Page 233 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

220 Lagrange’s Equation Chap. 7

----- Q 2
I
0 ^ > *2
- y i h
ZET ^EI^
_^ q
*2
io ^3 I ^

Figure 7.3-4. (d). Forces necessary to maintain equilibrium.

For ^3
0 0 0 ^0 ^

-2 El 2
M, 0 0 0
h <
AEI,
M2 0 0 ^3
~t t
1 i

The stiffness matrix for the system is the superposition of these three results:
/ \ 12£/i 6£/i ( \
0
/f
6EI. i AEE 4EE 2 EE
M, ) =
h r " - i T
2 El 2 4EE
M, 0 ^3
~E~ ~E~
I )
The mass matrix is found from the kinetic energy:

T = l{>^\ + "»z)«/? +

d d T ,

d d T
dt dq. “ ■'''^2

d d T
dt d q ,