17.1 Introduction

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Vibration testing is usually performed by applying a vibratory excitation to a test object and monitoring

the structural integrity of the object and its performance of its intended function. The technique may be

useful in several stages: (1) design development, (2) production, and (3) utilization of a product. In the

initial design stage, the design weaknesses and possible improvements can be determined through

the vibration testing of a preliminary design prototype or a partial product. In the production stage, the

quality of the workmanship of the final product can be evaluated using both destructive and

nondestructive vibrating testing. A third application termed product qualification, is intended for

determining the adequacy of a product of good quality for a specific application (e.g., the seismic

qualification of a nuclear power plant) or a range of applications.

17-1

© 2005 by Taylor & Francis Group, LLC

The technology of vibration testing has evolved rapidly since World War II and the technique has

been successfully applied to a wide spectrum of products ranging from small printed circuit boards

and microprocessor chips to large missiles and structural systems. Until recently, however, much of the

signal processing that was required in vibration testing was performed through analog methods. In

these methods, the measured signal is usually converted into an electric signal, which in turn is passed

through a series of electrical or electronic circuits to achieve the required processing. Alternatively,

motion or pressure signals can be used in conjunction with mechanical or hydraulic (e.g., fluidic)

circuits to perform analog processing. Today’s complex test programs require the capability for the fast

and accurate processing of a large number of measurements. The performance of analog signal

analyzers is limited by hardware costs, size, data handling capacity and computational accuracy. Digital

processing for the synthesis and analysis of vibration test signals and for the interpretation and

evaluation of test results, began to replace the classical analog methods in late 1960s. Today, specialpurpose

digital analyzers with real-time digital Fourier analysis capability are commonly used in

vibration testing applications. The advantages of incorporating digital processing into vibration testing

include: flexibility and convenience with respect to the type of the signal that can be analyzed and the

complexity of the nature of processing that can be handled; increased speed of processing, accuracy

and reliability; reduction in operational costs; practically unlimited repeatability of processing; and

reduction in the overall size and weight of the analyzer.

Vibration testing is usually accomplished using a shaker apparatus, as shown by the schematic diagram

in Figure 17.1. The test object is secured to the shaker table in a manner representative of its installation

during actual use (service). In-service operating conditions are simulated while the shaker table is

actuated by applying a suitable input signal. The shakers of different types, with electromagnetic,

electromechanical, or hydraulic actuators, are available. The shaker device may depend on the test

requirement, availability, and cost. More than one signal may be required to simulate three-dimensional

characteristics of the vibration environment. The test input signal is either stored on an analog magnetic

tape or generated in real-time by a signal generator. The capability of the test object or a similar unit to

withstand a “predefined” vibration environment is evaluated by monitoring the dynamic response

(accelerations, velocities, displacements, strains, etc.) and functional operability variables (e.g.,

temperatures, pressures, flow rates, voltages, currents). Analysis of the response signals will aid in

detecting existing defects or impending failures in various components of the test equipment. The

control sensor output is useful in several ways, particularly in feedback control of the shaker, frequencyband

equalization in real-time of the excitation signal, and the synthesizing of future test signals.

Analog/

Digital

Interface

Digital

Signal

Recorder,

Analyzer,

Display

Filter/

Amplifier

Signal

Generator

and Exciter

Controller

Reference (Required)

Signal (Specification)

Power

Amplifier

Mounting

Fixtures

Test

Object

Response

Sensor

Control

Sensor

Exciter

Filter/

Amplifier

FIGURE 17.1 A typical vibration-testing arrangement.

17-2 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

The excitation signal is applied to the shaker through a shaker controller, which usually has a built-in

power amplifier. The shaker controller compares the “control sensor” signal from the shaker– test object

interface with the reference excitation signal from the signal generator. The associated error is used to

control the shaker motion so as to push this error to zero. This is termed “equalization.” Hence, a shaker

controller serves as an equalizer as well.

The signals that are monitored from the test object include test response signals and operability signals.

The former category of signals provides the dynamic response of the test object, and may include

velocities, accelerations, and strains. The latter category of signals are used to check whether the test

object performs in-service functions (i.e., it operates properly) during the test excitation, and may

include flow rates, temperatures, pressures, currents, voltages, and displacements. The signals may be

recorded in a computer or a digital oscilloscope for subsequent analysis. When using an oscilloscope or a

spectrum analyzer, some analysis can be done on line and the results are displayed immediately.

The most uncertain part of a vibration test program is the simulation of the test input. For example,

the operating environment of a product such as an automobile is not deterministic and will depend on

many random factors. Consequently, it is not possible to generate a single test signal that can completely

represent all various operating conditions. As another example, in seismic qualification of equipment, the

primary difficulty stems from the fact that the probability of accurately predicting the recurrence of an

earthquake at a given site during the design life of the equipment is very small and that of predicting the

nature of the ground motions if an earthquake were to occur is even smaller. In this case, the best that one

can do is to make a conservative estimate for the nature of the ground motions due to the strongest

earthquake that is reasonably expected. The test input should have (1) amplitude, (2) phasing, (3)

frequency content, and (4) damping characteristics comparable to the expected vibration environment if

satisfactory representation is to be achieved. A frequency-domain representation of the test inputs and

responses can, in general, provide better insight regarding their characteristics than can a time domain

representation, namely, a time history. Fortunately, frequency-domain information can be derived from

time domain data by using Fourier transform techniques.

In vibration testing, Fourier analysis is used in three principal ways: first, to determine the frequency

response of the test object in prescreening tests; second, to represent the vibration environment by its

Fourier spectrum or its power spectral density (PSD) so that a test input signal can be generated to

represent it; and third, to monitor the Fourier spectrum of the response at key locations in the test object

and at control locations of the test table and use the information diagnostically or in controlling the

exciter.

The two primary steps of a vibration testing scheme are:

Step 1: Specify the test requirements;

Step 2: Generate a vibration test signal that conservatively satisfies the specifications of Step 1.

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