Lecture 7 Forced Vibrations Part 2

Question 1

What happens to phase as you increase freq in damped forced vibrations

Answer 1

at zero freq, force and displacement are in phase
at high freq the phase tends towards 180 degree completely out of phase
for an undamped system the phase changes suddenly at natural freq
for damped, phase change occur over a broader range of freq

Question 2

FRF

Answer 2

frequency response function

Question 3

receptance =

Answer 3

displacement divided by force

Question 4

mobility =

Answer 4

velocity divided by force

Question 5

inertance (accelerance)

Answer 5

acceleration divided by force

Question 6

Displacement FRF graph as w => 0 and w => inf

Answer 6

mag X/F = 1/k as w => 0

mag X/F = 1/ w^2 *m as w = > inf

Question 7

Velocity FRF graph as w => 0 and w => inf

Answer 7

mag X/F = w/k as w => 0

mag X/F = 1/ w*m as w = > inf

Question 8

Acceleration FRF graph as w => 0 and w => inf

Answer 8

mag X/F = w^2/k as w => 0

mag X/F = 1/m as w = > inf

Question 9

Draw a displacement FRF

Answer 9

see book

Question 10

Draw a velocity FRF

Answer 10

see book

Question 11

Draw an acceleration FRF

Answer 11

see book

Question 12

Quality factor

Answer 12

the displacement amplification factor at resonance (Q factor)

Question 13

Q =

Answer 13

mag @max X dyn / X stat = 1 /2*zeta * sqrt (1-zeta^2)

Question 14

Q at low damping

Answer 14

Q = 1/2*zeta

Question 15

amplitude of half power points

Answer 15

Q/ root 2

Question 16

What are the half power point

Answer 16

amplitude at which power abosrbed by the viscous damped is halved

Question 17

Equation for zeta using half power points

Answer 17

zeta = 1 / 2Q = w2 - w1 / 2wr