Module 2

Question 1

free vibration

Answer 1

when a structure is initially disturbed from its equilibrium position and then allowed to vibrate without external forces being applied

Question 2

undamped free vibration

Answer 2

udotdot + wn^2u = 0

Question 3

Tn

Answer 3

natural period

Tn = 2pi x sqrt(m / k)

Question 4

short, stiff structures

Answer 4

small Tn

Question 5

tall, slender structures

Answer 5

large Tn

Question 6

max displacement

Answer 6

will occur when velocity is zero

• set du/dt = 0
• find tmax
• sub into u equation to find umax

Question 7

damping ratio

Answer 7

= c / c(cr)

Question 8

c(cr)

Answer 8

critical damping coefficient

Question 9

damping ratio

Answer 9

system is underdamped

Question 10

damping ratio = 1

Answer 10

system is critically damped

Question 11

damping ratio > 1

Answer 11

system is overdamped

Question 12

damping ratio for most civil enineering structures

Answer 12

between 0 and 0.2

- therefore we can consider w(d) = w(n) and Td = Tn

Question 13

why is damping important

Answer 13

determines how quickly the amplitudes of the displacements will reduce to insignificant levels

Question 14

delta

Answer 14

logarithmic decrement

- used to determine damping ratio from plotted data

Question 15

j(50%)

Answer 15

number of cycles until a 50% reduction is observed in the initial displacement
j(50%) = ln(2) / delta

Question 16

Releationship between j(50%) and damping ratio

Answer 16

negative exponential relationship