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Eigenvalue Analysis

Eigenvalue Analysis

This analysis uses the data of tutorial/15_eigen_spring.

Analysis target

The objects of analysis are the same springs as in the Non-linear Static Analysis (Hyperelasticity, Part 2) in the previous section.

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

Analysis content

The displacements of the constrained surfaces shown in Figure 4.4.1 are constrained, and eigenvalue analysis is performed up to the fifth order. The analysis control data is shown below.

Analysis control data spring.cnt.

#  Control File for FISTR
## Analysis Control
 5, 1.0E-8, 60
## Solver Control
### Boundary Conditon
 XFIX, 1, 1, 0.0
 YFIX, 2, 2, 0.0
 ZFIX, 3, 3, 0.0
### Material
# define in mesh file
### Solver Setting
## Post Control
!surface 1

Analysis procedure

Execute the FrontISTR execution command fistr1.

$ cd FrontISTR/tutorial/15_eigen_spring
$ fistr1 -t 4
(Runs in 4 threads.)

Analysis results

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

Third vibration mode of a spring

Fig. 4.15.1: Third vibration mode of a spring

Analysis results log 0.log.

 fstr_setup: OK


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  9.2347E-09
    2  7.8716E+06  7.8593E-08
    3  3.2600E+07  1.0084E-07
    4  3.8366E+07  5.3113E-08
    5  1.2931E+08  6.8762E-08