# a. Vibration testing of a device primarily involves application of a test excitation to the device..

a. Vibration testing of a device primarily
involves application of a test excitation to the device and measuring the
resulting response at one or more key locations of the device. Identify four
general areas (not specific applications) where vibration testing is used in
practice.

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b. A piezoelectric accelerometer is a
motion sensor that is widely used in vibration measurement. Describe its
principle of operation. Why is it that the signal generated by a piezoelectric
accelerometer cannot be directly used without proper signal conditioning, for
the purposes of recording, analysis, and control? What type of signal
conditioning device is commonly used with a piezoelectric accelerometer?

c. The operating capability (ratings) of an
electrodynamic (electromagnetic) shaker (exciter) is shown in Figure P10.17, on
the frequency–velocity plane, to a log–log scale. Given this information, one
engineering student comments that it is practically useless because it is the
acceleration versus frequency capability that matters for an exciter, and not
the velocity versus frequency capability. A brilliant student who has recently
taken an undergraduate course in mechanical vibrations objects to this
statement, saying that the given information can be easily converted to a
rating curve on the frequency–acceleration plane, to a log–log scale using the
units Hz and m·s–2. You are that student.

i. Compute the coordinates at the two break
points between the straight-line segments of this acceleration rating curve.
Sketch this (acceleration versus frequency) curve.

ii. What is the displacement limit (in
units of cm), and the acceleration limit when testing a 4-kg object (in units
of g, the acceleration due to gravity), for this shaker?

iii. Suppose that a 4-kg object is tested
at 15 Hz. What are the limits of shaker head displacement (cm), velocity (m·s–1),
and acceleration (g) for this test? If a 5-kg object is tested at 15 Hz, how
would these limiting values change (an approximate estimate will be adequate)?