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15.2 Vibration Exciters

Back

Vibration experimentation may require an external exciter to generate the necessary vibration. This is the

case in controlled experiments such as product testing where a specified level of vibration is applied to the

test object and the resulting response is monitored. A variety of vibration exciters are available, with

different capabilities and principles of operation.

Three basic types of vibration exciters (shakers) are widely used: hydraulic shakers, inertial shakers,

and electromagnetic shakers. The operation-capability ranges of typical exciters in these three categories

are summarized in Table 15.1. Stroke, or maximum displacement, is the largest displacement the exciter

is capable of imparting onto a test object whose weight is assumed to be within its design load limit.

Maximum velocity and acceleration are similarly defined. Maximum force is the largest force that could

be applied by the shaker to a test object of acceptable weight (one within the design load). The values

given in Table 15.1 should be interpreted with caution. Maximum displacement is achieved only at very

low frequencies. The achievement of maximum velocity corresponds to intermediate frequencies in the

operating frequency range of the shaker. Maximum acceleration and force ratings are usually achieved at

high frequencies. It is not feasible, for example, to operate a vibration exciter at its maximum

displacement and its maximum acceleration simultaneously.

Consider a loaded exciter that is executing harmonic motion. Its displacement is given by

x ¼ s sin vt ð15:1Þ

in which s is the displacement amplitude (or stroke). Corresponding velocity and acceleration are

x_ ¼ sv cos vt ð15:2Þ

x€ ¼ 2sv2sin vt ð15:3Þ

Signal

Modification

System

Test

Object

Control

System

Vibration

Exciter (Shaker)

System

FIGURE 15.2 Interactions between major subsystems

of an experimental vibration system.

Vibration Instrumentation 15-3

If the velocity amplitude is denoted by v and the acceleration amplitude by a, it follows from Equation

15.2 and Equation 15.3 that

v ¼ vs ð15:4Þ

and

a ¼ vv ð15:5Þ

Box 15.1

VIBRATION INSTRUMENTATION

Vibration Testing Applications for Products:

* Design and Development

* Production Screening and Quality Assessment

* Utilization and Qualification for Special Applications

Testing Instrumentation:

* Exciter (excites the test object)

* Controller (controls the exciter for accurate excitation)

* Sensors and Transducers (measure excitations and responses and provide excitation error

signals to controller)

* Signal Conditioning (converts signals to appropriate form)

* Recording and Display (perform processing, storage, and documentation)

Exciters:

* Shakers

1. Electrodynamic (high bandwidth, moderate power, complex and multifrequency

excitations)

2. Hydraulic (moderate to high bandwidth, high power, complex and multifrequency

excitations)

3. Inertial (low bandwidth, low power, single-frequency harmonic excitations)

* Transient/Initial Condition

1. Hammers (impulsive, bump tests)

2. Cable Release (step excitations)

3. Drop (impulsive)

Signal Conditioning:

* Filters Amplifiers

* Amplifiers

* Modulators/Demodulators

* ADC/DAC

Sensors:

* Motion (displacement, velocity, acceleration)

* Force (strain, torque)

15-4 Vibration and Shock Handbook

TABLE 15.1 Typical Operation-Capability Ranges for Various Shaker Types

Shaker Type Typical Operational Capabilities

Frequency Maximum Displacement

(Stroke)

Maximum

Velocity

Maximum

Acceleration

Maximum

Force

Excitation

Waveform

Hydraulic

(electrohydraulic)

Low

(0.1 – 500 Hz)

High (20 in; 50 cm) Intermediate

(50 in/sec;

125 cm/sec)

Intermediate

(20 g)

High (100,000 lbf;

450,000 N)

Average flexibility (simple

to complex and random)

Inertial

(counter-rotating mass)

Intermediate

(2 – 50 Hz)

Low (1 in; 2.5 cm) Intermediate

(50 in/sec;

125 cm/sec)

Intermediate

(20 g)

Intermediate

(1,000 lbf; 4,500 N)

Sinusoidal only

Electromagnetic

(electrodynamic)

High

(2 – 10,000 Hz)

Low (1 in; 2.5 cm) Intermediate

(50 in/sec;

125 cm/sec)

High (100 g) Low to intermediate

(450 lbf; 2,000 N)

High flexibility and accuracy

(simple to complex and

random)

Vibration Instrumentation 15-5

An idealized performance curve of a shaker

has a constant displacement – amplitude region, a

constant velocity – amplitude region, and a constant

acceleration – amplitude region for low,

intermediate, and high frequencies, respectively,

in the operating frequency range. Such an ideal

performance curve is shown in Figure 15.3(a) on a

frequency – velocity plane. Logarithmic axes are

used. In practice, typical shaker performance

curves would be fairly smooth yet nonlinear,

curves, similar to those shown in Figure 15.3(b).

As the mass increases, the performance curve

compresses. Note that the acceleration limit of a

shaker depends on the mass of the test object

(load). Full load corresponds to the heaviest object

that could be tested. The “no load” condition

corresponds to a shaker without a test object. To

standardize the performance curves, they are

usually defined at the rated load of the shaker. A

performance curve in the frequency – velocity

plane may be converted to a curve in the

frequency – acceleration plane simply by increasing

the slope of the curve by a unit magnitude (i.e.,

20 db/decade).

Several general observations can be made from

Equation 15.4 and Equation 15.5. In the constantpeak

displacement region of the performance

curve, the peak velocity increases proportionally

with the excitation frequency, and the peak

acceleration increases with the square of the excitation frequency. In the constant-peak velocity region,

the peak displacement varies inversely with the excitation frequency, and the peak acceleration increases

proportionately. In the constant-peak acceleration region, the peak displacement varies inversely with the

square of the excitation frequency, and the peak velocity varies inversely with the excitation frequency.

This further explains why rated stroke, maximum velocity, and maximum acceleration values are not

simultaneously realized.

15.2.1 Shaker Selection

Vibration testing is accomplished by applying a specified excitation to the test package, using a shaker

apparatus, and monitoring the response of the test object. Test excitation may be represented by its

response spectrum. The test requires that the response spectrum of the actual excitation, known as the

test response spectrum (TRS), envelops the response spectrum specified for the particular test, known as

the required response spectrum (RRS).

A major step in the planning of any vibration testing program is the selection of a proper shaker

(exciter) system for a given test package. The three specifications that are of primary importance in

selecting a shaker are the force rating, the power rating, and the stroke (maximum displacement) rating.

Force and power ratings are particularly useful in moderate to high frequency excitations and the stroke

rating is the determining factor for low frequency excitations. In this section, a procedure is given to

determine conservative estimates for these parameters in a specified test for a given test package.

Frequency domain considerations are used here.

StrokeLimit

Max.

Acceleration

Max.

Velocity

Peak Velocity (cm/s)

0.1 1 10 100

Full

Load

(a) Frequency (Hz)

Peak Velocity (cm/s)

100

0.1 1 10 100

Full

Load

(b) Frequency (Hz)

FIGURE 15.3 Performance curve of a vibration exciter

in the frequency – velocity plane (log): (a) ideal; (b)

typical.

15-6 Vibration and Shock Handbook

15.2.1.1 Force Rating

In the frequency domain, the (complex) force at the exciter (shaker) head is given by

F ¼ mHðvÞasðvÞ ð15:6Þ

in which v is the excitation frequency variable, m is the total mass of the test package including

mounting fixture and attachments, asðvÞ is the Fourier spectrum of the support-location (exciter head)

acceleration, and H(v) is frequency response function that takes into account the flexibility and

damping effects (dynamics) of the test package apart from its inertia. In the simplified case where the

test package can be represented by a simple oscillator of natural frequency vn and damping ratio by zt ;

this function becomes

HðvÞ ¼ {1 þ 2jztv=vn}={1 2 ðv=vnÞ2 þ 2jztv=vn} ð15:7Þ

in which j ¼

ffiffiffiffi

21 p : This approximation is adequate for most practical purposes. The static weight of the

test object is not included in Equation 15.6. Most heavy-duty shakers, which are typically hydraulic,

have static load support systems such as pneumatic cushion arrangements that can exactly balance the

dead load. The exciter provides only the dynamic force. In cases where shaker directly supports the

gravity load, in the vertical test configuration Equation 15.6 should be modified by adding a term to

represent this weight.

A common practice in vibration test applications is to specify the excitation signal by its response

spectrum. This is simply the peak response of a simple oscillator expressed as a function of its natural

frequency when its support location is excited by the specified signal. Clearly, the damping of the simple

oscillator is an added parameter in a response spectrum specification. Typical damping ratios ðzr Þ used in

response spectra specifications are less than 0.1 (or 10%). It follows that an approximate relationship

between the Fourier spectrum of the support acceleration and its response spectrum is

as ¼ 2jzr ar ðvÞ ð15:8Þ

The magnitude lar ðvÞl is the response spectrum.

Equation 15.8 substituted into Equation 15.6 gives

F ¼ mHðvÞ2jzr ar ðvÞ ð15:9Þ

In view of Equation 15.7, for test packages having low damping the peak value of H(v) is

approximately 1=ð2jzt Þ; this should be used in computing the force rating if the test package has a

resonance within the frequency range of testing. On the other hand, if the test package is assumed to be

rigid, then HðvÞ ø 1: A conservative estimate for the force rating is

Fmax ¼ mðzr =zt Þlar ðvÞlmax ð15:10Þ

It should be noted that lar ðvÞlmax is the peak value of the specified (required) response spectrum (RRS)

for acceleration.

15.2.1.2 Power Rating

The exciter head does not develop its maximum force when driven at maximum velocity. Output power

is determined by using

p ¼ Re½FvsðvÞ􀀉 ð15:11Þ

in which vsðvÞ is the Fourier spectrum of the exciter velocity, and Re [ ] denotes the real part of a complex

function. Note that as ¼ jvvs: Substituting Equation 15.6 and Equation 15.8 into Equation 15.11 gives

p ¼ ð4mz2r

=vÞRe½jHðvÞa2r

ðvÞ􀀉 ð15:12Þ

It follows that a conservative estimate for the power rating is

pmax ¼ 2mðz2r

=zt Þ½lar ðvÞl2=v􀀉max ð15:13Þ

Vibration Instrumentation 15-7

Representative segments of typical acceleration RRS curves have slope n, as given by

a ¼ k1vn ð15:14Þ It should be clear from Equation 15.13 that the maximum output power is given by

pmax ¼ k2v2n21 ð15:15Þ

This is an increasing function for n . 1=2 and a decreasing function for n , 1=2: It follows that the power

rating corresponds to the highest point of contact between the acceleration RRS curve and a line of slope

equal to 1/2. A similar relationship may be derived if velocity RRS curves (having slopes n 2 1) are used.

15.2.1.3 Stroke Rating

From Equation 15.8, it should be clear that the Fourier spectrum, xs, of the exciter displacement time

history can be expressed as

xs ¼ 2zr ar ðvÞ=jv2 ð15:16Þ

An estimate for stroke rating is

xmax ¼ 2zr ½lar ðvÞl=v2􀀉max ð15:17Þ

This is of the form

xmax ¼ kvn22 ð15:18Þ

It follows that the stroke rating corresponds to the highest point of contact between the acceleration

RRS curve and a line of slope equal to two.

Example 15.1

A test package of overall mass 100 kg is to be

subjected to dynamic excitation represented by the

acceleration RRS (at 5% damping) as shown in

Figure 15.4. The estimated damping of the test

package is 7%. The test package is known to have a

resonance within the frequency range of the

specified test. Determine the exciter specifications

for the test.

Solution

From the development presented in the previous

section, it is clear that the point F (or P) in

Figure 15.4 corresponds to the force and output

power ratings, and the point S corresponds to

the stroke rating. The co-ordinates of these

critical points are F; P ¼ ð4:2 Hz; 4:0 gÞ; and S ¼ ð0:8 Hz; 0:75 gÞ: Equation 15.10 gives the force

rating as

Fmax ¼ 100 £ ð0:05=0:07Þ £ 4:0 £ 9:81 N ¼ 2803 N

Equation 15.13 gives the power rating as

pmax ¼ 2 £ 100 £ ð0:052=0:07Þ £ ½ð4:0 £ 9:81Þ2=4:2 £ 2p􀀉watts ¼ 417 W

Equation 15.17 gives the stroke rating as

xmax ¼ 2 £ 0:05 £ ½ð0:75 £ 9:8Þ=ð0:8 £ 2pÞ2􀀉m ¼ 3 cm

Acceleration (g)

Constant Displacement

Constant Velocity

Frequency (Hz)

F,P

0.1

1.0 10 100

1.0

FIGURE 15.4 Test excitation specified by an acceleration

RRS (5% damping).

15-8 Vibration and Shock Handbook

15.2.1.4 Hydraulic Shakers

A typical hydraulic shaker consists of a piston-cylinder arrangement (also called a ram), a servo-valve, a

fluid pump, and a driving electric motor. Hydraulic fluid (oil) is pressurized (typical operating pressure:

4000 psi) and pumped into the cylinder through a servo-valve by means of a pump that is driven by an

electric motor (typical power, 150 hp). The flow (typical rate: 100 gal/min) that enters the cylinder is

controlled (modulated) by the servo-valve, which, in effect, controls the resulting piston (ram) motion.

A typical servo-valve consists of a two-stage spool valve, which provides a pressure difference and a

controlled (modulated) flow to the piston, which sets it in motion.

The servo-valve itself is moved by means of a linear torque motor, which is driven by the excitationinput

signal (electrical). A primary function of the servo-valve is to provide a stabilizing feedback to the

ram. In this respect, the servo-valve complements the main control system of the test setup. The ram is

coupled to the shaker table by means of a link with some flexibility. The cylinder frame is mounted on the

support foundation with swivel joints. This allows for some angular and lateral misalignment, which

might be caused primarily by test-object dynamics as the table moves.

Two-degree-of-freedom (Two-DoF) testing requires two independent sets of actuators, and three-DoF

testing requires three independent actuator sets. Each independent actuator set can consist of several

actuators operated in parallel, using the same pump and the same excitation-input signal to the torque

motors.

If the test table is directly supported on the vertical actuators, they must withstand the total dead

weight (i.e., the weight of the test table, the test object, the mounting fixtures, and the instrumentation).

This is requirement is usually prevented by providing a pressurized air cushion in the gap between the

test table and the foundation walls. Air should be pressurized so as to balance the total dead weight

exactly (typical required gage pressure: 3 psi).

Figure 15.5(a) shows the basic components of a typical hydraulic shaker. The corresponding

operational block diagram is shown in Figure 15.5(b). It is desirable to locate the actuators in a pit in the

test laboratory so that the test tabletop is flushed with the test laboratory floor under no-load conditions.

This minimizes the effort required to place the test object on the test table. Otherwise, the test object has

to be lifted onto the test table with a forklift. Also, installation of an aircushion to support the system

dead weight is difficult under these circumstances of elevated mounting.

Hydraulic actuators are most suitable for heavy load testing and are widely used in industrial and civil

engineering applications. They can be operated at very low frequencies (almost direct current [DC]), as well

as at intermediate frequencies (see Table 15.1). Large displacements (stroke) are possible at low frequencies.

Hydraulic shakers have the advantage of providing high flexibility of operation during the test; their

capabilities include variable-force and constant-force testing and wide-band random-input testing. The

velocity and acceleration capabilities of hydraulic shakers are moderate. Although any general excitationinput

motion (for example, sine wave, sine beat, wide-band random) can be used in hydraulic shakers,

faithful reproduction of these signals is virtually impossible at high frequencies because of distortion and

higher-order harmonics introduced by the high noise levels that are common in hydraulic systems. This

is only a minor drawback in heavy-duty, intermediate-frequency applications. Dynamic interactions are

reduced through feedback control.

15.2.1.5 Inertial Shakers

In inertial shakers, or “mechanical exciters,” the force that causes the shaker-table motion is generated by

inertia forces (accelerating masses). Counter-rotating-mass inertial shakers are typical in this category.

To understand their principle of operation, consider two equal masses rotating in opposite directions at

the same angular speed v and in the same circle of radius r (see Figure 15.6). This produces a resultant

force equal to 2mv2r cos vt in a fixed direction (the direction of symmetry of the two rotating arms).

Consequently, a sinusoidal force with a frequency of v and an amplitude proportional to v2 is generated.

This reaction force is applied to the shaker table.

Figure 15.7 shows a sketch of a typical counter-rotating-mass inertial shaker. It consists of two identical

rods rotating at the same speed in opposite directions. Each rod has a series of slots in which to

Vibration Instrumentation 15-9

place weights. In this manner, the magnitude of

the eccentric mass can be varied to achieve various

force capabilities. The rods are driven by a

variable-speed electric motor through a gear

mechanism that usually provides several speed

ratios. A speed ratio is selected depending on the

required test-frequency range. The whole system is

symmetrically supported on a carriage that is

directly connected to the test table. The test object

is mounted on the test table. The preferred

mounting configuration is horizontal so that the

excitation force is applied to the test object in a

horizontal direction. In this configuration, there

are no variable gravity moments (weight £

distance to center of gravity) acting on the drive

mechanism. Figure 15.7 shows the vertical configuration.

In dynamic testing of large structures,

the carriage can be mounted directly on the

structure at a location where the excitation force

should be applied. By incorporating two pairs of

counter-rotating masses, it is possible to generate

test moments as well as test forces.

FIGURE 15.5 A typical hydraulic shaker arrangement: (a) schematic diagram; (b) operational block diagram.

m m

2mw2r cos wt

w w

FIGURE 15.6 Principle of operation of a counterrotating-

mass inertial shaker.

15-10 Vibration and Shock Handbook

Reaction-type shakers driven by inertia are widely used for the prototype testing of civil engineering

structures. Their first application dates back to 1935. Inertial shakers are capable of producing

intermediate excitation forces. The force generated is limited by the strength of the carriage frame. The

frequency range of operation and the maximum velocity and acceleration capabilities are also

intermediate for inertial shakers whereas the maximum displacement capability is typically low. A major

limitation of inertial shakers is that their excitation force is exclusively sinusoidal and that the force

amplitude is directly proportional to the square of the excitation frequency. As a result, complex and

random excitation testing, constant-force testing (for example, transmissibility tests and constant-force

sine-sweep tests), and flexibility to vary the force amplitude or the displacement amplitude during a test

are not generally feasible with this type of shakers. Excitation frequency and amplitude can be varied

during testing, however, by incorporating a variable-speed drive for the motor. The sinusoidal excitation

generated by inertial shakers is virtually undistorted, which gives them an advantage over the other types

of shakers when used in sine-dwell and sine-sweep tests. Small portable shakers with low-force capability

are available for use in on-site testing.

15.2.1.6 Electromagnetic Shakers

In electromagnetic shakers or “electrodynamic exciters,” the motion is generated using the principle of

operation of an electric motor. Specifically, the excitation force is produced when a variable excitation

signal (electrical) is passed through a moving coil placed in a magnetic field.

The components of a commercial electromagnetic shaker are shown in Figure 15.8. A steady magnetic

field is generated by a stationary electromagnet that consists of field coils wound on a ferromagnetic base

that is rigidly attached to a protective shell structure. The shaker head has a coil wound around it. When

the excitation electrical signal is passed through this drive coil, the shaker head, which is supported on

flexure mounts, will be set in motion. The shaker head consists of the test table on which the test object

is mounted. Shakers with interchangeable heads are available. The choice of appropriate shaker head is

based on the geometry and mounting features of the test object. The shaker head can be turned to

different angles by means of a swivel joint. In this manner, different directions of excitation (in biaxial

and triaxial testing) can be obtained.

FIGURE 15.7 Sketch of a counter-rotating-mass inertial shaker.

Vibration Instrumentation 15-11

15.2.2 Dynamics of Electromagnetic Shakers

Consider a single axis electromagnetic shaker (Figure 15.8) with a test object having a single natural

frequency of importance within the test frequency range. The dynamic interactions between the shaker

and the test object give rise to two significant natural frequencies (and correspondingly, two significant

resonances). These appear as peaks in the frequency response curve of the test setup. Furthermore, the

natural frequency (resonance) of the test package alone causes a “trough” or depression (antiresonance)

in the frequency response curve of the overall test setup. To explain this characteristic, consider the

dynamic model shown in Figure 15.9. The following mechanical parameters are defined for

Figure 15.9(a): m, k, and b are the mass, stiffness, and equivalent viscous damping constant, respectively,

of the test package, and me, ke, and be are the corresponding parameters of the exciter (shaker). Also, in

the equivalent electrical circuit of the shaker head, as shown in Figure 15.9(b), the following electrical

parameters are defined: Re and Le are the resistance and (leakage) inductance and kb is the back

electromotive force (back emf) of the linear motor. Assuming that the gravitational forces are supported

FIGURE 15.8 Schematic sectional view of a typical electromagnetic shaker, manufactured by Bruel and Kjaer,

Denmark.

15-12 Vibration and Shock Handbook

by the static deflections of the flexible elements, and that the displacements are measured from the static

equilibrium position, we have the following system equations:

Test object: my€ ¼ 2kðy 2 yeÞ 2 bðy_ 2 y_eÞ ð15:19Þ

Shaker head: mey€e ¼ fe þ kðy 2 yeÞ þ bðy_ 2 y_eÞ 2 key 2 bey_e ð15:20Þ

Electrical: Le

die

dt þ Reie þ kb _ye ¼ vðtÞ ð15:21Þ

The electromagnetic force fe generated in the shaker head is a result of the interaction of the magnetic

field generated by the current ie with coil of the moving shaker head and the constant magnetic field

(stator) in which the head coil is located. Here, we have

fe ¼ kbie ð15:22Þ

Note that v(t) is the voltage signal that is applied by the amplifier to the shaker coil, ye is the displacement

of the shaker head, and y is the displacement response of the test package.

It is assumed that kb has consistent electrical and mechanical units (V/m/sec and N/A). Usually,

the electrical time constant of the shaker is quite small compared with the primarily mechanical

time constants of the shaker and the test package. In such cases, the Ledie=dt term in Equation 15.21 may

be neglected. Consequently, the equations from Equation 15.19 through Equation 15.22 may be

expressed in the Laplace (frequency) domain, with the Laplace variable s taking the place of the derivative

d=dt; as

ðms2 þ bs þ kÞy ¼ ðbs þ kÞye ð15:23Þ

FIGURE 15.9 Dynamic models of an electromagnetic shaker and a flexible test package: (a) mechanical model;

(b) electrical model.

Vibration Instrumentation 15-13

½mes2 þ ðb þ beÞs þ ðk þ keÞ􀀉ye ¼ ðbs þ kÞy þ

v 2

ye ð15:24Þ

It follows that the transfer function of the shaker head motion with respect to the excitation voltage is

given by

v ¼

DðsÞ

DdðsÞ ð15:25Þ

where DðsÞ is the characteristic function of the primary dynamics of the test object

DðsÞ ¼ ms2 þ bs þ k ð15:26Þ

and DdðsÞ is the characteristic function of the primary dynamic interactions between the shaker and the

test object

DcðsÞ ¼ mmes4 þ ½mðbe þ b þ boÞ þ meb􀀉s3 þ ½mðke þ kÞ þ mek þ bðbe þ boÞ􀀉s2

þ ½bke þ ðbe þ boÞk􀀉s þ kke ð15:27Þ

where

bo ¼

Re ð15:28Þ

It is clear that under low damping conditions DdðsÞ will produce two resonances as it is fourth order in s,

and similarly DðsÞ will produce one antiresonance (trough) corresponding to the resonance of the test

object. Note that in the frequency domain, s ¼ jv; and hence the frequency response function given by

Equation 15.25, is in fact

v ¼

DðjvÞ

Dd ðjvÞ ð15:29Þ

The magnitude of this frequency response function for a typical test system is sketched in Figure 15.10.

Note that this curve is for the “open-loop” case where there is no feedback from the shaker controller.

In practice, the shaker controller will be able

to compensate for the resonances and antiresonances

to some degree, depending on its

effectiveness.

The main advantages of electromagnetic

shakers are their high frequency range of

operation, their high degree of operating flexibility,

and the high level of accuracy of the

generated shaker motion. Faithful reproduction

of complex excitations is possible because of the

advanced electronics and control systems used in

this type of shakers. Electromagnetic shakers are

not suitable for heavy-duty applications (large test

objects), however. High test-input accelerations

are possible at high frequencies when electromagnetic

shakers are used, but their displacement and

velocity capabilities are limited to low or

intermediate values (see Table 15.1).

10.0

1.0

1 10 100

Excitation Frequency (Hz)

Antiresonance

Resonance

Shaker Displacement Magnitude

Resonance

1000

FIGURE 15.10 Frequency response curve of a typical

electromagnetic shaker with a test object.

15-14 Vibration and Shock Handbook

15.2.2.1 Transient Exciters

Other varieties of exciters are commonly used in

transient-type vibration testing. In these tests,

either an impulsive force or an initial excitation is

applied to the test object and the resulting

response is monitored. The excitations and the

responses are “transient” in this case. Hammer

test, drop tests, and pluck tests fall into this

category. For example, a hammer test may be

conducted by hitting the object with an instrumented

hammer and then measuring the response

of the object. The hammer has a force sensor at its

tip, as sketched in Figure 15.11. A piezoelectric or

strain-gage type force sensor may be used. More

sophisticated hammers have impedance heads in

place of force sensors. An impedance head

measures force and acceleration simultaneously.

The results of a hammer test will depend on many

factors; for example, the dynamics of the hammer

body, how firmly the hammer is held during the

impact, how quickly the impact is applied, and

whether there are multiple impacts.

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