# Eigenvalue — Welcome to LS-DYNA Examples

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A coarsely meshed wheel and tire assembly is ‘kicked’ by a brief transient load. The dynamic response of a node at the top of the tire is monitored.

## Introduction

```LS-DYNA Implicit Workshop

Problem #2: Car Tire

Objective
* Learn to set up and run implicit dynamic and eigenvalue
analyses.
* Learn the advantages of implicit dynamic compared with
explicit dynamic analysis.

Problem Description
A coarsely meshed wheel and tire assembly is 'kicked' by a
brief transient load. The dynamic response of a node at the
top of the tire is monitored.

Input Filename: tire.k

Procedure
Copy the input file to your local directory. Using an editor,
view the input file and answer the following questions:

1. What loads and boundary conditions are applied to the tire?

Run the (explicit) simulation using the original input file.
Note the times below.

Copy the input deck to a new directory. Modify the input to run
an implicit eigenvalue analysis, computing the lowest 20
eigenvalues. Run the simulation and postprocess the results.

3. What is the lowest frequency? Hz
What is it period? sec.

Copy the input deck to a new directory. Modify the input to
run a linear implicit dynamic analysis. Increase the
termination time to 1.0 seconds and run the simulation.

Plot the Y-displacement of node ID 1000982 from the NODOUT
file, and compare with results from the explicit simulation.

5. Do the explicit and implicit results agree?
6. How much faster is the implicit simulation for this
(tiny) model?
7. How could results of the eigenvalue analysis be used to
select the time-step and output interval?

Copy the input deck to a new directory. Introduce some Newmark
damping (try GAMMA=0.60 and BETA=0.38). Run, plot the
Y-displacement of node ID 1000982 from the NODOUT file, and
compare with results from the previous simulations.

8. Does the damping most affect high or low frequency response?

Optional:
Copy the input deck to a new directory, and modify it to
perform a nonlinear implicit dynamic simulation. Reset the
termination time to 0.1 seconds and run the simulation.
Compare results for node ID 1000982.```

## Keywords

```*BOUNDARY_SPC_SET
*CONTROL_IMPLICIT_DYNAMICS
*CONTROL_IMPLICIT_EIGENVALUE
*CONTROL_IMPLICIT_GENERAL
*CONTROL_IMPLICIT_SOLUTION
*CONTROL_IMPLICIT_SOLVER
*CONTROL_TERMINATION
*DATABASE_BINARY_D3PLOT
*DATABASE_HISTORY_NODE
*DATABASE_NODOUT
*DEFINE_CURVE
*ELEMENT_SHELL
*END
*KEYWORD
*MAT_ELASTIC
*MAT_RIGID
*NODE
*PART
*SECTION_SHELL
*SET_NODE_LIST
*SET_SEGMENT
*TITLE```

## Reduced Input

```  *KEYWORD
*TITLE
dynamic tire kick
\$
\$----------------------------------------------
\$
*CONTROL_TERMINATION
\$#  endtim    endcyc     dtmin    endeng    endmas
0.100000         0       0.0       0.0       0.0
\$ 1.000000         0       0.0       0.0       0.0
\$
\$----------------------------------------------
\$
*CONTROL_IMPLICIT_GENERAL
\$#  imflag       dt0    imform      nsbs       igs     cnstn      form
0  0.001000
*CONTROL_IMPLICIT_DYNAMICS
\$#   imass     gamma      beta
1       0.0       0.0
\$        1      0.60      0.38
*CONTROL_IMPLICIT_EIGENVALUE
\$#    neig    center     lflag    lftend     rflag    rhtend    eigmth    shfscl
0       0.0         0       0.0         0       0.0         0       0.0
*CONTROL_IMPLICIT_SOLUTION
\$#  nsolvr    ilimit    maxref     dctol     ectol     rctol     lstol
0         0         0       0.0       0.0       0.0       0.0
\$#   dnorm    diverg     istif   nlprint    nlnorm
0         0         0         0
\$        0         0      9999         0
\$#  arcctl    arcdir    arclen    arcmth    arcdmp
0         0       0.0
*CONTROL_IMPLICIT_SOLVER
\$   lsolvr    lprint    negeig     order     drill     dparm   autospc    aspctl
0         0         0         0         0         0         0         0
\$        6         1         0         0         0         0         0         0
\$   lcpack     kdump
0         0
\$
\$----------------------------------------------
\$
*DATABASE_NODOUT
\$#      dt    binary
0.001000
*DATABASE_BINARY_D3PLOT
\$#      dt      lcdt      beam     npltc
0.100000
*DATABASE_HISTORY_NODE
\$#     id1       id2       id3       id4       id5       id6       id7       id8
1000982
\$
\$----------------------------------------------
\$
*BOUNDARY_SPC_SET
\$#    nsid       cid      dofx      dofy      dofz     dofrx     dofry     dofrz
522         0         1         1         1         1         1         1
*SET_NODE_LIST
\$#     sid       da1       da2       da3       da4
522       0.0       0.0       0.0       0.0
\$#    nid1      nid2      nid3      nid4      nid5      nid6      nid7      nid8
1001284   1001299   1001300   1001285   1000973   1000975   1000908   1000909
1000893   1000894   1000895   1000896   1000911   1000910   1000979   1000977
1001301   1001302   1001286   1001287   1001303   1001288   1000981   1000912
1000897
\$
\$----------------------------------------------
\$
\$#    ssid      lcid        sf        at
99        99     0.001       0.0
*DEFINE_CURVE
\$#    lcid      sidr       sfa       sfo      offa      offo    dattyp
99         0       0.0       0.0       0.0       0.0
\$#                a1                  o1
0.0                 0.0
0.01000000                 1.0
0.05000000                 0.0
9.00000000                 0.0
*SET_SEGMENT
\$#     sid       da1       da2       da3       da4
99       0.0       0.0       0.0       0.0
\$#      n1        n2        n3        n4        a1        a2        a3        a4
1001246   1001261   1001262   1001247       0.0       0.0       0.0       0.0
1001231   1001246   1001247   1001232       0.0       0.0       0.0       0.0
1001216   1001231   1001232   1001217       0.0       0.0       0.0       0.0
1001215   1001230   1001231   1001216       0.0       0.0       0.0       0.0
1001214   1001229   1001230   1001215       0.0       0.0       0.0       0.0
1001229   1001244   1001245   1001230       0.0       0.0       0.0       0.0
1001244   1001259   1001260   1001245       0.0       0.0       0.0       0.0
1001245   1001260   1001261   1001246       0.0       0.0       0.0       0.0
1001230   1001245   1001246   1001231       0.0       0.0       0.0       0.0
\$
\$----------------------------------------------
\$
*PART
\$# title
tire
\$#     pid     secid       mid     eosid      hgid      grav    adpopt      tmid
24001     24001    200092
*SECTION_SHELL
\$#   secid    elform      shrf       nip     propt   qr/irid     icomp     setyp
24001        16  1.000000         2         0       0.0
\$#      t1        t2        t3        t4      nloc     marea
4.000000  4.000000  4.000000  4.000000         0       0.0
*MAT_ELASTIC
\$#     mid        ro         e        pr        da        db  not used
2000929.1000e-10 50.000000  0.300000       0.0       0.0       0.0
\$
\$
*PART
\$# title
wheel
\$#     pid     secid       mid     eosid      hgid      grav    adpopt      tmid
24005     24005    200194
*SECTION_SHELL
\$#   secid    elform      shrf       nip     propt   qr/irid     icomp     setyp
24005         2  1.000000         2         0       0.0
\$#      t1        t2        t3        t4      nloc     marea
3.000000  3.000000  3.000000  3.000000         0       0.0
*MAT_RIGID
\$#     mid        ro         e        pr         n    couple         m     alias
2001947.7999e-092.0000e+05  0.300000       0.0       0.0       0.0
\$#     cmo      con1      con2
1.000000         0         0
\$#lco or a1       a2        a3        v1        v2        v3
0.0       0.0       0.0       0.0       0.0       0.0
\$
\$
*PART
\$# title
belt
\$#     pid     secid       mid     eosid      hgid      grav    adpopt      tmid
24011     24003    200089
*SECTION_SHELL
\$#   secid    elform      shrf       nip     propt   qr/irid     icomp     setyp
24003        16  1.000000         2         0       0.0
\$#      t1        t2        t3        t4      nloc     marea
2.250000  2.250000  2.250000  2.250000         0       0.0
*MAT_ELASTIC
\$#     mid        ro         e        pr        da        db  not used
2000897.8299e-092.0684e+05  0.280000       0.0       0.0       0.0
\$
\$----------------------------------------------
\$
*ELEMENT_SHELL
\$#   eid     pid      n1      n2      n3      n4
*END```