Multi Degree of Freedom system (Structural Dynamics)

[svishal03]

I have been reading the theory/math concerning the solution of multi degree of system-free and forced vibration.

I need to do this for an upcoming project which is to do with some development concerning vibrations and thus thought that I should see again over my Engineering school notes.

I'm attaching a power point presrntation which is in pdf form (MDOF_basics_2_25.pdf).

I shall be grateful if someone can help me understand this:

1) See page 8 and 9

2) Page 8 shows a 3 storied frame and its equivalent mass-damper-spring model

3) My question is if some one can help me undestand the free body diagram on page 9 and its corresponding terms, I shall be indebted.

4)Like what is u,z1,z2 - if someone can help understand the force term and their directions as shown on page 9, I shall be grateful.

Vishal

 

[LightHero]

For the free body diagram on page 9, the forces are labeled according to their direction. u stands for the vertical force, z1 is the horizontal force in the x-direction, and z2 is the horizontal force in the y-direction. The arrows indicate the direction of the force. The vertical force u is a force directly downwards, while the horizontal forces z1 and z2 are forces in the x and y directions respectively. Additionally, the arrows indicate whether the force is an applied force or an opposing force. An arrow pointing away from the body indicates an applied force, while an arrow pointing towards the body indicates an opposing force.