10.3 Methods Analogous to Classical Methods in Statical Analysis
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Fig. 10.2 Mode shapes of
two-span beam
Fig. 10.3 A freebody
diagram of a span
Let a pulsating moment M n sin pt act on the support n, that is, the right support.
This gives
M(L n , t) = M n sin pt.
(10.22a)
It can be shown by following the usual procedure that the shape function for this
beam is
Y =
M n
2E n I n λ 2
n
sin λ n x
sin λ n L n
−
sinh λ n x
sinh λ n L n
(10.22b)
Based on the shape function of Eqs. (10.22a, b), the shapes at the two ends are
Y
(0) =
M n
2E n I n λ n
1
sin λ n L n
−
1
sinh λ n L n
(10.23)
and