Lecture 11 System Models

Question 1

How can real vibrating systems be reduced to linear SDOF form

Answer 1

limit range of applicability
linearise properties
find equivalent mass, stiffness and damping

Question 2

Force due to spring

Answer 2

F = kx

Question 3

Work done/strain energy stored in a spring

Answer 3

W or U = 1/2 k x^2

Question 4

What happens at high deformation

Answer 4

force displacement often becomes nonlinear (get hardening, softening)

Question 5

For small oscillations what does k =

Answer 5

dF/dx at x,

can take stiffness as gradient of force displacement graph if oscillations around equilibrium point

Question 6

For small deflections beams, plates and other simple structures can be modeled as

Answer 6

linear springs

Question 7

Ip for bar

Answer 7

pi()*r^4 /2

Question 8

Spring in parallel rule

Answer 8

k eq = k1 + k2 + k3 + k4

Question 9

Springs in series

Answer 9

1/keq = 1/k1 + 1/k2 + 1/k3

Question 10

How to tell if springs in series

Answer 10

springs connect to each other and the force going through them is the same they are in series

Question 11

How to tell if springs are in parallel

Answer 11

Two or more springs move by the same amount and the removal of one does not disconnect the other, the springs are in parallel

Question 12

If springs are not in series or parallel what must be used

Answer 12

the strain energy under small deflection

Question 13

Strain energy of translation

Answer 13

U = 1/2 k x^2

Question 14

Strain energy of rotation

Answer 14

U = 1/2 * k *theta^2

Question 15

Main strain energy equivalent system equation

Answer 15

U = sum of 1/2 k x^2 + sum of 1/2 * k *theta^2

U can then be set as rotational or translation equivalent spring