SHOCK ANALYSIS USING THE PSEUDO VELOCITY SHOCK SPECTRUM PART 1 - PowerPoint PPT Presentation

1 / 87
About This Presentation
Title:

SHOCK ANALYSIS USING THE PSEUDO VELOCITY SHOCK SPECTRUM PART 1

Description:

Proofs that stress is proportional to velocity for rods, beams, plates. ... Railroad humping on acceleration shock. spectrum shows constant velocity. 34 ... – PowerPoint PPT presentation

Number of Views:1913
Avg rating:5.0/5.0
Slides: 88
Provided by: howardag
Category:

less

Transcript and Presenter's Notes

Title: SHOCK ANALYSIS USING THE PSEUDO VELOCITY SHOCK SPECTRUM PART 1


1
SHOCK ANALYSIS USING THE PSEUDO VELOCITY SHOCK
SPECTRUMPART 1
  • Howard A. Gaberson, Ph.D., P.E.
  • Consultant
  • 234 Corsicana Drive
  • Oxnard, CA 93036-1300
  • (805)485-5307
  • hagaberson_at_att.net

2
Dick Chalmers1931 - 1998
3
Joel Leifer
4
Henry Pusey
5
Points to Learn
  • Shock spectrum definitions
  • Equations Conceptual and Practical
  • Calculate Do loop, Filter, Residual
  • Plotting SS's with PV as ordinate on (4CP)
    log-log four coordinate paper.
  • Proofs that stress is proportional to velocity
    for rods, beams, plates.
  • Fundamental Maximum modal velocities
  • Shock data needs least range in velocities
  • PV use Civil/Structural, nuclear defense, Army
    Conventional Weapons Effect, Earthquake. Hall's
    chapter in Shock and Vibration Hdbk
  • (PV)2 ,energy, severe frequencies.
  • PVSS on 4CP asymptotes peak displ, severity or
    vel change, and peak accel.
  • PV vs Rel Vel, low freq. problem.
  • Integrated shock presentation

6
More Important Points
  • Half sine example. Compare to explosive and EQ
  • Tests of which motion analysis is best for
    damage. PV on 4CP wins.
  • Shaker shock wimp. Both synthesized or pre and
    post pulses.
  • Applies to MDOF
  • Susceptible Frequencies
  • Shock Isolation
  • Damping. Precludes swept sines.
  • Heavy damping shows polarity pos neg spectra.
  • Mean removal and detrending. Show El Centro Calc
    ss of a trend. Reasonable fudge Add trend to
    adjust net displacement.

7
Shock Spectrum Definition
  • SS is a plot of an analysis of a transient motion
    that calculates the maximum response of many
    different frequency damped SDOFs exposed to the
    motion. (explosions, earthquakes, package drops,
    railroad car bumping, vehicle collisions, etc.)
  • Can be positive, negative, or maximum of the
    two. Maximax maximum of the maximum (refers to
    residual and during)
  • Can be for during or after the motion or both.
    Residual means after. SDOF can be damped or
    undamped. And could use relative or absolute
    acceleration, velocity, or displacement, and
    pseudo velocity.
  • REPEAT FOR US ITS A PLOT OF AN ANALYSIS OF A
    MOTION.
  • .

8
ABSOLUTE ACCELERATION SHOCK SPECTRUM, SRS
  • LOG LOG PLOT OF ABSOLUTE ACCELERATION VS
    FREQUENCY MOST POPULAR SHOCK SPECTRUM FORM
    CALLED SRS. NOT GOOD FOR DAMAGE. ALLOWS WEAK
    SHOCKS TO APPEAR SEVERE.

9
PVSS on 4CP
  • Pseudo velocity is best for severity or capacity
    to cause damage.
  • PSEUDO VELOCITY EXACTLY MEANS PEAK RELATIVE
    DISPLACEMENT, Z, MULTIPLIED BY THE NATURAL
    FREQUENCY IN RADIANS, .
  • PVSS4CP (PSEUDO VELOCITY SHOCK SPECTRUM PLOTTED
    ON FOUR COORDINATE PAPER) IS A SPECIFIC
    PRESENTATION OF THE RELATIVE DISPLACEMENT SHOCK
    SPECTRUM THAT IS EXTREMELY HELPFUL FOR
    UNDERSTANDING SHOCK.

10
FOUR COORDINATE PAPER
The best way to plot PVSS is on 4CP
(tripartite.) 4CP is a logarithmic graph that has
four sets of lines relating frequency,
displacement, velocity, and acceleration of
sinusoidal motion. For a sine wave, the
displacement, velocity, and acceleration are
Equating maximum values yields
The equations mean
are related. Knowing two, can calculate other.
two. On loglog paper, lines of constant
versus
are all straight lines. Look at a 4CP plot.
11
4CP example. Lines slanting down to the right
are constant gs. Slanting down to left are
constant displacement. Horizontal pseudo
velocity. Vertical frequency.
12
On 4CP, if you know any two, you can get the
other two from
13
SHOCK SPECTRUM EQUATION DWGS THIS SYSTEM A
BOGY GETS THE SHOCK RATTLES THE MASS
14
Mental Model
15
Free Body Diagram
16
Shock Spectrum Equation
17
Duhamels Integral Solution
Use on digitized shock values and apply eqs. from
one data point to the next. Over and over for
whole, say, 10,000 point shock.
18
Aside Undamped
19
Calculating Details
Equations become
After integrating from 0 to h, we get O'Hara's
and EQ Eqs.
Manipulating you can get
These get during values. Pick off max and final
values and then calc residual
20
Residual Calculation
  • One way is to append at least one period of zeros
    to the shock and consider all of the file as
    during and pick off the max and min values.
  • Second procedure takes the final during
    displacement and velocity as initial conditions
    and evaluate the free damped vibration equations
    for the maximum and minimum values.
  • Both procedures have merit. I happen to use the
    second.

21
PLOTTING PVSS ON 4CPDISPLACEMENT, VELOCITY,
ACCELERATION
22
ACCELERATION MEANING ON 4CP
23
Response of a 20 Hz 15 damped SDOF
toExplosion.. Notice max acceleration does not
occur at same time as max displacement.
24
Arguments for shock spectra with PV as ordinate
on log-log 4CP
  • Velocity Theoretically stress proportional to
    modal velocity
  • Velocity Experimentally spectral and time plots
    require least range.
  • PVSS on 4CP relate experimentally severe shocks
  • Related to stored elastic energy Indicates
    capacity to deliver energy
  • Shows Three Regions
  • 1. Peak deflection, Rattle space reqts.
  • 2. High PV mid plateau, severe energy
    delivery frequencies.
  • 3. Max acceleration
  • Unmasks weak shocks with damping
  • Reveals polarity with damping

25
Why Pseudo Velocity and not Absolute or Relative
Velocities are Best For Shock Spectra
26
Precedent for PVSS on 4CP
  • Eubanks and Juskie "Shock Hardening of
    Equipment" SVB 1963
  • Crede in ASME, "Shock and Structural Response"
    1960
  • Fung in same ASME publication
  • Civil Seismic Community Hall's Chapt in recent
    SV Hdbk
  • Roberts in "Explosive Shock in our 1969 SVB
    Session
  • Vigness in 1964 SVB "Elementary Considerations of
    SS
  • Currently UERD, EQ, Structural, Nuclear

27
MECHANICAL SHOCK
  • Explosion, a shock wave in air or water,
    instantaneous intense pressure spike, 1000's of
    psi.
  • Impacts metal structure.
  • Excites 100's of modes.
  • Accelerometer sensing that motion reads the build
    up and ring down of modes as a complicated
    multi-frequency shock.

28
Near Miss Explosion, Army Tank
Near Miss Explosion, Army Tank
29
EXPERIMENTAL DATA REQUIRE THE LEAST DYNAMIC RANGE
WITH VELOCITY
  • From Walsh, J.P., A Review of the Report on
    the Cameron Trials, SVB, No. 4, p 62, July
    1947 Royal Navy "Cameron Trials", experiment.
  • Conducted an instrumentation study, of shock
    damage to specimen with many structure types
    (high/low freqs, brittle/ductile),
  • Specimen designed to provide failure modes like
    those of underwater blast.
  • Many different shocks applied to specimen until
    all designed failure modes occurred.

30
EXPERIMENTAL DATA REQUIRE THE LEAST DYNAMIC RANGE
WITH VELOCITY, II
EXPERIMENTAL DATA REQUIRE THE LEAST DYNAMIC RANGE
WITH VELOCITY, II
  • Analysis wide ranges of usual shock parameters
    were needed to describe failure levels for all
    modes designed into the specimen.
  • Accelerations associated with failure ranged from
    2.45 to 9x103 g's.
  • Displacements varied from 1.9 to 7.6x10-4 inches.
    Extremes in each would cause failure in one mode
    but not in another.
  • Velocity at these accelerations and displacements
    ranged from 30 to 240 inches/second.

31
EXPERIMENTAL DATA REQUIRE THE LEAST DYNAMIC RANGE
WITH VELOCITY, III
  • Accelerations range for damage was 3700 to 1.
  • Displacement range for damage was 2500 to 1.
  • Velocity range for damage was 8 to 1.
  • Expressed in dB 71 dB for acceleration 68
    dB for displacement 18 dB for velocity.
  • If their test specimen, representative, velocity
    was best parameter for shock.
  • Velocity was prominent during "Cameron Trials",
    and has been important in U. S. Navy ship shock
    trials since that time.

32
Gunfire Shock plotted as acceleration shock
spectrum shows constant velocity character
Data falling along 12 ips line
33
Railroad humping on acceleration shock spectrum
shows constant velocity
If this is g's it's 61.4 ips,
34
Existing Knowledge that stress proportional to
modal velocity
  • Reinhart's 1954 work cited by Roberts in 69 SVB
  • Hunt 1960, JASA
  • Ungar 1962, ASME Trans.
  • Crandall, late 62, ltr. to JASA
  • Ungar 71 used in Damping Chapt. In Beranek's
    Noise Vibe Control
  • Lyon, 75 used in SEA book
  • MIL Std 810F acknowledges
  • Gaberson Chalmers Modal Velocity 1969 SVB
  • Shock and Vibration Handbook Equipment Design

35
Stress is Proportional to Velocity
ABSOLUTELY ESSENTIALRIGHT HERE AND NOW THAT I
CONVINCE YOU THAT STRESS IS PROPORTIONAL TO
VELOCITY AND NOT ACCELERATION.
36
Shock Spectrum Equation,Variables and Constants
y is the shock. We calculate max z. Free body
diagram of m. F ma, gives
Divide by m and use
Shock Spectrum Equation
37
Strain in a rod
                         
 
38
F ma
               
 
39
Stress Velocity Rods
40
More Stress Velocity Rods
41
SUM UP STRESS VELOCITY IN RODS
42
BEAMS STRESS VELOCITY EQUATIONS
Develop beam vibration equation. From strength
of materials we have      
When the beam is vibrating, (accelerating up and
down) the ma load on the little chunk of beam
is, then uniform load on the
beam, (force per unit length) is
Substituting this value for w, in (1c) gives us
the Bernoulli Euler beam vibration equation  
43
STRESS VELOCITY IN BEAMS
44
MORE BEAM STRESS VELOCITY
45
BEAM SHAPE FACTORS
46
Ted Hunts Analysis(Frederick Vinton Hunt from
Harvard)
K was a beam shape factor, but Hunts careful
scholarly analysis in JASA, 1960, proves that the
relation.holds for plates, tapered rods, and
wedges. He felt that for practical situations the
constant stays under two, but found a value for a
cone of 6.89. He used the phrase half and order
of magnitude. He also argues that it applies to
sums of modes.
47
SEVERE VELOCITIES
 
 Velocity proportional to stress higher stress
allows higher velocity.   Vibrational velocity is
the parameter that proportional to stress, and as
such indicates the severity of the vibration in
structure. Only taught in statistical energy
analysis. Hunt 4 knew this well before 1960
Ungar 5 understands it. Crandall commented on
it 7. Lyon 6 knows this and uses it in his
book. But it still is not in machine design,
materials, or vibration texts. I keep bringing
it up to encourage its use.  
 
48
HIGH PVSS SHOWS SHOCK CAPACITY TO DELIVER ENERGY
TO AN SDOF SYSTEM
MAXIMUM PSEUDO VELOCITY IS RELATED TO THE ENERGY
STORED IN THE SDOF SPRING   The shock spectrum
algorithm finds the peak relative displacement
for a base excited SDOF. That's the spring
stretch which is how the SDOF system stores
energy.   Consider the elastic energy stored in
the spring, and remember k/m ?2,     This
is our pseudo velocity. Pseudo velocity is the
square root of twice the peak energy per unit
mass that is stored in the oscillator during the
shock. HIGH PV FREQUENCY RANGE IS WHERE IS WHERE
SHOCK HAS GREATEST CAPACITY TO DELIVER ENERGY.
49
Before I Look at the Extremely Important
Asymptotes
  • Consider Half Sine and other Simple Shocks First
  • Then well do
  • 3 Regions on the PVSS on 4CP
  • Important
  • Acceleration and Displacement Asymptotes
  • Severity

50
Half Sine and Other Simple Shocks
  • Include drop in analyzed signal. Have chuckle re
    Hdbk. SRS drop.
  • You need to learn why Drop needed for low
    frequency
  • No rebound
  • Other simple shocks same SS
  • Impact Velocity Change
  • Peak acceleration
  • Max displacement

51
PVSS-4CP Example 800 g, 1 ms half sine
52
ZERO MEAN SIMPLE SHOCK
  • THAT LAST SHOCK WAS A ZERO MEAN SIMPLE SHOCK.
  • ZERO MEAN ACCELERATION MEANS SHOCK BEGINS AND
    ENDS WITH ZERO VELOCITY
  • THE SHOCK INCLUDES THE DROP AND ANY REBOUND.
  • THE INTEGRAL OF THE ACCELERATION IS ZERO IF IT
    HAS A ZERO MEAN.
  • BY SIMPLE SHOCK I MEAN ONE OF THE COMMON SHOCKS
    HALF SINE, INITIAL PEAK SAW TOOTH, TERMINAL PEAK
    SAW TOOTH, TRAPEZOIDAL, HAVERSINE

53
ZERO MEAN, SIMPLE SHOCK, PVSS-4CP HILL SHAPE
  • WHEN A ZERO MEAN SIMPLE SHOCK PVSS IS PLOTTED ON
    4CP IT HAS A HILL SHAPE
  • THE LEFT UPWARD SLOPE IS A PEAK DISPLACEMENT
    ASYMPTOTE
  • THE RIGHT DOWNWARD SLOPE IS THE PEAK
    ACCELERATION ASYMPTOTE.
  • THE TOP IS A PLATEAU AT THE VELOCITY CHANGE
    DURING IMPACT.

54
Collision and Kickoff Shocks
  • Collision shock, (a car slamming into a wall)
  • Kickoff shock (environment on a ball when it is
    kicked)
  • Do not have a zero mean.
  • The collision starts with a high velocity and
    ends with zero velocity
  • The kickoff starts with zero velocity and ends
    with a high velocity.
  • These PVSS's on 4CP have damped max velocity
    change low frequency asymptote, vice down to the
    left maximum deflection asymptote line.

55
Half sine equations
56
HALF SINE SHOCK WITHOUT THE DROPI'm going to
plot this half sine shock along with it's two
integrals. Let's illustrate it with a moderately
severe shock with a 100 ips velocity change and a
peak acceleration of 200 g's. From the above
formula, we find the duration to be 2.035 ms.
Assume a shock machine table could do this, and
consider the integrals.
The shock machine table has a final velocity and
just keeps on going.
57
BAD SHOCK SPECTRUM OF HALF SINEThis what I want
everyone to learn to expect. Because the velocity
did not end at 0, this is an unrealistic SS.
It's indicating that a 0.1 Hz SDOF would have a
peak deflection of about 140 inches, 12 ft. No
way. However notice that the velocity change of
100 ips shows up as it should and the curve at
high frequency is assympotic to 200 g's, as it
must.
Here's its PVSS on 4CP. Get used to these 4
axes. AND 100 ips ands 200 gs
58
Correct concept. Half sine time history with
drop, and integrals
Include no rebound drop. Half sine brings to
rest. Realistic. Drop drop it 12.95. Use
half sine programmer.
59
SS of 100 ips, 200 g half sine with drop
Here's its PVSS
100 ips
13"
200 gs
Note The three regions 12.9" drop, 100 ips
velocity change, and the 200 g peak acceleration.
60
COSINE RAMP TRAPEZOID SHOCK EQUATIONS
Acceleration during cosine ramp to max in ?td
Integrate to get velocity change during ramp.
Final velocity change equation for cosine ramp
trap shock.
61
HOW MUCH COSINE RAMP IS REASONABLE
Now let's try and figure out how much of a cosine
ramp would be reasonable within the confines of
the IEC Specification, according to Figure 3., on
p40. I'm did it graphically in Matlab.   Now
studying this picture, their nominal trapezoid
has a linear ramp with phi0.1 the blue and
green limits allow one to increase td by 0.4, and
I used a cosine with a phi0.3. Ive drawn 0.3,
and by increasing the max and minimum levels.  
62
Trapezoid, 30 cosine ramp, 100 ips, 200 g with
drop
Simple pulses have similar PVSS's. Here's a 200
g, 100 ips trapezoidal shock, with a 30 cosine
ramp up and down.
Again it's caught by a programmer that brings it
to zero velocity.
63
Terminal peak sawtooth, 200 g. 100 ips, with 10
cosine fall off.
Here's the same for a 200 g, 100 ips terminal
peak shock.
64
Initial peak shock time plot
Here's the same for a 200 g, 100 ips initial
peak shock.
We shall see they all have a similar PVSS.
65
All the simple shocks are equally severe.
The simple pulses have similar shock spectra.
This is not well known, Vigness showed in 1964
paper, Gertel in 1967 Frankford Arsenal report..
If related by velocity change, they only differ
at high frequencies beyond PLATEAU, where
severity drops.
66
And with 5 damping we get the same result
No one knows this, but now you do. All simple
shocks have equally severe SSs. Gertel tossed
that comment off in a '67 report, and Vigness
plotted in his 64 SVB Paper Shock and Vibe
Hdbk, Rubin and Ayre Chpts go overboard on the
droop.
67
HIGH AND LOW FREQUENCY ASYMPTOTES FOR PVSS ON
4CP TRADITIONAL RATIONALIZATIONS
  • High frequency oscillators have very stiff
    springs and light masses. The mass follows the
    acceleration of the foundation thus, these SDOFs
    record a peak absolute acceleration equal to the
    peak acceleration of the shock.
  • Low frequency oscillators are very flexible. If
    their foundations are given a very quick or short
    duration wiggle, the mass barely moves until the
    foundation motion is over. If the shock being
    analyzed is one that begins and ends with zero
    velocity, the peak relative deflection will be
    the peak shock displacement.
  • For intermediate values of the frequency, the
    peak pseudo velocity is often almost constant.
    In this region the pseudo velocity closely
    approximates the relative velocity. This region
    is the high PV region contains the frequencies
    where the shock has the greatest capacity to
    deliver energy to the SDOFs.

68
Low Frequency Asymptote Carefully
  • In low frequency region, spring very soft, mass
    heavy. Mass just sits there during shock.
    Maximum spring stretch or zmax is just maximum y,
    ymax We plot ?zmax  
  • Since ymax is constant, log of the pv here is
    straight line with positive slope.

69
HIGH FREQUENCY ASYMPTOTE CAREFULLY
  • In the PVSS on 4CP, we are plotting ?z focus on
    that.
  • In high frequency region mass very light and
    spring very stiff Mass exactly follows input
    motion. Acceleration of mass equal to
    foundation. Max z, is spring force over
    stiffness, k.  
  • On log log paper, since the maximum acceleration
    is a constant, pv is a straight line with a
    negative slope.

70
PLATEAU, MID FREQUENCY
  • The mid frequency, plateau region of the spectrum
    is the important region. It shows the velocity
    change of a simple pulse.
  • No one explains it well. And this is the really
    important part.
  • Pick up any civil structural textbook and go to
    the earthquake section and read the traditional
    explanations.
  • Vigness 1 declared without any explanation that
    four regions exist on the shock spectrum, and
    broke the center region into two parts this is
    typical of our business.
  • This middle region is the most severe and thereby
    most important region of the of the shock's SS.
    Here the PV is at its maximum. Vigness's
    comments

71
VIGNESS ON MID FREQUENCY REGION
  • Vigness's very important, yet somewhat weakly
    justified paper 1964 paper "Elementary
    Considerations of Shock Spectra" from the SVB
    n34, pp 211-222.
  • In paragraph 16 which is on page 213, "At some
    intermediate frequency, region B, peaks in the
    shock spectral curves indicate sustained
    frequencies of the shock motions.
  • At some lower frequency (generally), a section of
    the shock spectral curve, region V, remains at a
    constant velocity value. This corresponds to a
    frequency region over which the shock motion can
    be considered to be an impulsive (step) velocity
    change."
  • That's a very interesting few sentences, probably
    correct, but not justified. In his intro to the
    paper he warns that these are observations, and
    suggestions, not necessarily new. So maybe in
    1964, many people had agreed on this.

72
Roberts, W.H., Explosive Shock, Shock and
Vibration, Bulletin 40, Part 2, Dec 1969, pp
1-10.
  • This is a difficult paper for me to follow and
    has not received attention.
  • However he reasons, he gets many of the right
    answers. For example
  • It is reasonable to conclude therefore, by
    analogy to the discussion on the shock spectrum
    that vibration velocity measures internal
    stresses, not vibration acceleration. This is
    exactly the result that our analyses lead to.
  • He uses Rinehart and Pearson, Behavior of Metals
    Under Impulsive Loads, 1954 Dover, which
    establishes 1200-2400 inches per second as
    theoretical wave velocity limits in structural
    materials. He cites his experience that
    structure tolerates 360 ips. He next reasons
    that mechanical components velocity limits are
    60 120 ips.
  • His reasoning allows him to conclude that the 3
    shock spectrum regions are logical.
  • Clarifying of how Roberts thinks would help me.

73
Roberts Drawing
74
UNDAMPED PLATEAUIMPORTANT CONVINCE YOURSELF
  • Instant shock
  • Bogey and mass fall h
  • Shock over before spring compresses
  • Uundamped free vibration equation govern

75
PLATEAU FINISH
76
PLATEAU SUMMARY
77
SUMMARIZE UNDAMPED ZERO MEAN SIMPLE SHOCK SSs
  • UNDAMPED SIMPLE DROP TABLE SHOCKS HAVE A FLAT
    CONSTANT PV PLATEAU AT THE VELOCITY CHANGE THAT
    TOOK PLACE DURING THE SHOCK.
  • THE HIGH FREQUENCY LIMIT OF THE PLATEAU IS SET BY
    THE MAXIMUM ACCELERATION OF THE SHOCK.
  • THE HIGH FREQUENCY ASYMPTOTE IS THE MAXIMUM
    ACCELERATION LINE.
  • THE LOW FREQUENCY LIMIT OF THE PLATEAU IS SET BY
    THE MAXIMUM DEFLECTION OF THE SHOCK.
  • THE LOW FREQUENCY ASYMPTOTE IS THE MAXIMUM
    DISPLACEMENT LINE

78
ADJUST A SPECTRUM
79
2g LINE CONCEPT UNDAMPED SIMPLE SHOCK NO
REBOUND DROP HEIGHT IS WHERE THE PLATEAU
INTERSECTS 2 gs
80
2 g Line for Drop Height of a Simple Pulse as a
Function of Velocity Change
The red line is the 2 g line. The drop height is
the displacement at the intersection of the red
line and the desired velocity change. Accurate
for simple pulses where deflection during the
pulse is small.
81
Exception Joshs 200ips, 5 g Halfsine
82
Velocity level when numerical value of
acceleration in gs equals numerical value of
frequency in Hz
  If Ng is numerical value of g level, and Nf is
numerical value of frequency, we find  
(1)
83
Explosive shock time history and integrals
Here's a chunk of an explosive test. I
removed the mean to make the velocity end at
zero.
Peak accel 918 g's Peak vel 302, total vel
change abt 400, during first 4-5 ms abt 300
ips Max displacement, 8.6 inches.
84
Explosive shock PVSS on 4CP
Here's its PVSS.
We see the 8.6 inches. The undamped is hovering
around 300 ips. I interpolated by 3 to get fs
150,000 Hz, to see if undamped would go to 900
gs. The damped is heading for 900 g's.
We could simulate with 9 inch bungee assisted,
13.8 g drop (to get 900 gs in 9 in), 300 ips,
900 g half sine.
85
Bad Editing Example Pyroshock ExampleHimelblau
Piersol 95-96 SVS Proceedings
86
Pyroshock Shock SpectrumVery High FrequencyBad
at 200 Hz
NOTE Axes on 4CP have had to be shifted
one decade to the right to allow frequencies to
100,000.
87
This completes Part I. In Part IIExperimental
and computational proof, additional concepts.
  • Pseudo velocity compared to relative velocity
    shock spectra indicating pitfalls for relative
    velocity.
  • Relative velocity low frequency problem.
  • Tests to determine which transient motion
    analyses method is the best indicator of damage
    potential.
  • The best damage potential analysis is the damped
    PVSS on 4CP.
Write a Comment
User Comments (0)
About PowerShow.com