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Meshless Methods and Their Numerical Properties
book

Meshless Methods and Their Numerical Properties

by Hua Li, Shantanu S. Mulay
February 2013
Intermediate to advanced content levelIntermediate to advanced
447 pages
14h 16m
English
CRC Press
Content preview from Meshless Methods and Their Numerical Properties
373
Appendix D: Derivation of ratio
of successive amplitude reduction
values for fixed–fixed beam using
explicit and implicit approaches
In this appendix, the derivation steps of the successive amplitude reduc-
tion ratio are given for the xed–xed beam with the explicit and implicit
approaches. The ODE ψ(t) obtained by the explicit approach is given in
Equation (5.71) as
ψ
∂ψ
+
∂ψ
=−ωk
tt
1
n
3
3
2
2
2
(D.1)
The roots of Equation (D.1) are computed by substituting
ψ=e
st
, and
solving ++ω=ks s 0
n
32 2
in MATLAB® to get the general solution as
ψ=
++
ψψψ
tCeCeCe()
ttt
123
123
(D.2)
where
ψ= β+
β
ψ= −β
β
β
ψ= −β
β
−β
β
kk
i
k
k
i
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Publisher Resources

ISBN: 9781466517462