Civil Engineering Reference
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freedom of the model. The solution is given as in-phase (real) and out-
of-phase (imaginary) components of the solution variables (displace-
ment, stress, etc.) as functions of frequency. The main advantage of this
method is that frequency-dependent effects (such as frequency-
dependent damping) can be modeled. The direct method is not only
the most accurate but also the most expensive steady-state harmonic
response procedure. The direct method can also be used
if nonsymmetric terms in the stiffness are important or if model param-
eters depend on frequency. ABAQUS [1.29] includes a full range
of modal superposition procedures. Modal superposition procedures
can be run using a high-performance linear dynamics software
architecture called SIM. The SIM architecture offers advantages over
the traditional linear dynamics architecture for some large-scale ana-
lyses. Prior to any modal superposition procedure, the natural frequen-
cies of a system must be extracted using the eigenvalue analysis
procedure. Frequency extraction can be performed using the SIM
architecture.
ABAQUS [1.29] provides different modal superposition procedures
comprising the following:
(1) Mode-based steady-state harmonic response analysis, which is a steady-
state dynamic analysis based on the natural modes of the system, can be
used to calculate a system's linearized response to harmonic excitation.
This mode-based method is typically less expensive than the direct
method. The solution is given as in-phase (real) and out-of-phase (imag-
inary) components of the solution variables (displacement, stress, etc.) as
functions of frequency. Mode-based steady-state harmonic analysis can
be performed using the SIM architecture.
(2) Subspace-based steady-state harmonic response analysis. In this analysis,
the steady-state dynamic equations are written in terms of a vector space
spanned by a number of eigenvectors. The eigenmodes of the system
extracted in a frequency extraction step are used as the global basis vec-
tors. The method is attractive because it allows frequency-dependent
effects to be modeled and is much cheaper than the direct analysis
method. Subspace-based steady-state harmonic response analysis can
be used if the stiffness is nonsymmetric and can be performed using
the SIM architecture.
(3) Mode-based transient response analysis, which provides transient
response for linear problems using modal superposition. Mode-based
transient analysis can be performed using the SIM architecture.
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