Vibration testing is usually performed by applying a vibratory excitation to a test object and monitoring the structural integrity and performance of the intended function of the object. The technique may be useful in several stages of (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 vibration testing of a preliminary design prototype or a partial product. In the production stage, the quality of 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. The technology of vibration testing has rapidly evolved since the Second World War

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 could be used in conjunction with mechanical or hydraulic (e.g., fluidic) circuits to perform analog processing. Today’s complex test programs require the capability of 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 the late 1960s. Today, special-purpose digital analyzers with real-time digital Fourier analysis capability (see Chapter 4, Chapter 9, and Appendix E) are commonly used in vibration testing applications. The advantages of incorporating digital processing in vibration testing include the 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 overall size and weight of the analyzer. Vibration testing is usually accomplished using a shaker apparatus as shown in

schematic diagram in Figure 10.1. 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, as discussed in Chapter 8. The shaker device may depend on the test requirement, availability, and cost. More than one signal may be required to simulate the 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). The 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, real-time frequency band equalization of the excitation signal, and synthesis of future test signals. 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 also serves as an equalizer. 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 is 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. Also, by using an oscilloscope

be done 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 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 could do would be to make a conservative estimate for the nature of the ground motions because of 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 (see Chapter 3 and Chapter 4) of the test inputs and responses, in general, can provide better insight regarding their characteristics in comparison to a time-domain representation; e.g., 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; 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.