Mechanical APDL Structural Analysis Guide

3.8. Comparing Mode-Extraction Methods

The basic equation solved in a typical undamped modal analysis is the classical eigenvalue problem:

φi ωi φ =i

2

where:

[K] = stiffness matrix

{Φi} = mode shape vector (eigenvector) of mode i

Ωi = natural circular frequency of mode i (

ω


is the eigenvalue)

[M] = mass matrix

Many numerical methods are available to solve the equation. Mechanical APDL offers these methods:
3.8.1. Block Lanczos Method
3.8.2. PCG Lanczos Method
3.8.3. Supernode (SNODE) Method
3.8.4. Subspace Method
3.8.5. Unsymmetric Method
3.8.6. Damped Method
3.8.7. QR Damped Method
3.8.8. Storage of Complex Results

The damped and QR damped methods solve different equations. For more information, see Damped
Method and QR Damped Method in the Mechanical APDL Theory Reference.

The Block Lanczos, PCG Lanczos, and Supernode mode-extraction methods are the most commonly
used:

Table 3.5: Symmetric System Eigensolver Options

Disk Re-

quired

Memory

Re-

quired

Eigensolver Application

To find many modes (about 40+) of large models. Recom- Medium High

mended when the model consists of poorly shaped solid

Block

Lanczos

and shell elements. This solver performs well when the

model consists of shells or a combination of shells and

solids.

To find few modes (up to about 100) of very large models Medium Low

(500,000+ degrees of freedom). This solver performs well

PCG Lanczos

when the lowest modes are sought for models that are

dominated by well-shaped 3-D solid elements (that is,

models that would typically be good candidates for the

PCG iterative solver for a similar static or full transient

analysis).

To find many modes (up to 10,000) efficiently. Use this Medium Low

method for 2-D plane or shell/beam structures (100 modes

or more) and for 3-D solid structures (250 modes or more).

Supernode

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Comparing Mode-Extraction Methods