Example of report:

Field	Description
Mode Number	Mode number
Freq	Frequency (in Hertz)
Period	Period (in sec)
Perticip. Factor X	Participation Factor (along X)
Particip. Factor Y	Participation Factor (along Y)
Particip. Factor Z	Participation Factor (along Z)
Capt. Modal Mass X	Captured Modal Mass (Along X)
Capt. Modal Mass Y	Captured Modal Mass (Along Y)
Capt. Modal Mass Z	Captured Modal Mass (Along Z)
Capt. Average Mass	Percent Average
Total Capt. Modal Mass X	Cumulative Modal Mass (Along X)
Total Capt. Modal Mass Y	Cumulative Modal Mass (Along Y)
Total Capt. Modal Mass Z	Cumulative Modal Mass (Along Z)
Total  Mass	Total Mass of system

 

Notes

#1:

Natural frequency and mode shapes are property of the structure and depend on the mass and elasticity. They describe the tendency of the structure to vibrate when subjected to dynamic loading. Number of frequencies and mode shapes with which a structure can vibrate depends on the number of mass degrees of freedom in the structure. Mode shapes describe relative displacement of the structure (mass normalized). Number of mode shapes and frequencies required depends on the frequency of the applied load.

#2:

Mode shape #1 occurs at a frequency, that is the fundamental frequency or the 1st natural frequency. Each mode shape after that frequency up to the cut-off frequency are additional natural frequencies of the system.

#3:

The participation factors are the mass participation factors which are used directly in a dynamic analysis to calculate the dynamic response. The sum of the participation factors times the mode shape at each natural frequency should equal 1.

The mass participation factors indicate an amount of the lump mass in the system which contributes to the mode shape. Typically the higher values of mass participation factors appear in the first modes.

These  Participation Factors are normalized by the equation:  

However, not to be confused with mass normalized which means that the  modal displacements are divided by the the following transformation:

Participation Factors are not so much as an indication of percentage of mass associated with each mode, but more the actual lumped mass in the system associated with each mode. 

One reference book is "dynamics of structures" by Klough and Penzien

#4:

When looking at the frequency output report, the last column on the far right (Percent Average) provides the user with how much of the mode shape is contributing to the total captured mass of the system. As an iterative approach the modal analysis settings "cut-of frequency"  in the model can be incrementally increased to achieve a suggested total of between   75% - 100% participation. As higher cut-off frequencies are entered there will be a point where the higher modes do not contribute as much to the total vs the lower modes. Therefore, no need to analyze with any higher modes as they are not contributing to the results. 

Comments, Questions, and Answers with AutoPIPE's Output "Mode Shape" Sub Report:

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Item #1: What options are available to increase the participation factors in a model with multiple disconnected systems?

Item #2: Why a simple cantilever system doesn't match hand calculations for Modal Analysis?

Item #3: Why does frequency sub-report for all the pipe runs have the same results?

Item #4: What is the meaning of "Total captured modal mass (%)" in a Frequencies sub-report

Item #5: Why are there different Participation Factors and Captured Modal Mass results on different analysis runs where nothing has been changed in the Frequencies sub-report?

Item #6: Where exactly is the note at the end of the Frequencies sub-report, " Note: Participation factors and captured modal mass apply ..." referring too?

Item #7: What are the Participation Factors and the Captured Modal Mass in AutoPIPE's frequency report?

To watch the on-demand webinar "Maximizing AutoPIPE Standard and Custom Reporting Capabilities", click here.

See Also

Analysis Sub-report

Bentley AutoPIPE