Exam

Question 1

Phase angle = 180 degrees

Answer 1

completely out of phase

• w / wn&raquo_space; 1
• high frequency response
• small amplitude
• force rapidly changing
• response controlled by mass of system

Question 2

Phase angle = 90 degrees

Answer 2

resonance: w = wn
large amplitude
- Rd very sensitive to damping
- response controlled by damping

Question 3

phase angle = 0 degrees

Answer 3

in phase

• w / wn &laquo_space;1
• low frequency response
• quasistatic response u0 = p0/k
• force slowly varying
• amplitude of dynamic response controlled by stiffness of system

Question 4

Ritz vectors

Answer 4

• used to find approximate natural frequencies

- use estimated vectors of mode shaped based on good judgement

Question 5

earthquake: max strain energy

Answer 5

= 1/2 m v^2

Question 6

earthquake: max force

Answer 6

= mA

Question 7

fundamental assumption in earthquake response analysis:

Answer 7

structures subjected to a random motion tend to vibrate at various amplitudes but with a frequency very near to lowest natural frequency
e.g. the sinusoidal relationshp A = wn D is approximately valid

Question 8

convergence

Answer 8

means that the solution tends towards the exact solution as the time step becomes smaller

Question 9

stability

Answer 9

means that the algorithm is stable in relation to small disturbances such as round of errors and does not diverge due to these disturbances

Question 10

unconditionally stable

Answer 10

• Newmark’s method - average acceleration special case

- gamma = 0.5, beta = 0.25

Question 11

Requirements of time-stepping procedures

Answer 11

1) convergence
2) stability to round of errors
3) accuracy and efficiency

Question 12

classical damping

Answer 12

if C is diagonalisable

Question 13

Rayleigh Damping

Answer 13

C = alpha m + beta k
(alpha and beta constants)
- classical damping

Question 14

Modal Damping

Answer 14

each mode can be assigned a damping ratio

- c is a sum of matrices found by “expanding” the mode vectors

Question 15

impulse

Answer 15

I = m v(0)

Question 16

Response spectrum

Answer 16

shows the maximum response (D,V,A) for a spectrum of buildings in terms of (wn, damping) subjected to a particular earthquake

Question 17

Design Spectrum

Answer 17

an idealised maximum response for a large number of (historic or synthetic) earthquakes - the envelope of responses

Question 18

wn relationship to fn

Answer 18

wn = 2 * pi * fn

Question 19

fn relationship to Tn

Answer 19

fn = 1 / Tn

Question 20

Requirements in designing isolators

Answer 20

• Stiffness
• Isolation
• Damping

Question 21

Essential properties of rubber

Answer 21

• Elasticity
• Damping
• Incompressibility
• isotropy
• rate and amplitude dependance
• temperature dependance
• damage effects

Question 22

Essential properties of shock absorbers

Answer 22

• spring characteristic
• deformation behaviour
• strain energy capacity
• fatigue sensitivity

Question 23

material make up of carbon black filled rubber

Answer 23

• crosslinks (give rubber part of its elasticity)
• polymer chains
• carbon black (soot)
  helps to make much stiffer material

Question 24

pulse loading : td &laquo_space;Tn

Answer 24

impulse
I = integral ( p(t) dt ) = m v(0)

u(0) = I / (m * wn)

Question 25

pulse loading td >> Tn

Answer 25

quasi-static | u(0) = p(0) / k

Question 26

Shock absorption energy

Answer 26

W = deltaT W = integral(F dx) = Fmean * dx deltaT = 1/2 m v(0)^2

Question 27

Fmean (shock absorption)

Answer 27

Fmean = m * v(0) ^ 2 / (2 * delta(x) )

Question 28

Shock absorption: impulse and momentum

Answer 28

I = deltaG I = integral Fdt = Fmean dt deltaG = mv(0)

Question 29

deltat (shock absorption)

Answer 29

delta(t) = m * v(0) / Fmean

Question 30

TR

Answer 30

TR = f(t0) / p(0) where f(t0) = k * u(0)

Question 31

Reduction methods

Answer 31

- Static condensation - Modal Truncation - Generalised SDOF system - Rayleigh-Ritz method

Question 32

Static condensation

Answer 32

DOFs without inertia are eliminated (partitioned system)

Question 33

Modal Truncation

Answer 33

higher modes neglected in modal expansion | - approximation good if spatial distribution of external forces triggers lower modes

Question 34

Generalised SDOF system

Answer 34

approximation of first mode to obtain SDOF system | - useful for determining the lowest natural frequency

Question 35

Approximation by Ritz Vectors

Answer 35

special set of base vectors to express the displacements Choice of vectors can be based on: 1) physical insight 2) an automatic procedure giving Ritz vectors that conform with the spatial distribution of the load

Question 36

non-classical damping

Answer 36

C is not able to be diagonalised (by premultiplying with Phi transpose)

Question 37

Construction of Classical Damping Ratios

Answer 37

1) Rayleigh Damping | 2) Superposition of modal damping matrices