understanding the mass participation factor

8/11/2019 Understanding the Mass Participation Factor

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UNDERSTANDING THE MASS

PARTICIPATION FACTOR

In my postExample of how to use the mass participation factor in SolidWorksyou can find a practical

example where this methodology is implemented.

Introduction

Every structure has the tendency to vibrate at certain frequencies, called natural or resonant frequencies.

Each natural frequencyis associated with a certain shape, called mode shape, that the model tends to assume

when vibrating at that frequency.

When a structure is properly excited by a dynamic load with a frequency that coincides with one of its natural

frequencies, the structure undergoes large displacements and stresses. This phenomenon is known as resonance.

Several programs such as SolidWorks are provided with a Finite Element Analysis module, FEA, which

helps to calculate properties as the mode shapes, stresses, displacements, strains, velocities, accelerations,

When I started using this type ofmodal analysisI needed to answer some questions that somehow haunted me:

Q1: How do I know if a certain dynamic load will make resonate the structure where it isinstalled?

Q2:When I am doing a modal analysis, how many resonant modes should I check?

Q3:When a mode shape should be considered or not?

Q4:What is the effective mass participation factor?

Q5:How could I make the most of the effective mass participation factor?

Firstly, I will give a very direct answer to the first question applying a criterion limiting

the exciting frequencies (it uses the idea of the Design Factor of Safety presented in the postWhat is your

Design Factor?).

Frequency limits criterion - Answer to Q1

After studying different information about modal analysis, I found out a criterion as follows (this criterion is

also followed by the ASHRAE, an association with an important role in a lot of engineering fields):

> 1-0,6 = 0,4 (it is 60% lower) Eq. 1

, where is the exciting frequency (i. e. is the frequency of the expected dynamic load) and is a

particular resonant frequency and represents the integral multiples of the exciting frequency (generally, youcan use the first six integral multiples to obtain reliable results). To make it clear, if I want to avoid resonance

problems, I should perform the design so that the resonant frequencies under consideration are 40% or less of

the expected exciting frequency, which means using a DFoS of 0,4. In the same way, we can support that:

> 1+0,6 = 1,6 (it is 60% higher) Eq. 2
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which means that the resonant frequencies under consideration should be 60% or more of the expected

exciting frequency, which means using a DFoS of 1,6.

-60% +60%

[-------------------------o-------------------------]

should not be in here

This criterion shall be applied to each natural frequencytaken under consideration to evaluate if the

phenomenon of resonance appears, but a new question arises. Now, you will need to answer the second

question:How many resonant modes should I consider?Or, how do you know if you have chosen sufficient

modes?

As a general rule, you probably want to look at as many modes as it takesto fully explore the frequency

excitation range youre expecting.For example, for structural excitations you can check 6 modes minimum

(obvious) and dont normally evaluate more than 10 modes or a couple of hundred Hz (say 500 Hz). However,

this methodology is not always the right method and that is why I will introduce you to the term

of Effective Mass Participation Factor, EMPF (also known as Mass Participation Factor).

What is the Effective Mass Participation Factor? - Answer to Q4 and Q5

Basically, the EMPF provides a measure of the energy contained within each resonant modesince

it represents the amount of system mass participating in a particular mode. For a particular structure, with a

mass matrix , normalized mode shapes and a ground motion influence coefficient , participation of

each mode can be obtained as the effective mass participation factor:

Eq. 3

Therefore, we can assure the following ideas:

A mode with a large effective massis usually a significant contributorto the response of the

system.

It is possible to calculate a EMPF for a particular direction (x,yorz).

The sum of the effective masses for all modes in a given response direction must equal the total

mass of the structure.

How Can I Calculate EMPF Using SolidWorks?

To list mass participation factors:

1. Run a frequency or a linear dynamic study.

2. Right-click the Results folder and select List Mass Participation (Figure 1).

3.

The Mass Participation (Normalized) dialog box opens.

4. Click Save to save the listed information to an Excel (*.csv) file or to a plain text (*.txt) file.


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Figure 1. List of mass participation factor

Number of modes criterion - Answer to Q2

Priestley et al (1996), among other authors, confirm that a sum of all EMPF (known as Cumulative Effective

Mass Participation Factor, CEMPF) of 80% to 90% in any given response direction can be considered

sufficient to capture the dominant dynamic response of the structure:

Eq. 4

, where is the number of modes taken under consideration. Therefore, if for example we expect a vibration

in thexdirection, we need to keep calculating modes until the sum of all EMPF in the xdirection is about 80-

90%. This should ensure a consistency in the results since we can compare the exciting frequency with the

sufficient natural frequencies. In the previous example, you can see that the sum of the EMPF for each

direction is higher than 80%.

Participation criterion - Answer to Q3

The frequency limits criterion is not the unique criterion that we must apply to evaluate if

the expected dynamic load generates a resonance effect. For example, it may be the case that the exciting

frequency is close to one of the natural frequencies but the energy contained within this resonant modeis a

small value and hence there is no resonance effect. That is why we need to use another criterion:

Eq. 5

One common rule is that a mode should be considered if it contributes more than 1% of the total mass.
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Methodology for performing a good, coherent and precise modal analysis

Lets finish the post summarizing the main presented ideas and sort those key ideas as follows:

1. Evaluate the expected dynamic loads (frequencies and directions).

2.

Run a frequency or a linear dynamic study for an initial number of modes .

3. Check if the CEMPF is between 80% and 90% for those directions (x,yorz) where

you expect a dynamic load. If not, increase the number of considered modes and re-run the

simulation (Number of modes criterion).

4. Check any EMPF where the value is higher than 1% (Participation criterion).

5.

Apply the Frequency limits criterion for those .

In my postExample of how to use the mass participation factor in SolidWorksyou can find a practical

example where this methodology is implemented.

I hope this post has been useful and if you have any concerns or questions feel free to contact me

[email protected]

If you liked itDontforget to share!

References:

ASHRAE publications:

Vibration Isolation and Control

A shot of isolation to prevent an outbreak of vibration

Priestley, M. J. N., Seible, S., Calvi, G. M., Seismic Design and Retrofit of Bridges,John Wiley and Sons,

1996. p 184,242.

Giancarlo Genta, (1998).Vibration of Structures and Machines: Practical Aspects.Springer; 3rd edition.

Tom Irvins webpage:http://www.vibrationdata.com/

SolidWorks help:Mass Participation (Normalized)
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EXAMPLE OF HOW TO USE THE MASS PARTICIPATION

FACTOR IN SOLIDWORKS

Introduction

In a previous postUnderstanding the mass participation factorI have talked about the modal analysis in

SolidWorks and how to make the most of it. I presented the results that you can obtain using that software:

mode shapes, resonant frequencies, effective mass participation factors, cumulative effective mass

participation factors, what information havethose values, how to interpret the results, Beside that basic

introduction it is also necessary to do a practical example to fully understand the topic.

An example makes it easier to understand

Let us imagine that we need to simulate an structure using SolidWorks. After evaluating the expected

dynamic loads (we consider a dynamic load of 5 Hz in the direction X) and simulating, SolidWorks provides

the following data:
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Table 1. Resonant frequencies and effective mass participation factors

Only part of that data is avaliable in the previous table; if you are looking for further informationclick herefor

the whole table.

As you can see, theCEMPFis between 80% and 90% for the direction X (Number of modes criterion)and so

the number of modes calculated is enough. Furthermore, the next figure shows the cumulative values:

Figure 2. Representation of the cumulative effective mass participation factor

515 Hz is the value of the resonant frequency where theCEMPFfor the direction X reaches 80%.

Using the data in the table it is also possible to check if any EMPFhas a value higher than 1% (Participation

criterion). Additionally, we can represent that information graphically (to facilitate the visualitation there is

only a representation of the first 80th modes):
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Figure 3. First 80th resonant frequencies and their respective effective mass participation factors

Since 76.4 Hz ( ) is the resonant frequency closer to 5 Hz ( ) which has aEMPFhigher than 1% in the

direction X, we need to apply theFrequency limits criterionfor that frequency:

That means the structure will not have resonant problems with a dynamic load of 5 Hz in the direction X.
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