Max. No. of Eigenvalues Calculated - CAESAR II - Help

CAESAR II Users Guide

Language
English
Product
CAESAR II
Search by Category
Help
CAESAR II Version
12

(Available for: Modal, Spectrum, and Time History)

Specifies the number of modal responses to be included in the system results through a mode number cutoff. Enter a value for Setting. Enter 0 to limit modes extracted to the value of Frequency Cutoff (HZ). Enter higher values as described below.

The first stage of the spectrum and time history analyses (and the only step for modal analysis) is the use of the Eigensolver algorithm to extract piping system natural frequencies and mode shapes. For the spectrum and time history analyses, the response under loading is calculated for each of the modes, with the system response being the sum of the individual modal responses. The more modes that are extracted, the more the sum of those modal responses resembles the actual system response. This algorithm uses an iterative method for finding successive modes, so extraction of many modes usually requires much more time than does a static solution of the same piping system. The object is to extract enough modes to get a suitable solution, without straining computational resources.

This parameter is used, in combination with Frequency Cutoff (HZ), to limit the maximum number of modes of vibration to be extracted during the dynamic analysis. If this parameter is entered as 0, the number of modes extracted is limited only by the frequency cutoff and the number of degrees-of-freedom in the system model.

Example

A system has the following natural frequencies:

Mode Number

Frequency (Hz)

1

0.6

2

3.0

3

6.1

4

10.7

5

20.3

6

29.0

7

35.4

8

40.7

9

55.6

The modes extracted for different values of Max. No. of Eigenvalues Calculated and Frequency Cutoff are:

Max. No. of Eigenvalues Calculated

Frequency Cutoff

No. of Modes extracted

0

33

7

0

50

9

3

33

3

9

60

9

If you are more interested in providing an accurate representation of the system displacements, request the extraction of a few modes, allowing a rapid calculation time. However, if an accurate estimate of the forces and stresses in the system is the objective, calculation time grows as it becomes necessary to extract far more modes. This is particularly true when solving a fluid hammer problem in the presence of axial restraints. Often modes with natural frequencies of up to 300 Hz are large contributors to the solution.

To determine how many modes are enough, extract a certain number of modes and review the results. Repeat the analysis by extracting five to ten additional modes and comparing the new results to the old. If there are significant changes between the results, repeat the analysis again, adding five to ten more modes. This iterative process continues until the results taper off, becoming asymptotic.

This procedure has two drawbacks. First is the time involved in making the multiple analyses and the time involved in extracting the potentially large number of modes. The second drawback, occurring with spectrum analysis, is less obvious. A degree of conservatism is introduced when combining the contributions of the higher order modes. Possible spectral mode summation methods include methods that combine modal results as same-sign (positive) values: SRSS, ABSOLUTE, and GROUP. Theory states that the rigid modes act in phase with each other, and should be combined algebraically, permitting the response of some rigid modes to cancel the effect of other rigid modes. This is what occurs in a time history analysis. Because of this conservatism, it is possible to get results which exceed twice the applied load, even though the Dynamic Load Factor (DLF) of an impulse load cannot be greater than 2.0.