Lecture 8 Forced Vibrations Part 3

Question 1

Force of the spring and force of the damper are

Answer 1

90 degrees out of phase

Question 2

Force transmitted =

Answer 2

fT = cx. + kx

Question 3

force transmission refers to

Answer 3

forces felt by surrounding features eg the base due to vibrations

Question 4

Force transmission equation =>

Answer 4

FT/F = (k + jwc)/(k - w^2m + jwc)

Question 5

Force transmission equation in system properties =>

Answer 5

FT/F = (1 + j2zetar)/(1-r^2 + j2zetar)

Question 6

equation of motion for base motion

Answer 6

mx.. + c(x.-y.) + k(x-y) = 0

Question 7

free body diagram of base motion

Answer 7

see book

Question 8

Transmissibility =

Answer 8

X/Y = FT/F

Question 9

Characteristics of transmissibility

Answer 9

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

Question 10

As damping increases what happens to phase change at resonance for transmissibility

Answer 10

as damping increases, the phase change decreases (also becomes less dramatic)

Question 11

How is relative motion described in base motion

Answer 11

Z = X - Y

Question 12

Z/Y =

Answer 12

w^2 m / k - w^2 m + jwc

r^2 / 1 - r^2 + j2zeta*r

Question 13

what can unbalance in rotating machines lead to

Answer 13

vibration

Question 14

common ways of modelling period and unbalance forces to give vibrations

Answer 14

single rotating mass

twin discs

Question 15

equation of motion of system excited by rotating unbalance

Answer 15

mx.. + cx. + kx = Mew^2 *exp (jwt)
where e is eccentricity of the unbalance
and M the mass of the eccentricity

Question 16

Displacement response of rotating unbalance

Answer 16

X = Me/m * (r^2) / (1 - r^2 + j2zeta*r)

Question 17

For rotating eccentric mass what are the key freatures of the dynamic magnification graph

Answer 17

x axis is mX/Me

passes through the origin, peak moves backwards with increased zeta

Question 18

For rotating unbalance what are they key feactures

Answer 18

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

Question 19

frequency response to any steady state loading can be obtained from

Answer 19

the system characteristics

the forcing and measurement involved

Question 20

Equation of frequency response =>

Answer 20

X(w) = H(w) * F(w)

X is displacement, H is response, F is force