Modal analysis is, along with linear static analysis, one of the 2 most common types of FE analysis. If you don’t know about those, you’ll have to review your fea basics. That’s what we’ll do here!

In this short article, I’ll talk about:

- What is modal analysis
- Why it is important to know about it

## The difference between static and dynamic analysis

Static analysis means that we are making the assumption that the system we are simulating **doesn’t depend on time.**

Whatever the time period we observe the system, it will remain always the same.

It implies of course that the loads and boundary conditions don’t depend on time either.

In reality, this is a hypothesis, because every load has to be applied from a time t=0 sec

To take that in account, in static analysis, we just say that the load is applied « infinitely slowly » so there is no discontinuity during the load application.

Now…we can only do static analysis in certain cases where we can effectively do the assumption that the model can be considered as static…

**There are cases in which the loading itself (or the system) is dynamic** and thus we have to perform a dynamic analysis.

For example:

If you want to analyze an object falling on the ground, this is an **impact**… you understand intuitively that the reaction of the floor will first not apply when the object is in the air and AS SOON AS the object touches the ground, the reaction of the ground suddenly applies and impact the object. The application of the load is short AND intense. This type of phenomenon is 100% dynamic.

Here is an illustration (pardon my poor drawing skills…):

Dynamic Loadings can have various temporal distributions and it definitely **has an impact on the system**.

To Resume:

- In
**static analysis**, the system and the boundary conditions**don’t depend on time**. What matters is the intensity of the load. - In
**dynamic analysis**, there is a**time dependency**. What matters is the intensity of the load AND the temporal distribution of the loading.

## Cyclic loadings (fea basics)

I think that this is generally understood, but a short reminder is always good.

Cyclic loads have a certain frequency, period and intensity.

Cyclic loadings are transient loads. If you want to understand more about transient and steady-state and really understand the difference, I wrote another article about the topic in the past here.

## The response of mechanical systems to cyclic loadings

To explain things **simply**, you can say that the response of a system to a dynamic loading can be like the following:

- The intensity of the response can converge
- The system can oscillate
- The intensity of the system can diverge

In all cases, we want to avoid the 3^{rd} type of response, because it means that the system will break

**Example:**

Consider a kid on a swing.

The swing is the mechanical system and the kid provides a forced excitation input.

If the kid’s excitation load has a frequency which becomes close to the swing’s natural frequency, the swing goes up and up and the oscillations increase.

This phenomenon is called « resonance ».

(You can imagine that if the kid continues to push, he will be ejected—> that’s dangerous ;-) )

The same can happen for any mechanical system that oscillates or vibrates.

Resonance can be dangerous… and in case you don’t know… bridges have broken like that in the past because the frequency of the wind was matching the natural frequency of the bridge!

Watch this video if you don’t believe me:

**When does it happen?**

It happens when the system enters in « resonance » with the frequency of the input loading.

Which means:

When the frequency of the input load is equal to the « resonance » frequency of the system.

Now that you know that, you understand that it is absolutely critical to be able to calculate the resonance frequency of a system

**—> **That’s what Modal analysis does for you! :)

(Note that the « resonance » frequencies and commonly called « natural frequencies » or « mode frequencies »)

**So what is modal analysis??**

To explain it simply, modal analysis is a simple way to calculate the natural frequencies of your system so you know which frequencies can be destructive and dangerous for it.

Here a video I just created to show you how to perform simple modal analysis:

**Why there is no load in a modal analysis?**

That’s a question I often get about fea basics

Modal analysis calculates the natural frequencies of the system alone.

Modal is the simplest analysis and the only thing it does is telling you what are the “resonance frequencies” of your geometry. It isn’t related to a loading at this stage, only to the geometry. Resonance frequencies change due to the shape of your model and the way it is constrained only.

Because generally, once you noted the dangerous natural frequencies, you actually want to know:

“If I excite my model at this dangerous frequency, how much deformation will I really get?”

This is done use other types of analysis called « Time response dynamic analysis » or « Frequency response dynamic analysis » fea basics

**What is the input I need to provide for the EIGL Card?**

Some FEA Software call the input for modal analysis an EIGL Card for fea basics

The EIGRL Card is just a way to enter the parameters for the modal analysis, which are in general:

1- The initial frequency you want to start searching (V1)

2- The last frequency you want to stop searching (V2)

–> You could search the full frequency spectrum but you understand that it is not efficient if you know that you are only interested in the resonance frequencies which are in a certain range

3- The number of modes (N)

–> The modes of vibration are theoretically infinite but generally you only want to get the ones that will lead to the largest deformation

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**Do you like this article? Leave a comment and let me know!**

Mani says

Thank you for clear explanation

Cyprien says

You’re welcome Manideep! :)

Sriram Hariharan says

Good to know.

Thank you very much for sharing your experience.

Sri Harsha says

Thanks for your explanation :)

Tushar says

Great, presentation is like story telling

ALOZ OKEZIE says

Thanks for the explanation.

Vishnu says

Generally we say when the operating frequency match with the natural frequency a resonance is created and component fails. My question is, for an example

The first natural frequency of the component is 18 Hz

And my operating frequency is say 20 Hz.

Will the resonance will be creating???

If it so then why do we are extrating more than one natural frequences.

Kindly explane if i am wrong

Cyprien says

Hi Vishnu, you are right… the closer you get to the natural frequency, the stronger will be the response. To know exactly what will be the response, you have to perform a frequency response analysis. Then you will be able to observe and measure the actual response of the system.

Vishnu says

The displacements and stresses obtain from model analysis are not realastic. Is it so??

Cyprien says

That’s right. Modal analysis doesn’t provide you with this information. It only gives you the mode frequencies and the mode shapes.

Samir P. Jabre says

How find the vibration velocity (mm/s) of a shatf rotating mixer model?

Cyprien says

What do you mean by “Vibration velocity” Samir?

Walter says

thats was a good explanation

Akonyi Nasiru says

Thank you for your the in depth explanation.

Łukasz says

Hey!

This is great!

Also I LOVE the graphics of this article – they are simply awesome :)

Cheers!

Łukasz

Cyprien says

Really? I spent 5 min to draw that, haha :)

Aadith Om says

Thanks for your efforts in writing the article. I enjoyed reading it. Every time I read a technical article use to learn something new which I was not aware before, this became true for your article too.

I think that Natural frequencies and Resonance Frequency should be used in different context. Natural frequency is PURELY a structural behavior it’s function of stiffness and mass distribution or in other words function of geometry and support conditions. Loading has no role to play.

If the structure resonate at a particular natural frequency then that frequency is called resonance frequency. A structure can have multiple natural frequencies and their corresponding mode shapes but the structure is not going to resonate at all these natural frequencies. When a natural frequency becomes a resonance frequency depends on the how the external loading ( direction and distribution to excite one or more natural frequencies) is acting on the structure and hence it’s function of loading too.

Though there has been attempts in this article to explain the difference between these two, I think that at some places they are used interchangeably. This shall give a room at some beginner mind to think that they are both one and the same. I learned this from my technical boss after many years of praticing experience.

So in my humble opinion Model analysis mostly the termm Natural frequencies should be used and perhaps at very few places the terms Resonance frequencies can be used to explain when a natural frequency can be called as resonance frequency.

Thanks.

Cyprien says

Thanks for your long and interesting comment! You are right :) I kind of simplified a bit the phenomenon to make it better understandable for beginners. There is for sure more to say about it if you want to be rigorous :-) Thanks again for taking the time to explain your thinking!

Manoj Mittal says

Dear Cyprien…Real good article…

I just wanted to add something which may look irrelevant wrt this topic but I am finding myself difficult to stop…:))

It is about dynamic analysis you explained above…I worked a lot on dynamic analysis for many different purpose …currently I am using my little knowledge of dynamic analysis for analyzing offshore mechanical structure and full systems…

After multiple years of experience I could easily say it is static analysis which really solves my problem and make me understand deeply what happening in my system. For example I take example from your article above…you mentioned impact of ball on ground. In my personal view dynamic analysis is all about to understand and debate about that critical moment when ball going to hit ground…I mean here that particular moment from whole dynamic analysis is important for me and knowing about what exactly happen to my ball at that time for example if I interested in loads coming on ball. That’s it…….

Now it is my static analysis skills going to help me to understand how ball ( not going too deep on material non linearity ) going to behave because of this impact and how I can improve my design ….blablablaaa:)

Hence I feel doing FEA is more static then dynamic ……In static analysis we understand FEA results deeply….once we understand static then let go to add complexity to problem one by one and understand FEA results individually and later at the end we can combine whole physics togather…

Pl tolerate me guysss because I want to be knowingly ignorant about complex maths people many time confuse me rather talking about solution to engineering..

You are doing real great work….and important you are explaining purpose of doing FEA…In my view whether we structural, CFD, Thermal, Electrical …..Purpose is each physics is improving performance and efficiency of machine/system/subsystem…is not it too simple :))

Best Regards,

Manoj Mittal

mittalmanoj2k@gmail.com

Cyprien says

Thank you very much Manoj for your impressive comment and also for sharing your experience here on this article. I believe that sharing experience between engineer is necessary to make progress in this world and I am grateful that you took the time to write your view of the topic.

Antti Lehikoinen says

Okay, this is a bit more advanced sidenote, but I simply cannot leave it unsaid :D Here goes:

I think you can also use the eigenmodes for really lightweight analysis. I mean that once you have the frequency response, you can extract a few of the most significant resonance frequencies (say 3 of them). You can then use those 3 modes to approximate the system response to arbitrary loading.

Not really an expert on this topic, but I did see one demo where they simulated a freaking bridge on a mobile phone using that kind methodology. Impressive, to say the least :O

Cyprien says

Hi Antti, I think that you are talking about the modal superposition method right? It’s a good idea to write also about that! Thanks

Antti Lehikoinen says

Errmmm yeah that seems to be the case, based on quick googling :D I had simply used the term “reduced basis” for any method that somehow reduces the number of unknowns for the same mesh :)

talha ensar says

Thanks for your valuable share Cyprien.

Have you ever shared any tutorial about rotor dynamics (undamped critical speed analysis, unbalance response analysis, damped eigenvalue analysis and stability analysis)? If not, can you share?

Best Regards,

Talha

balaji modepalli says

Great Article on Modal Analysis. Thank you for that.

Can you write a article on Campbell diagram, which will be plotted once we get the natural frequencies of the system from modal analysis ?

GOPAL SINGH says

Hi,

I wanted to know difference in modal analysis with constraints and without constraints to understand the natural frequency of the system.

Suppose I have a fixture being mounted on vibration shaker. I can do a modal analysis of it with no constraints and other one with constraints at the mounting locations.

In without constraint case, we get first 6 rigid modes and then actual mode shapes and same is not the case with constraint one.

I have tried both but differences in natural frequency due to boundary condition, which is more useful to avoid the resonance phenomena.

It seems that the constraint one depicts the actual physical thing and no constraint case is generally used as free-free run.

Kindlyl let me know about this.

Thank you.

Cyprien says

Hi Gopal, You’re perfectly right! Good luck with your analysis.

Manoj Mittal says

Dear Gopal…

I am thinking on this…You do onething next week first thing of your day…open same assembly which was not constrained …in your assembly select any one component which u like most and make loose connection to rest of assembly….now run your modal analysis…pl tell us how many rigid nodes u see in FEA results???

If you see rigid modes more than 6…then it means by running modal analysis you can also find out how many components in ur assembly loosely connected…..

Hureee in case my above observation right…you discovered real practical use of modal analysis and quickly can find for complex assemblies how many components are loosely connected…

Thx Manoj Mittal

mittalmanoj2k@gmail.com

abhinav shrivastava says

for sinusoidal loading , the knowledge of natural frequencies is must, but what about random loading? how we can predict which mode is dangerous(coz all the frequencies are present all the time). Does mode shape also gives some information,means can we say that this shape can be dangerous?

Cyprien says

For random frequency loading, there is a special type of analysis to analyze it called “Random frequency response”. It works basically like a frequency response analysis but with a certain type of random input defined by a certain spectrum distribution that you can define.

amit says

I am seeing a very nice explanation of Modal analysis.

I am analyzing an ultrasonic horn whose one face is attached with a vertical rotating tool, while other face is attached with transducer.

Now pls tell me should i fix the horn from transducer side for modal analysis, leaving free at rotating tool side.

and what i do for harmonic study.

Manoj Mittal says

Hi Amit..

I exactly did not understood your problemmm..It would be really nice if you can share some simple hand images of ur problemmm….but any wayyyy…I can share few common things about structural boundary conditions…

Pl never get messed up with boundary conditions…seriously it is one area in FEA where I personally advise every my fellow FEA friends never ever decide boundary conditions in hurry…let ur boss keep crying but you please take your own time untill your heart and mind understan it completely…This is single most important stuff in FEA and if you go wrong ….consequencies could be really dangerous…

I beleive you are not doing any multibody dynamics…Your aim seems to be doing to confirm first natural frequency of your system…hence your aim should be to identify

1. Most conservative boundary condition

2. To compare real physical condition with ur software bounadry conditions. Example a simple beam both end fixed and you applied vertical load…after running simulation…you should expect displacement/deformation of beam should be downward and no rotation should be at ends…….in case you animation in post shows something diffrently …..which means There is something wrong in your boundary condition…keep correcting your boundary conditions untill you donot see what u wanted to see in post processor…once u happy with ur animations in ur post processor…u win half racee..

3. Also please keep checking reactions and moments looking good..

Just a thought ….May be I am wrong…pl make your own informed decision based on system u seeing in front of ur eyes..

Thx

Manoj Mittal

mittalmanoj2k@gmail.com

siddu says

Thanks!!! a lot sir for you great help to understand the concept modal analysis…

yashwant says

Hello,

I have two questions

1) Which one should be considered either Free-Free Modal analysis or Constrained modal analysis and Why ?

2) What do you mean by mass participation factor in Modal analysis?

Juan Costa says

Thanks for your interesting explanation,

I have a question, how many vibration modes is recommended to calculate for a convencional study?

Cyprien says

Hi Juan,

What is important is to be able to find the main modes that will impact your specific analysis. More you have modes and more you will have chances that the important modes for you are included inside, but you still have to find which ones. That’s why modal analysis is almost always coupled with another type of analysis such as frequency or time response.

If your structure is simple, then 10 modes should be okay. If you have a more complex system to analyse, you may want to increase your “search for modes”…