Lecture 8 Forced Vibrations Part 3 Flashcards
Force of the spring and force of the damper are
90 degrees out of phase
Force transmitted =
fT = cx. + kx
force transmission refers to
forces felt by surrounding features eg the base due to vibrations
Force transmission equation =>
FT/F = (k + jwc)/(k - w^2m + jwc)
Force transmission equation in system properties =>
FT/F = (1 + j2zetar)/(1-r^2 + j2zetar)
equation of motion for base motion
mx.. + c(x.-y.) + k(x-y) = 0
free body diagram of base motion
see book
Transmissibility =
X/Y = FT/F
Characteristics of transmissibility
1 at low freq
less than 1 for all freq greater than wn * root 2
all freq less than wnroot 2 increasing damping reduces response,
above wnroot 2, increasing damping increases response
As damping increases what happens to phase change at resonance for transmissibility
as damping increases, the phase change decreases (also becomes less dramatic)
How is relative motion described in base motion
Z = X - Y
Z/Y =
w^2 m / k - w^2 m + jwc
r^2 / 1 - r^2 + j2zeta*r
what can unbalance in rotating machines lead to
vibration
common ways of modelling period and unbalance forces to give vibrations
single rotating mass
twin discs
equation of motion of system excited by rotating unbalance
mx.. + cx. + kx = Mew^2 *exp (jwt)
where e is eccentricity of the unbalance
and M the mass of the eccentricity
Displacement response of rotating unbalance
X = Me/m * (r^2) / (1 - r^2 + j2zeta*r)
For rotating eccentric mass what are the key freatures of the dynamic magnification graph
x axis is mX/Me
passes through the origin, peak moves backwards with increased zeta
For rotating unbalance what are they key feactures
x axis is mX/Me
all curves begin at zero response amplitude
ratio mX/Me goes to 1 at high freq
highest response occurs around resonance
frequency response to any steady state loading can be obtained from
the system characteristics
the forcing and measurement involved
Equation of frequency response =>
X(w) = H(w) * F(w)
X is displacement, H is response, F is force
