Page 375 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

362 Mode-Summation Procedures for Continuous Systems Chap. 11

The next step is to calculate the generalized mass from the equation
rl
m/j = / m{x)4>,{x)<t>j{x) dx
•'()
For subsection (D, we have

mil = f cbc = i ^ ( y ) dx = 0.20 ml

m ^2 "" f ^4>\4>2^ f j ] ^ ^ 0.166m/ = m 2i
'
*() •'() ^ ^ '
j
mil = ^m4>(f>2 ^ ^ ^ ^ ( t ) ^ ^ 0.1428m/
2
The generalized mass for subsection (2) is computed in a similar manner using (/>3
to (/>y
m33 = 1.0 m/
m34 = 0.50m/ =
= 0.20 m/ =
m44 = 0.333m/
m43 = 0.166m/ =
me 0.1 1 1 m/
= 1.0m/
Because there is no coupling between the longitudinal displacement U2 and the
lateral displacement n>2, "" ^^64 ^65 "" 0*
The generalized stiffness is found from the equation
/c,^. = f W :'c/>; dx
•'()
Thus,
£7
'
= E lj‘^4>\4>’[ dx = = 4 | 3

All ~ 1 2 |i
FI
k,, = 28.8-^
All other /c,, are zero.