Harris C.M., Piersol A.G. Harris Shock and vibration handbook

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and/or test specifications. This can be accomplished by using a simple resonant fix-

ture (usually a plate) instead of the complex structures described above. When such

a fixture is excited into resonance by a mechanical impact, its response can provide

an adequate pyroshock simulation to an attached test item. Excitation of the fixture

can be achieved as the result of the impact of a projectile, pendulum hammer, pneu-

matic piston, or the like on the fixture.The response of the fixture is dependent on a

large number of parameters including: (1) plate geometry and material, (2) impact

mass or speed, (3) impact duration, which is controlled with various impact materi-

als (e.g., metals, felt, elastomers, wood, etc.), (4) impact location, (5) test item loca-

tion, and (6) various clamps and plate suspension mechanisms. In theory these

parameters could be varied with the aid of an analytical model, but they are usually

evaluated experimentally. A significant effort is therefore required to obtain each

pyroshock simulation.

Mechanical Impulse Pyroshock (MIPS) Simulator. The MIPS simulator

20, 21

a well-developed embodiment of the trial-and-error resonant fixture methods. It is

universally referred to by its acronym and is widely used in the aerospace industry. Its

design facilitates the easy variation of many of the parameters described above. The

MIPS simulator configuration shown in Fig. 26.16 consists of an aluminum mounting

plate which rests on a thick foam pad. The shock is generated by a pneumatic actua-

tor which is rigidly attached to a movable bridge, facilitating various impact loca-

tions. The impactor head is interchangeable so that different materials (lead,

aluminum, steel, etc.) may be used to achieve variation of input duration. Although a

triaxial acceleration measurement is usually made at the control point near the test

item, it is unlikely that the test requirement will be met simultaneously in all axes.

Separate test configurations must normally be developed for each test axis. Once the

test configuration and procedures are determined, the results are very repeatable.

The configuration for a new test specification can be obtained more quickly if records

of previous setups and results are maintained for use as a starting point for the new

PYROSHOCK TESTING 26.27

FIGURE 26.16 MIPS simulator. The mounting plate is excited

into resonance by an impact from the actuator. The plate response

simulates far-field pyroshock for the attached test item. (Courtesy of

Martin Marrietta Astrospace.)

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specification. Reference 19 provides some general guidelines for parameter varia-

tion, as well as results obtained from several different test configurations.

Tuned Resonant Fixtures with Fixed Knee Frequency. It is possible to greatly

reduce the amount of trial and error required by the MIPS simulator and other res-

onant fixture test methods. In order to do this, a simple resonant fixture is designed

so that its dominant response frequency corresponds to the dominant frequency in

the shock response spectrum test requirement. These tuned resonant fixtures are

primarily limited to pyroshock environments which exhibit more or less typical

characteristics with knee frequencies up to 3000 Hz (or higher for small test items).

The basic design principle is to match the dominant fixture response frequency

(usually the first mode) to the shock response spectrum knee frequency. When this

fixture is excited into resonance, it will “automatically” have the desired shock

response spectrum knee frequency and the typical 9-dB/octave initial slope. This

concept was originally developed using a plate excited into its first bending mode

and a bar excited into its first longitudinal mode.

The methods described in the

following sections require relatively thick and massive resonant fixtures compared

to the structures to which the test item might be attached in actual use. Because of

this, the motion imparted to the test item attached to a resonant fixture is approxi-

mately in-phase from point-to-point across the mounting surface. Whereas, the

actual pyroshock motion may not be in-phase if the test item is mounted to a thin

structure in actual use. The in-phase motion of resonant fixtures yields some degree

of conservatism when selecting these methods for qualification testing. One signif-

icant advantage of using a thick resonant fixture is that its response is not greatly

influenced by the attached test item. This allows the same test apparatus to be used

for a variety of different test items.

Each of the tuned resonant fixture test methods described below produces a

simulated pyroshock environment with the same basic characteristics. These simi-

larities are illustrated in Fig. 26.17, which shows a typical acceleration record and

shock response spectrum from the tunable resonant beam apparatus described

later. The other methods produce pyroshock environments with initial shock

response spectra slopes that are slightly less than 9 dB/octave due to a small veloc-

ity change inherent with these other methods. The shock response spectrum shown

in Fig. 26.17 exhibits the desired typical shape, and the energy is concentrated at the

knee frequency. The absence of significant frequency content above the knee fre-

quency may cause the shock response spectrum to be too low at these frequencies.

In practice the attached test item adds some frequency content above the knee fre-

quency, which tends to increase the shock response spectrum. These test methods

allow good control and repeatability of the shock response spectrum, especially

below the knee frequency.

When using tuned resonant fixtures, the test item is usually attached to an inter-

mediate fixture such as a rectangular aluminum plate. This adapter fixture must be

small enough and stiff enough so that the input from the resonant fixture is not sig-

nificantly altered. Since the resonant fixture is designed to produce the pyroshock

simulation in only one direction, the adapter fixture should be designed so that it

may be rigidly attached to the resonant fixture in three orthogonal orientations (e.g.,

flat down and on each of two edges). The acceleration input should be measured

next to the test item on the adapter fixture. It is good practice to measure the accel-

eration in all three axes because it is possible (although infrequently) to simultane-

ously attain the desired test specification in more than one axis.

A number of different techniques are used to provide the mechanical impact

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required by the tuned resonant fixture methods described below. Pendulum hammers

of the general type shown in Fig. 26.8 have been used, as well as pneumatically driven

pistons or air guns. The method which is selected must provide repeatability and con-

trol of the impact force, both in magnitude and duration. The magnitude of the impact

force controls the overall test amplitude, and the impact duration must be appropriate

to excite the desired mode of the tuned resonant fixture. In general the impact dura-

tion should be about one-half the period of the desired mode. The magnitude of the

impact force is usually controlled by the impact speed, and the duration is controlled

by placing various materials (e.g., felt, cardboard, rubber, etc.) on the impact surfaces.

Resonant Plate (Bending Response). The resonant plate test method

23, 24

illustrated in Fig. 26.18, which shows a plate (usually a square or rectangular alu-

minum plate) freely suspended by some means such as bungee cords or ropes.A test

item is attached near the center of one face of the plate, which is excited into reso-

nance by a mechanical impact directed perpendicular to the center of the opposite

face. The resonant plate is designed so that its first bending mode corresponds to the

knee frequency of the test requirement.The first bending mode is approximately the

same as for a uniform beam with the same cross-section and length. Appendix 1.1

provides a convenient design tool for selecting the size of the resonant plate. The

plate must be large enough so that the test item does not extend beyond the middle

third of the plate. This assures that no part of the test item is attached at a nodal line

of the first bending mode. Usually, the resonant fixture with an attached test item is

insufficiently damped to yield the short-duration transient (5 to 20 milliseconds)

required for pyroshock simulation. Damping may be increased by adding various

attachments to the edge of the plate, such as C-clamps or metal bars. These attach-

ments may also lower the resonance frequency and must be accounted for when

designing a resonant plate.

PYROSHOCK TESTING 26.29

FIGURE 26.17 Typical shock response spectrum and acceleration time-

history from a tuned or tunable resonant fixture test. The shock response

spectrum is calculated from the inset acceleration time-history using a 5 per-

cent damping ratio.

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Resonant Bar (Longitudinal Response). The resonant bar concept

23,24

is illus-

trated in Fig. 26.19, which shows a freely suspended bar (typically aluminum or steel)

with rectangular cross section. A test item is attached at one end of the bar, which is

excited into resonance by a mechanical impact at the opposite end.The basic princi-

ple of the resonant bar test is exactly the same as for a resonant plate test except that

the first longitudinal mode of vibration of the bar is utilized.The bar length required

for a particular test can be calculated by

l = (26.4)

where l = length of the bar

c = wave speed in bar

f = first longitudinal mode of the bar (equal to desired knee frequency)

The other dimensions of the bar can be sized to accommodate the test item, but they

must be significantly less than the bar length.As with the resonant plate method, the

response of the bar can be damped with clamps if needed. These are most effective

if attached at the impact end.

Tunable Resonant Fixtures with Adjustable Knee Frequency. The tuned res-

onant fixture methods described above can produce typical pyroshock simulations

with knee frequencies that are fixed for each resonant fixture. A separate fixture



26.30 CHAPTER TWENTY-SIX, PART II

FIGURE 26.18 Resonant plate test method. The first bending

mode is excited by an impact as shown. The plate’s response simu-

lates far-field pyroshock for the attached test item.The plate is sized

so that its first bending mode frequency corresponds to the desired

knee frequency of the test.

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must be designed and fabricated for each test requirement with a different knee fre-

quency, so that a potentially large inventory of resonant fixtures would be necessary

to cover a variety of test requirements. For this reason tunable resonant fixture test

methods were developed which allow an adjustable knee frequency for a single test

apparatus.

Tunable Resonant Bars. The frequency of the first longitudinal mode of vibra-

tion of the resonant bar shown in Fig. 26.19 can be tuned by attaching weights at

selected locations along the length of the bar.

If weights are attached at each of the

two nodes for the second mode of vibration of the bar, then the bar’s response will be

dominated by the second mode (2f). Similarly, if weights are attached at each of the

three nodes for the third mode of the bar, then the third mode (3f ) will dominate. It

is difficult to produce this effect for the fourth and higher modes of the bar since the

distance between nodes is too small to accommodate the weights. This technique

allows a single bar to be used to produce pyroshock simulations with one of three dif-

ferent knee frequencies. For example a 100-in. (2.54-m) aluminum bar can be used for

pyroshock simulations requiring a 1000-, or 2000-, or 3000-Hz knee frequency. If the

weights are attached slightly away from the node locations, the shock response spec-

trum tends to be “flatter” at frequencies above the knee frequency.

Another tunable resonant bar method

can be achieved by attaching weights

only to the impact end of the bar shown in Fig. 26.19. This method uses only the

first longitudinal mode, which can be lowered incrementally as more weights are

added. A nearly continuously adjustable knee frequency can thus be attained over

a finite frequency range.The upper limit of the knee frequency is the same as given

by Eq. (26.3) and is achieved with no added weights. In theory, this knee frequency

could be reduced in half if an infinite weight could be added. However, a realizable

lower limit of the knee frequency would be about 25 percent less than the upper

limit.

Tunable Resonant Beam. Figure 26.20 illustrates a tunable resonant beam

apparatus

which will produce typical pyroshock simulations with a knee frequency

that is adjustable over a wide frequency range. In this test method, an aluminum

beam with rectangular cross section is clamped to a massive base as shown. The

clamps are intended to impose nearly fixed-end conditions on the beam. When the

beam is struck with a cylindrical mass fired from the air-gun beneath the beam, it will

resonate at its first bending frequency, which is a function of the distance between

the clamps. Ideally, the portion of the beam between the clamps will respond as if it

had perfectly fixed ends and a length equal to the distance between the clamps. For

this ideal case, the frequency of the first mode of the beam varies inversely with the

square of the beam length. In practice, the end conditions are not perfectly fixed, and

the frequency of the first mode is somewhat lower than predicted.This method pro-

PYROSHOCK TESTING 26.31

FIGURE 26.19 Resonant bar test method. The first longitudinal bar mode is excited by

an impact as shown. The bar is sized so that its first normal mode frequency corresponds

to the desired knee frequency in the test.

8434_Harris_26_b.qxd 09/20/2001 11:54 AM Page 26.31

vides a good general-purpose pyroshock simulator, since the knee frequency is con-

tinuously adjustable over a wide frequency range (e.g., 500 to 3000 Hz). This tun-

ability allows small adjustments in the knee frequency to compensate for the effects

of test items of different weights.

REFERENCES

1. Valentekovich, V. M.: Proc. 64th Shock and Vibration Symposium, p. 92 (1993).

2. Moening, C. J.: Proc. 8th Aerospace Testing Seminar, p. 95 (1984).

3. Himelblau, H.,A. G. Piersol, J. H. Wise, and M. R. Grundvig: “Handbook for Dynamic Data

Acquisition and Analysis,” IES Recommended Practice 012.1, Institute of Environmental

Sciences, Mount Prospect, Ill. 60056.

4. Smallwood, D. O.: Shock and Vibration J., 1(6):507 (1994).

5. Baca, T. J.: Proc. 60th Shock and Vibration Symposium, p. 113 (1989).

6. Shinozuka, M.: J. of the Engineering of the Engineering Mechanics Division, Proc. of the

American Society of Civil Engineers, p. 727 (1970).

7. Smallwood, D. O.: Shock and Vibration Bulletin, 43:151 (1973).

8. Mark, W. D.: J. of Sound and Vibration, 22(3):249 (1972).

9. Bendat, J. S., and A. G. Piersol: “Engineering Applications of Correlation and Spectral

Analysis,” John Wiley & Sons, Inc., 2d ed., p. 325, 1993.

10. Bateman, V. I., R. G. Bell, III, and N. T. Davie: Proc. 60th Shock and Vibration Symposium,

1:273 (1989).

26.32 CHAPTER TWENTY-SIX, PART II

FIGURE 26.20 Tunable resonant beam test method. A beam, clamped near each end to a massive

concrete base, is excited into its first bending mode by an impact produced by the air-gun.

8434_Harris_26_b.qxd 09/20/2001 11:54 AM Page 26.32

11. Bateman, V. I., R. G. Bell, III, F. A. Brown, N. T. Davie, and M. A. Nusser: Proc. 61st Shock

and Vibration Symposium, IV:161 (1990).

12. Valentekovich, V. M., M. Navid, and A. C. Goding: Proc. 60th Shock and Vibration Sympo-

sium, 1:259 (1989).

13. Valentekovich, V. M., and A. C. Goding: Proc. 61st Shock and Vibration Symposium, 2 (1990).

14. Czajkowski, J., P. Lieberman, and J. Rehard: J. of the Institute of Environmental Sciences,

35(6):25 (1992).

15. Fandrich, R. T.: Proc. Institute of Environmental Sciences Annual Technical Meeting,

p. 269 (1974).

16. Luhrs, H. N.: Proc. Institute of Environmental Sciences Annual Technical Meeting, p. 17

(1981).

17. Powers, D. R.: Shock and Vibration Bulletin, 56(3):133 (1986).

18. Bateman, V. I., and F.A. Brown: J. of the Institute of Environmental Sciences, 37(5):40 (1994).

19. Bateman, V. I., F. A. Brown, J. S. Cap, and M. A. Nusser: Proceedings of the 70th Shock and

Vibration Symposium,Vol. I (1999).

20. Dwyer,T. J., and D. S. Moul: 15th Space Simulation Conference, Goddard Space Flight Cen-

ter, NASA-CP-3015, p. 125 (1988).

21. Raichel, D. R., Jet Propulsion Lab, California Institute of Technology, Pasadena (1991).

22. Bai, M., and W. Thatcher: Shock and Vibration Bulletin, 49(1):97 (1979).

23. Davie, N. T.: Shock and Vibration Bulletin, 56(3):109 (1986).

24. Davie, N. T., Proc. Institute of Environmental Sciences Annual Technical Meeting, p. 344

(1985).

25. Shannon, K. L., and T. L. Gentry:“Shock Testing Apparatus,” U. S. Patent No. 5,003,810, 1991.

26. Davie, N. T., and V. I. Bateman: Proc. Institute of Environmental Sciences Annual Technical

Meeting, p. 504 (1994).

PYROSHOCK TESTING 26.33

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CHAPTER 27

APPLICATION OF

DIGITAL COMPUTERS

Marcos A. Underwood

INTRODUCTION

This chapter introduces numerous applications and tools that are available on and

with digital computers for the solution of shock and vibration problems. First, the

types of computers that are used, the associated specialized processors, and their

input and output peripherals, are considered.This is followed by a discussion of com-

puter applications that fall into the following basic categories: (1) numerical analy-

ses of dynamic systems, (2) experimental applications that require the synthesis of

excitation (driving) signals for electrodynamic and electrohydraulic exciters (shak-

ers), and (3) the acquisition of the associated responses and the digital processing of

these responses to determine important structural characteristics.

The decision to employ a digital computer–based system for the solution of a

shock or vibration problem should be made with considerable care. Before particu-

lar computer software or hardware is selected, the following matters should be care-

fully considered.

1. The existing hardware and/or software that is or is not available to perform the

required task.

2. The extent to which the task or the existing software/hardware must be modified

in order to perform the task.

3. If no applicable software/hardware exists, the extent of the development effort

necessary to create the suitable software and/or hardware subsystems.

4. The detailed assumptions needed in the software/hardware in order to simplify

its development (e.g., linearity, proportional damping, frequency content, sam-

pling rates, etc.).

5. The ability of the software/hardware to measure and compute the output infor-

mation required (e.g., absolute vs. relative motion, phase relationships, rotational

information, etc.).

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6. The detailed input and output limitations of the needed system software and/or

hardware (types of excitation signals, voltage ranges, minimum detectable signal

amplitudes, calculation rates, control speed, graphic outputs, setup parameters,

etc.).

7. The processing power and time needed to perform the task.

8. The algorithms and hardware features that are needed to perform the task.

After these matters are resolved, the user must realize that the results obtained

from the output of a computer system can be no better than its available inputs. For

example, the quality of the natural frequencies and mode shapes obtained from a

structural analysis software system depends heavily on the degree to which the

mathematical model employed represents the actual mass, stiffness, and damping of

the physical structure being analyzed (see Chap. 21). Likewise, a spectral analysis of

a signal with poor signal-to-noise ratio will provide an accurate spectrum of the sig-

nal plus the measurement noise, but not of the signal amplitudes that fall below the

noise floor (see Chap. 22).

DIGITAL COMPUTER TYPES

The digital computer types that are used to solve shock and vibration problems are

varied. There are general-purpose or specialized digital computers. It is generally

better to use general-purpose computers whenever possible, since these types of dig-

ital computers are supported with the best graphics, applications development, sci-

entific and engineering tools, and the wider availability of preexisting applications

software. However, even within these general categories, there are various processor

or computer configurations available to help solve shock and vibration problems.

The following sections provide definitions, descriptions, and discussions of the appli-

cability of general-purpose computers and specialized processors that can help solve

shock and vibration problems.

GENERAL PURPOSE

General-purpose computers are computers designed to solve a wide range of prob-

lems. They are optimized to allow many individual users to access the particular

computer system’s resources. They range from large central systems like main-

frames, which can handle thousands of simultaneous users, to personal computers,

which are designed to serve one interactive user at a time and provide direct and

easy access to the computer system’s computational capability through thousands of

existing applications and its graphical user interface. These are personified by per-

sonal computers based on Wintel (i.e., Windows and Intel) or Power PC technolo-

gies. In the following, mainframes, workstations, personal computers, and palmtop

digital computers are discussed from the viewpoint of their applicability to solve

shock and vibration problems.

Mainframes. Mainframe computers are computer systems that are optimized to

serve many users simultaneously. They typically have large memories, many parallel

central processing units, large-capacity disk storage, and high-bandwidth local net-

work and Internet connections.These systems, when available, can be used to solve the

largest shock and vibration simulations, where very large finite element models or

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other discrete system models require large memories and the processing power that

mainframes provide. They are also used for web or disk server functions to networked

workstations and personal computers. Mainframe computers are increasingly being

replaced by either powerful workstation or personal computer–based systems.

Workstations. Workstations are computer systems that provide dedicated com-

puter processing for individual users that typically are involved in technically spe-

cialized and complex computing activities. These computer systems usually run a

version of the UNIX operating system using a graphical user interface that is based

on X-windows; X-windows is a set of libraries of graphical software routines, devel-

oped by an industry consortium that provide a standard access to the workstation’s

graphics hardware through a graphical user interface. Workstations often are based

on reduced instruction set computer systems, to be discussed in a later section, with

significant floating point processing power, sophisticated graphic hardware systems,

and access to large disk and random access memory systems. This suits them for

computer-assisted engineering activities like large-scale simulations, mechanical and

electrical system design and drafting, significant applications in the experimental

area that involve many channels of data acquisition and analysis, and the control of

multiexciter vibration test systems. They are designed to efficiently serve one user,

but are inherently multiuser, multitasking, and multiprocessor in nature, and can

serve as a suitable replacement for mainframes in the server arena. These systems

are now mature, with capability still expanding, but merging in the future with high-

powered personal computers. However, due to their maturity, they have an inherent

reliability advantage over personal computers, and thus have a higher suitability for

mission-critical applications. Newer versions of UNIX, like LINUX, allow personal

computer hardware to be used as a workstation, affording the power and reliability

of workstations with the convenience of personal computer hardware.

Personal Computers. Personal computers (PCs) are computer systems that are

intended to be used by casual users and are designed for simplicity of use. PCs orig-

inally were targeted to be used as home- and hobby-oriented computers. Over the

years, PCs have evolved into systems that have central processing units that rival

those of workstations and some older mainframes. PC operating systems have also

evolved to provide access to large disk and random access memories, and a sophisti-

cated graphical user interface. They have many applications in the shock and vibra-

tion arena that are available commercially. These applications include sophisticated

word processors, spreadsheet processors, graphics processors, system modeling tools

like Matlab, design applications, and countless other computer-aided engineering

applications.

There are also many experimental applications like modal analysis, signal analy-

sis, and vibration control systems that are implemented using PCs. These types of

systems are typically less expensive when they are built using PCs rather than work-

stations. At this time, however, workstations still provide greater performance and

reliability than PCs. PC operating systems are not as robust as those that run on

workstations, although this may change in the future. PCs, however, are ubiquitous

and the hardware and software used to make them continues to expand in capabil-

ity and reliability. It is likely that the PC and workstation categories will ultimately

merge, hopefully preserving the best of both worlds. Currently, most PCs are based

on Wintel technologies, with a smaller percentage based on Power PC technologies.

Palmtops. Palmtop computers (also called hand-held computers) are computer

systems that are designed for extreme portability and moderate computing applica-

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