A method that derives an approximate equivalent static load to a base excitation shock analysis is described. The transient analysis in the current level of NASTRAN, level 16, does not directly provide for either input acceleration forcing functions or enforced boundary displacement. In the suggested alternate analysis format, equivalent force input functions are applied to the constrained locations by using the artifice of placing a large mass, with respect to the total system mass, at the desired acceleration input points. This shortcut static analysis approach is presented to approximate the expensive and time consuming dynamics analysis approach to the base excitation shock analysis

Denver, R. E.

Menichello, J. M.

English

NASA Technical Reports Server

ALTERNATE APPROACHES TO VIBRATION AND SHOCK ANALYSIS USING NASTRAN
Richard E. Denver and Joseph M. Menichello
IBM Federal Systems Division
ABSTRACT
In analyzing sinusoidal steady-state vibration of structures, the NASTRAN
(NASA Structural Analysis) program provides Rigid Formats 8 and 11 for direct
and modal frequency and random response solutions. The dynamic solution of the
sinusoidal steady state vibration problem usually requires very large memory
core allocations and very long computational time. Our experience of analyzing
the Proteus system structures revealed an alternate solution set composed of
modifying the eigenvector output of normal modes analysis, resulting in signifi-
cant cost savings. This paper gives a step-by-step approach for the use of
this alternate algorithm to the sinusoidal steady-state vibration problem.
The paper then deals with a method that derives an approximate equivalent
static load to a base excitation shock analysis. The transient analysis in the
current level of NASTRAN, level 16, does not directly provide for either input
acceleration forcing functions or enforced boundary displacement. In the
suggested alternate analysis format, equivalent force input functions are
applied to the constrained locations by using the artifice of placing a large
mass, with respect to the total system mass, at the desired acceleration input
points. This shortcut static analysis approach is presented to approximate the
expensive and time-consuming dynamics analysis approach to the base-excitation
shock analysis.
Each of these methods has proved to be a reliable mechanical design guide
and has correlated closely with empirical results.
INTRODUCTION
As the Environmental Design Analysis group at IBM's Federal Systems Divi-
sion (FSD), Owego, NY, facility, our primary function is to guide the mechanical
design of FSD hardware during concept and development phases. Vibration and
shock requirements associated with these products are often quite severe, as
illustrated in figures la, Ib, Ic, and Id.
Structural analysis in support of the mechanical design of electronics
equipment is necessary to ensure compliance with the dynamic environmental
requirements. Initially, the harmonic and random vibration excitation formats,
as well as direct and modal transient shock capability of NASTRAN, have been
exercised to validate structural design. As the designs progress, many changes
are incurred due to customer request, product improvement, compatibility with
199
https://ntrs.nasa.gov/search.jsp?R=19780004515 2020-03-22T06:38:25+00:00Z
fabrication techniques, and results of analysis, each requiring analytical
evaluation. In general, these changes must be assessed quickly and accurately
and must result in minimum effect on cost and schedule. Because of long turn-
around time and long computation time associated with the rigid formats we have
been using, we began a study for an alternate, more efficient algorithm for
this solution phase.
The two methods resulting from this investigation for representing struc-
tural deformations and stresses under the influence of vibration and shock
environments are discussed under the headings "Vibration Stress Analysis" and
"Shock Stress Analysis."
VIBRATION STRESS ANALYSIS
The following steps give the structural analyst a simplified shortcut in
determining maximum stresses in structural members during sinusoidal steady-
state vibration at resonant frequency. This approach foregoes the direct or
modal frequency and random response analysis, Rigid Format 8 or 11, respec-
tively, which requires very large memory core allocations and very long compu-
tation time, and uses normal modes analysis, Rigid Format 3, and static analy-
sis, Rigid Format 1, with an appropriate ALTER package given in the presenta-
tion:
1) First, run a normal modes analysis (Rigid Format 3) to determine
fundamental strutural resonances in three principal directions.
a) Specify MAX in the NORM field of the'EIGR continuation card.
This normalizes maximum structural displacement for use in
conjunction with the ALTER package given below.
b) Use CHKPNT YES in the Executive Control deck to checkpoint
all the necessary data and to recover the data in restart.
This step will result in significant savings when used with
the ALTER package or to calculate additional vibratory modes.
2) To restart the checkpointed run to determine structural deformation
and vibration stresses at resonance, the following items have to be
specified:
a) Specify a maximum structural displacement at the structural
resonance, (8). This can be estimated from the following
relationship for a single-degree-of-freedom system.
ft 386.1 x G x 0
b =
 2 2
4TT X f
where
8 = single amplitude of response of structure (inches)
G = input steady state sinusoidal peak acceleration
Q = transmissibility at resonance
f = structural natural frequency
200
In the above relationship, it is assumed that G is a known
quantity, and £ has been determined^in the NASTRAN analysis
using Rigid Format 3. The transmissibility at resonance may
be determined from test data of a prototype or similar structure.
If this data is not available, however, experience has shown
that a range of 0.05 < C/Cr < 0.10 is typical of three-dimen-
sional frame structures of standard construction. Figure 2
illustrates the interrelationship between structural damping
and amplification factor at resonance.
b) Insert the following ALTER package* in the. NASTRAN Executive
Control deck, which scales all output, and which includes struc-
tural deformations and stresses. (F°r Level 16)
ALTER 108, 108
SDR1 USET,,PHIA,,,GO,GM,,KFS,,/
PHIGG,QG/C,N,1/C,N,REIG $
ADD PHIGG,/PHIG/C,Y,ALPHA=(1.0.0.0)7
C,Y,BETA = (0.0,0.0) $
ADD QGG,/QG/C,Y,ALPHA=(1.0.0.0)7
C,Y,BETA=)0.0,0.0) $
ENDALTER
c) In conjuction with the ALTER package, the user would also have
to specify the value of ALPHA on a PARAM card in the BULK DATA
deck. This value of ALPHA corresponds to the maximum structural
response, 8, calculated in the step 2a) of the procedure.
Example of this procedure follows:
Input vibration level = 2 g peak sinusoidal
Natural frequency of structure = 68 Hz
Transmissibility of structure = 10
g
 = 386.1 x G x q m 386.1 x 2 x 10 Q^2 ±nch
47T x f 4x(3.14) x(68)
Specifying in the BULK DATA deck
IPARAM [ALPHA 10.042 |0.0 | |\
will result in linear scaling of all the output data blocks by
a factor of 0.042. Obviously, because of the assumptions used,
this method is restricted to linear analysis only.
Note: If the user were interested in a RESTART capability,
DMAP statement 109 should also be altered to check-
point data block PHIGG as well as PHIG and QG in
the Rigid Format 1.
*The authors wish to express their gratitude to the staff of the NASTRAN Sys-
tems Management Office, NASA Langley Research Center, Hampton, Virginia,
particularly to Mr. Joseph Walz for assistance offered in preparation of the
ALTER packages presented in this paper.
201
SHOCK STRESS ANALYSIS
The NASTRAN program provides two rigid formats for analyzing shock excita-
tion problems. The transient analysis capability in the current level of
NASTRAN, level 16, however, does not directly provide for input acceleration-
forcing functions or enforced boundary displacement. To overcome this defi-
ciency in the program, modifications* had to be made to use the program for
our specific application of base shock excitation of structures.
The following modifications were necessary to use Rigid Format 9 (Direct
Transient):
1) Modify the math model as follows:
a) Place large seismic masses at all boundary points. These large
seismic masses at the support points are necessary to reduce
the effects of feedback from the structural responses.
b) Use multipoint constraint (MFC) equations so that all boundary
points will move together, allowing motion only in the direction
of the shock.
c) Calculate a forcing function, f(t), which will produce the
desired acceleration function on the overall mass, structural
mass plus seismic mass, to satisfy the relationship F=ma at
different time intervals.
d) Input the forcing function, f(t), at the boundary points using
the DAREA card in the BULK DATA deck.
2) Cold start Rigid Format 9.
The following modifications were necessary to use the Rigid Format 12
(Transient Modal Analysis):
1) Run a normal modes analysis, Rigid Format 3, (we suggest using
the Inverse Power method) to determine the fundamental structural
resonance in each principal direction along which shock pulse is to
be applied. Be sure to checkpoint this run. In this run, seismic
masses should not be attached to the boundary points in the math
model.
2) Modify the math model as follows:
a) Place large seismic masses at all boundary points; approximately
times the structural mass.
*The authors would like to thank Mr. Leon H. Arnold, IBM Owego, and Dr. Han
Chung Wang, IBM Endicott, for their technical assistance in developing the
alternate solution methods and implementing them in the NASTRAN program.
202
b) Use MFC equations for all the boundary points to allow the .
boundary points to move only in the direction of the shock.
c) Calculate a forcing function in the same manner as in using
Rigid Format 9.
d) Input the forcing function at the boundary points; these are
structural attachment points either at the base or bulkhead of
aircraft, shipboard, submarine, or other test fixture frames.
3) Restart Rigid Format 12 using the structural resonance data obtained
in Rigid Format 3,
a) Bound the resonance of interest by using the PARAM LFREQ and
PARAM HFREQ cards in the BULK DATA deck; the smaller the bandwidth,
the more rapid the computation time. To minimize convergence
time, specify the same frequency range on the EIGR card as
specified on the preceding PARAM LFREQ and PARAM HFREQ cards.
NOTE: In all rigid formats, it is imperative to use a pre-
processor program, such as BANDAID or BANDIT to reduce
the semi-bandwidth of structural matrices.
The excessive time associated with model preparation and solution to shock
analyses using NASTRAN Rigid Formats 9 and 12 reduced their usefulness for the
specific application of mechanical design guidance in the earliest phases of
design.
The following method has been developed which approximates the effect of
the shock pulse on the system through the use of a single-degree-of-freedom
idealization, assuming that the fundamental mode parallel to the direction of
the pulse is the sole contributor to maximum deformation and corresponding
stresses. This method utilizes a combination of Rigid Formats 3 and 1 in place
of Rigid Format 9 or 12. Its implementation is described in the following
lists:
1) Perform a natural frequency analysis, Rigid Format 3, using the Inverse
Power method to determine the fundamental structural resonance in each
plane in which a shock pulse is to be applied. The use of Inverse
Power eigenvalue extraction will prove most efficient since only a few
of the resonant modes are of interest.
Note: One can force the program to search for resonant modes in
numerically ascending order by specifying ND = small, NE =
large (~100xND) in the EIGR card. This will reduce the
computation time required to find the lowest natural fre-
quency. It will significantly reduce the possibility of
terminating via termination codes 6 or 7 without determining
the fundamental mode.
2) Calculate the dimensionless parameter t /T in which
o
ti = pulse period (seconds) of the shock to be applied
T = fundamental period of responding structure = 27T/ cu(seconds)
203
3) Using the plotted data in figure 3, extracted in part from reference
4, determine x/A (acceleration amplitude magnification factor)
where
A = peak acceleration of input pulse (g)
x = maximum response acceleration of structure (g)
As shown in figure 3, the solution to the equation of motion and its
derivatives for the single-degree-of-freedom idealization are depend-
ent on the degree of viscous damping exhibited by the responding sys-
tem. This value may be determined from test data by examining the
transmissibility (Q) at resonance and correlating Q with the damping
factor (C/Cr) through the use of graphs specified in reference 2,
repeated in figure 2 for illustration. If test data is not available,
experience has shown that a value of damping of 0.05<C/Cr < 0.10 is
typical of most three-dimensional framed structures of standard
construction.
4) Cold start in Rigid Format 1 specifying a loading, G, through the use
of the NASTRAN GRAY card in which
G
 -
 AX!
where
A = peak acceleration of input shock pulse, g
• • '
J£
-T- = dynamic load factor determined in step 3
A.
CONCLUSIONS
The two methods discussed previously have proved to be a valuable engineer-
ing aid during the developmental phase of mechanical designs. They have proved
to be more cost- and time-effective than their counterparts in NASTRAN Rigid
Formats 9, 10, 11, and 12. Tables 1 and 2 summarize the time and cost compari-
sons of the various solutions. In addition, the solutions have proved to yield
acceptable accuracy as evidenced in tables 3 and 4.
204
REFERENCES
1. Dr. Richard Eppink: A Comparison of Direct Integration vs Modal Methods of
Analysis for Transient Response Analysis in NASTRAN. University of Virginia.
2. Application Selection Guide. Barry division of Barry Wright Corporation.
3. C.M. Harris and C.E. Crede: Shock and Vibration Handbook. New York:
McGraw Hill, 1961, pp 23-1 through 23-37.
4. Robert R. Luke: The Impact Response of Single-Degree-of-Freedom System
with Viscous Damping. University of Texas, Structural Mechanics Research
Laboratory, Austin, Texas.
5. NASTRAN User's Manual, NASA SP-222(03). Scientific and Technical Informa-
tion Office, National Aeronautics and Space Administration, March, 1976.
6. NASTRAN Theoretical Manual, NASA SP-221-(03). Scientific and Technical
Information Office, National Aeronautics and Space Administration, March,
1976.
7. NASTRAN Programmers Manual, NASA SP-223(03). Scientific and Technical
Information Office, National Aeronautics and Space Administration, March,
1976.
8. Dr. Gordon C. Everstine: The BANDIT Computer Program for the Reduction of
Matrix Bandwidth for NASTRAN. Computation and Mathematics Department,
Naval Ship Research and Development Center, Bethesda, MD 20034, March, 1972,
Report No. 3827.
205
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DOF - degree of freedom
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EXCP - Execute Channel program
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TABLE 3. - RESULTS COMPARISON OF ALTERNATE SOLUTION METHODS
FOR OBTAINING MAXIMUM VIBRATION DISPLACEMENTS AND STRESSES
Unit
analyzed
Proteus
Analyzer
Unit
Solution
method
Modal
frequency &
random
response
Alternate
solution
method
Engineering
development
test
Direction
X
Y
Z
X
Y
Z
X
Y
Z
Fundamental
natural
frequency
(Hz)
66
188
406
66
188
406
72*
190*
420*
Maximum peak
axial stress
2
(Ibf/in )
10,400**
NA
NA
13,710
-
-
NA
NA
NA
Notes:
*Variation in test/analytical results attributed to weight discrepancy ( 50 Ib)
and modified structural configuration „
**Based on 20% damping; 5% damping yielded 40,100 Ibf/in maximum stress
TABLE 4. - RESULTS COMPARISON OF ALTERNATE SOLUTION METHODS
FOR OBTAINING MAXIMUM SHOCK DISPLACEMENTS AND STRESSES
Unit
analyzed
Proteus
STM/
TACTAS
Electronics
Rack
Eigenvalue extraction
Direction
-
X
Y
Z
X
Y
Z
Natural
frequency
(Hz)
-
124
70, 125,
146
Not found
122
70, 124,
146
Not found
Loading
condition
Navy
high impact
Medium Weight,
inclined ,
hammer-
drop
shock
test
Shock stress analysis
Solution
method
Direct
transient
analysis
Alternate
solution
method
Engineering
development
testing
Maximum peak
axial stress
(Ibf/in2)
31,770
28,905
29,000
208
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0.002
0.001
Saturn /
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•~\\
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10 20 30 50 100 200300 500 1000 2000
Frequency (Hz)
Figure la. Typical Spacecraft Random Vibration Levels
209
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1,000
100
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Frequency (Hz)
Figure Ib. Shock Requirements,
Pyrotechnic Shock Spectrum
u. i •
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0.0003
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I 10 20 30 50 100 200 500 1000 2000
Frequency (Hz)
Figure Ic. Typical Aircraft Sinusoidal
Vibration Requirements
210
360-
270-
3 90-
c
o
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-90-
-180-
-270-
-360
0 0.00610.01210.018 0.024I0.0300.03610.04210.048 Time (Sec)
Figure Id. Typical Navy Medium-Weight-Hammer-
'Drop Anvil Response
0.01 0.1 0.2 0.4 0.6 1
Ratio (fd/fn)
4 6 10
Figure 2. Family of Transmissibility Curves
for a Single-Degree-of-Freedom System
211
:x
1
re
_
i
0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6
0.4
i
• re
u.
_o
re
0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 16
Time Ratio (t-j/T)
Figure 3. Shock Transmissibility Curves for a
Single-Degree-of-Freedom System with Directly Coupled
Viscous Damping Subjected to Sinusoidal and
Terminal-Peak Sawtooth Shock Pulses
212


Alternate approaches to vibration and shock analysis using NASTRAN

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