Mechanical APDL Structural Analysis Guide

Eigensolver Eigenvalue Eigenvector

the eigenvalue. (stabil-

ity)

If the eigenvalue is real,

the corresponding modal

shape is real (the imagin-

ary slot will be zero).

Real Part: Mode shape

associated to the Ima-

Real Part (σ): measure of the

stability of the system

DAMP

• Imaginary Part (Ω): steady- ginary Part of the ei-
  state circular frequency of
  the system

QRDAMP

genvalue. (Natural fre-

quency)

A negative σ gives an exponen-

tially decreasing, or stable, re-

sponse.

Imaginary Part: Mode

shape associated to

the real part of the ei-

genvalue. (Stability)

A positive σ gives an exponen-

tially increasing, or unstable, re-

sponse.

3.9. Modal Analysis Tools for Subsequent Mode Superposition Analysis

The following modal analysis tools are available for subsequent mode superposition analyses:

3.9.1. Using the Residual-Vector Method to Improve Accuracy

3.9.2. Reusing Eigenmodes

3.9.3. Generating and Using Multiple Loads in Mode-Superposition Analyses

3.9.4. Restarting a Modal Analysis

3.9.5. Enforced Motion Method for Mode-Superposition Transient and Harmonic Analyses

3.9.6. Using Mode Selection

3.9.1. Using the Residual-Vector Method to Improve Accuracy

The residual vector method improves the accuracy of a mode-superposition transient,mode-superpos-
ition harmonic,PSD, or spectrum analysis.

A mode-superposition solution tends to be less accurat e when the applied dynamic loads excite the
higher resonant frequency modes of a structure. Many modes are often necessary to render an accurate
mode-superposition solution.

The residual vector method can help in such cases. The method's improved convergence properties
require fewer natural frequencies and modes from the eigensolution.

3.9.1.1. Understanding the Residual Vector Method

To use the residual vector method, you must first calculate residual vectors in the modal analysis. You
can use either of these modal analysis mode-extraction methods:

• Block Lanczos (MODOPT,LANB)


• PCG Lanczos (MODOPT,LANPCG)

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Modal Analysis