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Modal Analysis

This analysis uses the data in tutorial/15_eigen_spring.

Analysis Target

The analysis target is the same spring as in the preceding section, Nonlinear Static Analysis (Hyperelasticity, Part 2).

Item Description Notes Reference
Analysis type Modal analysis !SOLUTION, TYPE=EIGEN
Number of nodes 78,771
Number of elements 46,454
Element type 10-node quadratic tetrahedral element !ELEMENT,TYPE=342
Material name MAT1 !MATERIAL,NAME=MAT1
Boundary conditions Constraint
Matrix solution Direct method !SOLVER,METHOD=DIRECT

Analysis Details

The displacements of the constrained surface shown in Figure 4.4.1 are constrained, and modal analysis is performed up to the fifth mode. The analysis control data is shown below.

Spring geometry

Figure 4.4.1 Spring geometry

Analysis Control Data spring.cnt

#  Control File for FISTR
## Analysis Control
!VERSION
 3
!SOLUTION, TYPE=EIGEN
!EIGEN
 5, 1.0E-8, 60
!WRITE,RESULT
!WRITE,VISUAL
## Solver Control
### Boundary Conditon
!BOUNDARY
 XFIX, 1, 1, 0.0
 YFIX, 2, 2, 0.0
 ZFIX, 3, 3, 0.0
### Material
# define in mesh file
### Solver Setting
!SOLVER,METHOD=DIRECT
## Post Control
!VISUAL,metod=PSR
!surface_num=1
!surface 1
!output_type=VTK
!END

Analysis Procedure

Run the FrontISTR executable command fistr1.

cd FrontISTR/tutorial/15_eigen_spring
fistr1 -t 4

(Run with 4 threads)

Analysis Results

Using the analysis result data file spring.res.0.3, the third vibration mode (compression and extension of the spring in the y direction) is created with REVOCAP_PrePost and shown in Figure 4.15.1. The deformation scale factor is set to 1000. In addition, the list of natural frequencies output to the analysis result log file is shown below as numerical analysis result data.

Third vibration mode of the spring

Figure 4.15.1 Third vibration mode of the spring

Analysis Result Log 0.log

 fstr_setup: OK

********************************
*RESULT OF EIGEN VALUE ANALYSIS*
********************************

NUMBER OF ITERATIONS =       47
TOTAL MASS =   3.4184E-06

                   ANGLE       FREQUENCY   PARTICIPATION FACTOR                EFFECTIVE MASS
  NO.  EIGENVALUE  FREQUENCY   (HZ)        X           Y           Z           X           Y           Z
  ---  ----------  ----------  ----------  ----------  ----------  ----------  ----------  ----------  ----------
    1  7.8307E+06  2.7983E+03  4.4537E+02  1.0289E+00 -8.8939E-02 -7.0520E-01  1.3006E-06  9.7176E-09  6.1094E-07
    2  7.8716E+06  2.8056E+03  4.4653E+02  6.9687E-01  1.0755E-01  1.0106E+00  6.1290E-07  1.4598E-08  1.2890E-06
    3  3.2600E+07  5.7097E+03  9.0872E+02  4.8622E-03  1.2364E+00 -7.9172E-02  4.0069E-11  2.5908E-06  1.0624E-08
    4  3.8366E+07  6.1940E+03  9.8581E+02 -2.9654E-02  3.3849E-01 -6.7819E-03  9.8232E-10  1.2799E-07  5.1379E-11
    5  1.2931E+08  1.1372E+04  1.8098E+03  5.1856E-01  4.7604E-02  6.7703E-01  2.8377E-07  2.3915E-09  4.8371E-07

    Iter.#   Eigenvalue    Abs. Residual
    1  7.8307E+06  2.4730E-08
    2  7.8716E+06  1.0144E-08
    3  3.2600E+07  1.9866E-07
    4  3.8366E+07  3.1463E-08
    5  1.2931E+08  2.6103E-07