Applied Structural and Mechanical Vibrations 2009 Part 1 pot
Applied Structural and Mechanical Vibrations 2009 Part 1 pot
...
References
11 Probability and statistics: preliminaries to random vibrations
11 .1 Introduction
11 .2 The concept of probability
11 .3 Random variables, probability distribution functions and
probability ... remarks
References
12 Stochastic processes and random vibrations
12 .1 Introduction
12 .2 The concept of stochastic process
12 .3 Spectral representation of random pr...
Applied Structural and Mechanical Vibrations 2009 Part 7 pot
... Since
and we can substitute their values into eq (7 .11 6a) to get
(7 .11 6b)
which is, as expected, the same as the (1, 1) element of matrix (7 .11 2). The
same applies for the other FRF functions and ... (7.28) and (7.34b))
(7.45)
where j, k =1, 2, 3. Let us suppose further that we obtained an entire column
of the receptance matrix, say the first column, i.e. the functions R
11
, R...
Applied Structural and Mechanical Vibrations 2009 Part 9 pot
... Mass., 19 47.
15 . Leissa, A.W., Vibration of Plates, NASA SP -16 0, 19 69.
16 . Gerardin, M. and Rixen, D., Mechanical Vibrations: Theory and Applications
to Structural Dynamics, John Wiley, New York, 19 94.
17 . ... Dover,
New York, 19 65.
11 . Page, C.H., Physical Mathematics, D. van Nostrand, Princeton, NJ, 19 55.
12 . Bazant, Z.P. and Cedolin L., Stability of Structu...
Applied Structural and Mechanical Vibrations 2009 Part 10 potx
... graphs of mobilities
M
11
, M
12
and accelerances A
11
, A
12
are shown in Figs. 10 .16 10 .19 : part (a)
of each figure plots the magnitude on dB(y)–linear(x) scales, while part (b)
plots the magnitude ... (10 .14 ) it is immediately evident that when
we have
(10 .15 a)
and, from the first of eq (10 .14 ),
(10 .15 b)
Equation (10 .15 a) is well known and is precisely...
Applied Structural and Mechanical Vibrations 2009 Part 13 pot
... two-
port devices:
(13 .19 a)
(13 .19 b)
(13 .19 c)
(13 .19 d)
The terms and K
fe
(s) are the open-circuit effort-, short-
circuit flow-, short-circuit effort-to-flow- and open-circuit flow-to-effort-
transfer ... Vol. 3, pp.
14 55 14 66, Wiley Eastern Ltd., New Delhi, 19 95.
3. Papoulis, A., Signal Analysis, McGraw-Hill, New York, 19 81.
4. Bendat, J.S. and Piersol, A...
Applied Structural and Mechanical Vibrations 2009 Part 4 pdf
... 5 .1 (eqs (5 .10 ) and (5 .11 )), but now we proceed from eq (5 .11 ) by
substituting the appropriate initial conditions (5 .12 ) to obtain an explicit
expression for the ‘free vibration era’ t>t
1
. ... force
transmissibility T of equations (4.53) and (4.54).
Graphs of eqs (4.53) and (4.54) are shown in Figs 4 .10 and 4 .11 for the
two values of damping
and
Fig. 4 .10 Tran...
Applied Structural and Mechanical Vibrations 2009 Part 5 doc
... then replace K
1
and M
1
by
γ
K
1
and
γ
M
1
and
express
i
and p
i
as (well-behaved and rapidly converging) power series in
γ
.
In the final result
γ
can be set equal to 1.
The perturbed ... times and calculating the constants of
integration from the boundary conditions of eqs (5 .13 0) and (5 .13 1) we get
(5 .13 8)
which can be used in eq. (5 .13 5) to obtai...
Applied Structural and Mechanical Vibrations 2009 Part 6 docx
... if x=x
1
is given a unit displacement (i.e.
u
1
=1) and u
j
=0 for the forces at points 1, 2 and 3 required to maintain
this displacement configuration are exactly k
11
, k
21
and k
31
, i.e. ... translational and rotational motion.
Copyright © 2003 Taylor & Francis Group LLC
Equations (6 .11 9) and (6 .12 1) can be put together to express the family
of orthogonality...
Applied Structural and Mechanical Vibrations 2009 Part 8 pdf
... hence the second of eq (8 .11 4) becomes
(8 .11 5)
which is Bessel’s equation of order n having the solution
(8 .11 6)
where J
n
and Y
n
are the Bessel functions of the first and second kind,
respectively. ... stiffness
othogonality follows because and the mass-orthonormal
functions
φ
n
(x) are given by
(8 .13 5)
so that and Finally, if we let
in eqs (8 .13 3) and (8 .13 4a)...
Applied Structural and Mechanical Vibrations 2009 Part 12 doc
... of eq (12 .11 1) which deserves particular attention is the case of a
Gaussian process, i.e. a process with distribution function
(12 .11 2)
Substitution of eq (12 .11 2) into eq (12 .11 1) leads ... form
(12 .12 1)
which, in turn, is a special case of the one-parameter Weibull distribution
(eq (12 .12 0b) with and ), i.e.
(12 .12 2)
From eq (12 .12 2) we obtain the Weibull p...
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