Lecture 6 Forced Vibrations

Question 1

what are the two types of sources of excitation

Answer 1

steady state

transient

Question 2

what is an example of a steady state source

Answer 2

rotating/reciprocating machinery

Question 3

example of transient source

Answer 3

one off events, explosion, impact random or unstabke

Question 4

steady state response to harmonic excitation is also

Answer 4

harmonic

Question 5

if forcing f is harmonic what does f =

Answer 5

e^jwt

Question 6

resulting motion of forced vibration x=

Answer 6

Xa *e^(jwt - phi)

Question 7

equation of motion of forced damped system

Answer 7

mx.. + cx. + kx = f(t)

Question 8

normalised frequency r =

Answer 8

w / wn

Question 9

Dynamic magnification =

Answer 9

X / Xstat where X stat = F/k

Question 10

what is the magnification factor equal for an undamped forced vibration system

Answer 10

1/ (1 - r^2)

Question 11

What happens to dynamic magnification as you approach normalised frequency r = 1

Answer 11

tends to + inf from the below and - inf from above

Question 12

what is the theoretical magnitude of response of a undamped system at r = 1

Answer 12

infinity

Question 13

what happens to phase angle as your pass through r =1 for undamped system

Answer 13

it switches suddenly by 180 degrees

Question 14

phase angle at r = 1 ie phi =

Answer 14

90 degrees

Question 15

Force vibration equation X/F =

Answer 15

1/ (k -w^2 m + jwc)

Question 16

Force vibration equation using system terms X/Xtat =

Answer 16

1/ (1 - r^2 + j *2 * zeta * r)

Question 17

Graph of damped frequency response
real part FRF and normalised freq
imaginary part FRF and normalised freq

Answer 17

see book

Question 18

Magnitude of damped frequency response

Answer 18

Xdyn / X stat = 1/sqrt((1-r^2)^2 + (2zetar)^2)

Question 19

phase angle =

Answer 19

tan(phi) = 2zetar/(1-r^2)

Question 20

Damped frequency response graph

Answer 20

see book

Question 21

at w = wn what happnes

Answer 21

spring forces balances inertia force

damping force equals excitation force

Question 22

maximum response occurs

Answer 22

near resonance frequency

magnitude controlled by damping

Question 23

what happnes to phase

Answer 23

180 degree change as we go through resonance

damping makes the change more gradual

Question 24

What effect does damping have far away from r = 1

Answer 24

damping does not change the response

Question 25

as forcing freq approaches zero what happens to dynamic magnification

Answer 25

goes to unity

Question 26

When does the maximum response occur

Answer 26

r = sqrt ( 1 - 2*zeta^2) when zeta is less than 1/root 2

Question 27

What is the maximum response equal to at zeta less than 1/root 2

Answer 27

Xk/F = 1 / 2*zeta * sqrt ( 1 - zeta^2)