Applied Structural and Mechanical Vibrations 2009 Part 6 docx
Applied Structural and Mechanical Vibrations 2009 Part 6 docx
... eq
(6. 168 ) in the generalized eigenproblem gives and since
we arrive at
(6. 169 )
where we have defined the matrix Now, premultiply eq (6. 169 ) by
N
–1
, insert the identity matrix between K and ... LLC
Equations (6. 119) and (6. 121) can be put together to express the family
of orthogonality conditions
(6. 122)
6. 6 Unrestrained systems: rigid-body modes
Suppose that, for a giv...
Applied Structural and Mechanical Vibrations 2009 Part 15 docx
... to its midband value,
and it decreases at a 20 dB/decade (or 6 dB/octave) rate for The
phase shift is
π
/2 at low frequency becomes
π
/4 at
ω
1
, and tends to
zero for
If both
1
and
2
are ... follower) and a low-output
impedance. R
T
and C
T
include the impedance of the transducer, of the
amplifier input and of the ranging capacitor if present. The product R
T
C
T
give...
Applied Structural and Mechanical Vibrations 2009 Part 1 pot
... LLC
Applied Structural and
Mechanical Vibrations
Theory, methods and measuring
instrumentation
Paolo L.Gatti and Vittorio Ferrari
Copyright © 2003 Taylor & Francis Group LLC
Applied Structural ... 1959–
Applied structural and mechanical vibrations: theory, methods,
and measuring instrumentation/Paolo L.Gatti and Vittorio Ferrari.
p. cm.
Includes bibliographi...
Applied Structural and Mechanical Vibrations 2009 Part 4 pdf
...
(5 .60 a)
or, alternatively
(5 .60 b)
or, in complex notation
(5 .60 c)
where
establish the relation between eqs (5 .60 a) and (5 .60 b), and
give the relation between eq (5 .60 a) and the ... (eq (2.6b) or (2.10))
(5 .61 )
for the expression of eq (5 .60 a) and
(5 .62 )
for the complex representation of eq (5 .60 c).
The mean (over one period) and mean-square...
Applied Structural and Mechanical Vibrations 2009 Part 5 doc
... Section 6. 3.1,
eq (6 42a)) and get
(6. 67b)
It is then easy to verify the orthogonality relationships, i.e.
or
and if we decide to use the eigenvectors of eqs (6. 67a)—to obtain the modal
masses and ... eq (6. 42) is
(6. 44)
so that the concise form of eqs (6. 42b) and (6. 44) now reads
(6. 45)
where P is the modal matrix formed with the vectors p
i
(sometimes called
the weighted...
Applied Structural and Mechanical Vibrations 2009 Part 7 pot
... H(
ω
) and hence
(7.47)
where, for brevity, we write H
Re
and H
Im
for the real and imaginary part of
H, respectively. In addition, we can express h(t) as
(7.48)
divide the real and imaginary parts ... to eq (7 .67 ) and leads, in the end, to
(7.82)
6. The matrix of right eigenvectors S can be partitioned into two n×2n
matrices as
(7.83a)
and, by the same token, it is also con...
Applied Structural and Mechanical Vibrations 2009 Part 8 pdf
... the differential operators K and M
parallels the symmetry of the matrices K and M, the othogononality
conditions (6. 44) and (6. 42b) are the counterpart of eqs (8.128) and the
expansion theorem is ... boundary conditions in eq (8.58) leads to
and to the frequency equation
(8 .60 )
which implies and hence
(8 .61 )
The eigenfunctions are then given by
(8 .62 )
and have the sam...
Applied Structural and Mechanical Vibrations 2009 Part 9 pot
... Plates, NASA SP- 160 , 1 969 .
16. Gerardin, M. and Rixen, D., Mechanical Vibrations: Theory and Applications
to Structural Dynamics, John Wiley, New York, 1994.
17. Timoshenko, S. and Woinowsky-Krieger, ... inconvenience,
because we have shown in Chapter 6 (Section 6. 8, eqs (6. 165 ) and (6. 166 ))
that the generalized eigenvalue problem can be transformed into a standard
e...
Applied Structural and Mechanical Vibrations 2009 Part 10 potx
... assumption, the excitation and the response are usually broadband signals
(for example, random or impact) and the tests are often performed by using
a two channel analyser and a single-input single-output ... referring, for
example, to DOFs 1 and 2 for the measurements at point 1 and 2, respectively,
along the x direction and to DOFs 3 and 4 for the measurements at points
1 and...
Applied Structural and Mechanical Vibrations 2009 Part 12 doc
... (12 .69 a) we have
Then, the variance of the derived process is obtained by combining the
results of eq (12 .62 ) and the first of eqs (12. 46) to get
where H(
ω
) is given by eq (12 .67 a) and ... cross-relationships
(12 .65 )
from which we can obtain another expression for H(
ω
). In fact, putting
together eq (12 .61 b) and the second of eqs (12 .65 ) we have
from which i...