Mechanical APDL Structural Analysis Guide

= λ

Where the eigenvalues λ and {x} are output as symmetric modes to Jobname.MODESYM. The [K]

matrix in the above expression is the stiffness matrix, symmetrized as outlined in QR Damped

Method in the Mechanical APDL Theory Reference.

2. Then in the first and all the subsequent load steps, the symmetric Lanczos eigenmodes are used to build
   the subspace eigenproblem and create the Jobname.MODE. This mode file contains the complex eigen-
   modes of the non-symmetric eigenproblem, given by:
   u u = λu u

Where λu and {xu} are output as unsymmetric modes to Jobname.MODE.

3. The Lanczos eigenmodes from the symmetrized eigenproblem written out to the Jobname.MODESYM
   mode file are available for later use by the QRDAMP eigensolver.

When analyzing for brake squeal or Campbell plot generation in rotordynamics, the reuse approach
can improve performance by avoiding the Block Lanczos run that typically occurs in a QRDAMP ei-
gensolution. Exercise caution when comparing eigensolutions from a reuse run with a non-reuse run,
as symmetrization differs in these runs. In a non-reuse run the [K] matrix gets symmetrized at each load
step of a QR damp eigenanalysis. In a reuse run the symmetrization occurs at the first load step and
the symmetric normal modes are reused in all subsequent load steps.

The QRDAMP eigensolver will attempt to reuse the normal modes from Jobname.MODESYM if the file
is present in the folder where the job is run, so ensure that Jobname.MODESYM is created by the same
model as the subsequent QR damp model.

3.7.5. Calculate the Complex Mode Contribution Coefficients (CMCC)

In a brake squeal analysis, the complex mode contribution coefficients (CMCC) can be used to determine
how much the symmetric normal modes contribute to the complex modes. They can be directly output
from the solver to a text file using the CMCCoutKey on the QRDOPT command. The CMCC are the
components of vector {y} defined in Equation 14.210 in the Mechanical APDL Theory Reference. The
equations to recalculate the CMCC are described in this section. Using the upper part of Equation 14.212
in the Mechanical APDL Theory Reference, the relationship between the real and the complex modes can
be written as:

{ψ}=[φ]{y}

Where:

ψ


is the vector of complex modes (upper part only) in:

 

 

 

ψ

ψ

ψ

=











ɺ 

φ

is the matrix of real modes (upper part only) in:

 

 

 

φ

φ

φ

=











ɺ

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Modal Analysis Examples