigen_0.log$ cp hecmw_ctrl_freq.dat hecmw_ctrl.dat
\$ fistr1 -t 4


### Analysis results

The relationship between the frequency and displacement amplitude of a monitoring node (node number 1) specified in the analysis control data is shown in Figure 4.17.3, created using Microsoft Excel. A part of the analysis result log file is shown below as numerical data for the analysis results.

Fig.4.17.3 Relationship between frequency and displacement amplitude of the monitoring nodes

#### Analysis result log 0.log

 fstr_setup: OK
Rayleigh alpha:   0.0000000000000000
Rayleigh beta:   7.1999999999999999E-007
start mode=           1
end mode=           5
start frequency:   14000.000000000000
end frequency:   16000.000000000000
number of the sampling points          20
monitor nodeid=           1
14100.000000000000      [Hz] :    8.3935554530220141E-002
14100.000000000000      [Hz] :            1 .res
14200.000000000000      [Hz] :    9.1211083510158913E-002
14200.000000000000      [Hz] :            2 .res
14300.000000000000      [Hz] :    9.9579777897537178E-002
14300.000000000000      [Hz] :            3 .res
14400.000000000000      [Hz] :   0.10914967595035865
14400.000000000000      [Hz] :            4 .res
14500.000000000000      [Hz] :   0.11992223203402431
14500.000000000000      [Hz] :            5 .res