Lecture 13 Damping Flashcards
Effect of damping on free vibration
causes vibration to step,
reduction in oscillation frequency
effect of damping on steady state forced response
amplitude is reduced around resonance
difference between undamped natural frequency and resonance (usually small)
can increase transmissibility at high freq
Most common damping model in vibration
viscous damping
where oscillation causes movement in a fluid
viscous model of damping states
f = cx. reaction force is proportional to relative velocity across the damper f= damper force c = viscous damping coefficient x. = relative velocity
if both ends are moving in a viscous damper x. =
x.2 - x.1
Power dissipation by viscous damper
dW/dt = force * velocity = cx.^2
energy dissipation of viscous damper
DELTAW = pi() * c* w *X^2
What does hysteresis in materials refer to
materials absorb energy when deformed
fricition occurs between planes in microstructure
area inside loop is energy loss per cycle
Draw a typical Hysteresis curve
see book
How does the hysteretic model compare to the spring damper model
spring damper model is perfect elipse, hysteretic model is a curved parallelogram
but similarity
simplest representation in hysteretic damping
DETLAW = pi() h X^2
an equivelent viscous unit for hysteretic damping
ceq = h/w = eta * keq / w
spring and hysteretic damper under the general harmonic excitation equation of motion
f = h/w *x. + kx Fe^jwt = h/w * jwX*e^jwt + kX*e^jwt
For hysteretic damper model what does F/X =
jh + k = k(1 + j*eta)
What is the complex stiffness of hysteretic damping
k(1 + j*eta)
