Errata

Errata
May 3, 2012 / JJT
J.J. Thomsen: Vibrations and Stability; Advanced Theory, Analysis, and Tools
2nd ed., Springer, Berlin Heidelberg, 2003
Corrections are underlined,; raised/lowered numbers: line number from top/bottom page.
Reporting of other misprints or errors to the author (jjt@mek.dtu.dk) is greatly appreciated.
Essential Corrections
p. 33-10 [Print and paste Replacement Text 1(see below) over existing lines]
p.76
j ...the form cos(
t
e j
β
ω t + ψ j ) ...
p.19 14
...at fixed boundaries...
p.23 2,5
p.251
p.27 12
[Line 2:] ...ϕiϕj””..., [Line 5:] ...( j i π/l) 4 q i...
...x0 → 1l/2
Algebraic and matrixdifferential EVPs ...
p.298 λ [k+1] = u T [k+1]z [k]/r 2 [k+1]
p.37 [Eq.(2.24):] ...sin(ωt+ψ)
p.62 18
bc) Assuming...
p.81 [Eq.(3.41:] ...[a1 a12]
p.91 [Eq. (3.82):] ...ωω=(1–...)
p.96 5
...of the Krylov-Bogoliubov method.
p.98 9
p.102
...cos(ω0T0)...
7
(3.1167)
p.102 9 (3.1256)
p.112 [The analysis in the subsection "Nonlinear Elasticity" is incorrect:
The first measure for κ in (3.152) should be used, not the second. This
3
1
changes the constant − 8 in (3.158) to + 8 , i.e. nonlinear elasticity is
hardening, not softening, as incorrectly claimed on p.113 6 . See e.g.
Lacarbonara & Yabuno (2006), 'Refined models of ...'; Bolotin
p.117
(1964), Dynamic Stability ...; Atluri (1973), 'Nonlinear Vibrations ...']
2 2
[Eq. (3.179):] ... + 3A A e 0 0 iωT ) + cc,
p.128 15 Thus we assume that let u(t) = ...
p.131 12
...the undamped linear...
p.134
k
[Eq. (3.254):] ... + cosψ
a
p.285 [Eq. (6.69):] ...+εγy 3
= εpΩ 2 cos(Ωt), ε

2 Vibrations and Stability – Errata
1
2
p.360 [Eq. (B.20):] u + ... δ ( x−
) /( ρ AL ) + ...
p.361 [Eq. (B.24):] f vdW , i = ...
p.362 5 where...( H −h− l + Ly)
p.3655 β = √ [change to “±“]
0 ...
T
2
2
/( ρ AL )
ρ .
2
/( AL )
p.366 1
[Eq. (C.5):] c k = T
p.374 [under “a) Clamped-clamped”:] (=cantilever)
p.3751 ...where qθ is the angle...
Replacement Text 1 (page 33-10)
where H0 = F0/k is the zero-frequency deflection, ω is defined by (1.3), and ζ by
(1.5). When Ω ≈ ω large-amplitude resonant vibrations occur, and the natural frequency
ω is also termed the resonance frequency 1 . At sharp resonance, Ω = ω, the
response magnitude is H/H0 = 1/(2ζ), which approaches infinity as the damping
ratio vanishes. Actually the response is strongest for Ω slightly less than ω,
2
2
namely at Ω= ω 1−2ζ≤ ω ≤ω
, where H H0= 1(2ζ 1 − ζ ) . For Ωω
the deflection is in phase with the exciting force, ϕ→0, while at resonance ϕ = π/2,
and as Ωω then ϕ→π (i.e. deflection and force are in antiphase).
Less Essential Corrections
p.XXI 5 X X
p.37 [Add footnote mark: “..resonance frequency 1 p.30
..”]
[Add footnote:] 1 Sometimes resonance frequency is defined as the fre-
2
quency of maximum response (e.g. Harris 1996). Then ω 1−2ζis the
(displacement) resonance frequency, ω is the velocity resonance frequency,
and ω
2
1−2ζis the acceleration resonance frequency.
p.221 ...using and (1.82)...
p.25 2
Solve ... and u (0) = 0 ., and 0 ≤ ζ

p.160 2
p.200 4
p.228 3
p.289 19
Vibrations and Stability – Errata 3
...Tcherniak and Thomsen and Tcherniak 2001...
...this bifurcations...
... raised to p = 0.2530
... averaging operatorOperator:averaging...
p.317 13 ...has a finite number of simple zeroes during one period of fast motions.
p.383 6 [Add reference.:] Chen Y (1966) Vibrations: Theoretical Methods.
Addison-Wesley, Reading, Massachusetts.
p.38519 Inman DJ (2001) Engineering Vibrations.