Module 3

Question 1

types of loading considered harmonic

Answer 1

• structures supporting vibrating machines
• certain types of wind loading
• pedestrian loading

Question 2

applied force of harmonic vibration

Answer 2

p(0)sinwt
where
p(0) is the amplitude of the force
w is the excitation frequency

Question 3

two parts to harmonic excitation solution

Answer 3

• steady state component

- transient solution

Question 4

steady state solution (undamped)

Answer 4

particular solution

- represents oscillation at the frequency of the forcing function w

Question 5

transient solution (undamped)

Answer 5

complimentary solution

- represents oscillation at the natural frequency of the SDOF, w(n)

Question 6

what happens when introduce damping to harmonic loading

Answer 6

transient solution dies away over time and total displacement tends toward steady state solution

Question 7

Special case

Answer 7

RESONANCE

w = w(n)

Question 8

transient response (damped)

Answer 8

oscillates at damped natural frequency, w(d)

- term decays in amplitude over time

Question 9

steady state response (damped)

Answer 9

oscillates at excitation frequency, w

- does not decay with time

Question 10

speed with which transient response decays

Answer 10

is a function of the damping ratio

Question 11

for a given w/w(n) what happens as damping ratio is decreased

Answer 11

Rd increases

Question 12

at very small w/w(n)

Answer 12

dynamic response amplitude effectively the same as static response

Question 13

at very large w / w(n)

Answer 13

dynamic response tends to zero (very flexible structure)

Question 14

max Rd

Answer 14

doesnt always occur at w / w(n) = 1

Question 15

special case at w / w(n) = 1

Answer 15

always has a phase lag of 90 degrees, regardless of damping ratio

Question 16

small damping ratio at w / w(n) = 1

Answer 16

causes rapid change in phase lag

Question 17

vibration generators

Answer 17

work by having two masses rotating in opposite directions about a vertical axis
- mass of vibration generator small compared to structure

Question 18

vibration generator exciting force

Answer 18

p(t) = (m(e) e w^2) sinwt

Question 19

fT

Answer 19

force transmitted to supports of system

fT = fs + fD

Question 20

TR

Answer 20

transmissibility

TR = fT,max / p(0)

Question 21

effect of damping on transmitted force

Answer 21

• increased damping decreases transmitted force for frequency ratios less than sqrt(2)
• increases transmitted force for w/w(n) > sqrt(2) so ideally no damping then

Question 22

natural frequency so that transmitted force is less than applied force

Answer 22

w / w(n) > sqrt(2) by having a small enough w(n)

Question 23

trade off with damping and transmitted force

Answer 23

for w / w(n) > sqrt(2)

trade off between soft spring to reduce transmitted force and an acceptable static displacement