Lecture 9 Time Domain Vibration

Question 1

What does force generally do in real life

Answer 1

vary with time

Question 2

What are the four methods for predicting time domain forced response

Answer 2

analytical methods - trail solution and laplace transform

Time domain Numerical Methods - Convolution Integral and Time Marching calculations

Question 3

Where is the convolution integral applied

Answer 3

linear systems,

Question 4

issues with convolution integral

Answer 4

analytical form can be cumbersome

discrete form very useful

Question 5

what does the convolution integral do

Answer 5

break arbitrary force history up into many impulse measures
calculate impulse response
sum up responses to individual impulses

Question 6

What does an impulse reponse look like

Answer 6

initial motion follow by free vibration

Question 7

For a unit impulse the chance in velocity is

Answer 7

x.t1 - x.t0 = 1/m

Question 8

initial conditions for free vibrations after impulse is applied

Answer 8

x(t=0) = 0 insufficient time to move
x.(t=0) = 1/m from unit impulse chance in velocity when DETLA T is small

Question 9

equation of all impulse response

Answer 9

x(t) = Sum from 0 to t, f(tau)h(t-tau)DELTAtau

where tau is time shifted to allow initial momentum change

Question 10

derive convolution integral from x(t) = Sum from 0 to t, f(tau)h(t-tau)DELTAtau

Answer 10

DETLAtau -> 0 becomes integral 0 to t of f(tau)h(t-tau) dtau
substitute theta = t - tau
x(t) = integral from - inf to t of f(t-theta)h(theta)*dtheta

Question 11

Fourier transform of the impulse response

Answer 11

H(w) = integral -inf to +inf of h(t) exp(-jwt) dt

Question 12

impulse reponse from steady state freq response

Answer 12

h(t) = 1/2Pi() * integral from -inf to + inf H(w)*exp(jwt)dw