... DIN 4150 (1986) Part 3, Structural Vibration in Buildings: Effects on Structures.
(Part 1 (Principles, Predetermination and Measurement of the Amplitude of
Oscillations) and Part 2 (Influence ... Standard ISO 2631 [4] applies to vibrations in both
vertical and horizontal directions and deals with random and shock vibration
as well as harmonic vibration. In this standard, t...
... recognize eq (4.42) and we understand that the FRF representation
gives information on both the magnitude of response and the phase angle of
lag between response and excitation. This particular form ... been
obtained in Chapter 2 and here it is solved in the undamped and damped
cases, considering free vibrations first (homogeneous equation: no forcing
external excitation) and th...
... clamped and
free. Without reference to any particular set of coordinates (rectangular, polar,
etc.), we denote by s and n the coordinates in the tangential and normal
directions to the contour and ... 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
exp...
... orders of the
perturbation calculation. We 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 ... (or Laplace) transform: h(t) and H(
ω
) are a
Fourier transform pair and, likewise, h(t) and H(s) are a Laplace transform
pair.
Unfortunately, both the time-domain and the fr...
... or
180° and real numbers suffice for a complete description.
6.5 Structure and properties of matrices M, K and C: a few
considerations
A fundamental part of the analysis of MDOF systems and of ... determined
from the kth eigenvecctor and the damping, mass and stiffness matrices.
6.8 Generalized and complex eigenvalue problems:
reduction to standard form
For conservative and n...
... Gerardin, M. and Rixen, D., Mechanical Vibrations: Theory and Applications
to Structural Dynamics, John Wiley, New York, 1994.
17. Timoshenko, S. and Woinowsky-Krieger, S., Theory of Plates and Shells, ... not
difficult and it can be shown that the eigenvalues of the two eigenproblems
in which the n×n matrices K and M are obtained by bordering and (of
order (n–1)×(n–1))...
... 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...
... say X(t) and Y(t´), and follow the discussion of Chapter
11 to define their joint pdfs for various possible sets of the index parameters
t and t’.
Now, since we can characterize a random variable ... narrow-band and wide-band random processes,
these definitions having to do with the form of their spectral densities.
Working, in a sense, backwards we can investigate what kind of time h...