DHARM818 GEOTECHNICAL ENGINEERING20.2.4 Resonance
When the frequency of the exciting force in a forced vibration of a body or a system equals one
of the natural frequencies of the body or, system, the amplitude of motion tends to become
excessively large. This condition or phenomenon is called ‘Resonance’. The particular value of
the frequency of the exciting force producing resonant conditions is called the ‘Resonant fre-
quency’ under that specific mode of vibration.
Since resonance produces excessively large amplitudes, it has dangerous implications
for any engineering structure, machine, or system in causing failure. Hence one of the impor-
tant endeavours of an Engineer dealing with Soil Dynamics and Design of a Machine Founda-
tion is to avoid resonant conditions.20.2.5 Damping
‘Damping’ in a physical system is resistance to motion, and may be one of the several types
mentioned in the following paragraphs.
(i) Viscous Damping. This type of damping occurs in lubricated sliding surfaces, dashpots
with small clearances etc. Eddy current damping is also of viscous nature. The magnitude of
damping depends upon the relative velocity and upon the parameters of the damping system.
For a particular system, the damping resistance is proportional to the Velocity:F = cdz
dt ...(Eq. 20.8)
where F = damping force,
dz
dt = Velocity,
and c = damping coefficient.
This affords relatively easy analysis of the system, since the differential equation of the
system becomes linear with this type of damping. This is why a system is often represented to
include an equivalent viscous damper even if the damping is not truly viscous.
(ii) Friction or Coulomb Damping. This kind of damping occurs when two machine parts
rub against each other, dry or unlubricated. The damping force in this case is practically con-
stant and is independent of the velocity with which the parts rub each other.
(iii)Solid, Internal or Structural Damping. This type of damping is due to the internal
friction of the molecules. The stress-strain diagram for a vibrating body is not a straight line
but forms a hysterisis loop, the area of which represents the energy dissipated due to molecu-
lar friction per cycle per unit volume. The area of the loop depends upon the material of the
vibrating body, frequency, and the magnitude of the stress. Since this involves internal loss of
energy by absorption, it is also called ‘internal damping’.
(iv) Slip or Interfacial Damping. Energy of vibration is dissipated by microscopic slip on
the interfaces of machine parts in contact under fluctuating loads. Microscopic slip also occurs
on the interfaces of the machine elements forming various types of joints. The magnitude of
damping depends, amongst other things, upon the surface roughness of the parts, the contact
pressure, and the amplitude of vibration. This type of damping is essentially of a non-linear
type.