TM 5-818-1 / AFM 88-3, Chap. 7
DESIGN FOR EQUIPMENT VIBRATIONS AND SEISMIC LOADINGS
Furthermore, persons may notice vibrations that are
about 1/100 of the value related to safety of structures.
a. Vibrations caused by steady state or transient
loads may cause settlement of soils, excessive motions
of foundations or structures, or discomfort or distress to
17-2. Single degree of freedom, damped, forced
personnel. Some basic design factors for dynamic
loading are treated in this section.
Design of a
a. Vibrations of foundation-soil systems can
foundation system incorporates the equipment loading,
adequately be represented by simple mass-spring-
subsurface material properties, and geometrical
dashpot systems. The model for this simple system
consists of a concentrated mass, m, supported by a
b. Figure 17-1 shows some limiting values of
linear elastic spring with a spring constant, k, and a
vibration criteria for machines, structures, and personnel.
viscous damping unit (dashpot) having a damping
On this diagram, vibration characteristics are described
constant, c. The system is excited by an external force,
e.g., Q = Qo sin (ωt), in which Qo is the amplitude of the
in terms of frequency and peak amplitudes of
acceleration, velocity, or displacement.
exciting force, ω = 2πfo is the angular frequency (radians
frequency constitute the abscissa of the diagram and
per second) with fo the exciting frequency (cycles per
peak velocity is the ordinate.
Values of peak
second), and t is time in seconds.
displacement are read along one set of diagonal lines
b. If the model is oriented as shown in the
and labelled in displacement (inches), and peak
insert in figure 17-2(a), motions will occur in the vertical
or z direction only, and the system has one degree of
diagonal lines and labelled in various amounts of g, the
freedom (one coordinate direction (z) is needed to
acceleration of gravity. The shaded zones in the upper
describe the motion). The magnitude of dynamic vertical
right-hand corner indicate possible structural damage to
motion, Az, depends upon the magnitude of the external
walls by steady-state vibrations. For structural safety
excitation, Q, the nature of Qo, the frequency, fo, and the
during blasting, limit peak velocity to 2.0 inches per
system parameters m, c, and k. These parameters are
customarily combined to describe the "natural frequency"
exceeding 3 cycles per second. These limits may
occasionally have to be lowered to avoid being
excessively annoying to people.
fn = 2π m
c. For equipment vibrations, limiting criteria
consist of a maximum velocity of 1.0 inch per second up
and the "damping ratio" as
to a frequency of about 30 cycles per second and a peak
acceleration of 0.15g above this frequency. However,
this upper limit is for safety only, and specific criteria
must be established for each installation. Usually,
c. Figure 17-2(a) shows the dynamic response
operating limits of equipment are based on velocity
of the system when the amplitude of the exciting force,
criteria; greater than 0.5 inch per second indicates
Qo, is constant. The abscissa of the diagram is the
extremely rough operation and machinery should be shut
dimensionless ratio of exciting frequency, fo, divided by
down; up to 0.10 inch per second occurs for smooth,
the natural frequency, fn, in equation (17-1).
well-balanced equipment; and less than 0.01 inch per
ordinate is the dynamic magnification factor, Mz, which is
second represents very smooth operation.
the ratio of Az to the static displacement, Az = (Qo/k).
d. Figure 17-1 also includes peak velocity
Different response curves correspond to different values
criteria for reaction of personnel to steady-state
vibrations. Peak velocities greater than 0.1 inch per
d. Figure 17-2(b) is the dynamic response of
second are "troublesome to persons," and peak
the system when the exciting force is generated by a
velocities of 0.01 inch per second are just "barely
rotating mass, which develops:
noticeable to persons." It is significant that persons and
Qo = me ( e ) 4π fo
machines respond to equivalent levels of vibration.