In the last article, I described in depth Modal Analysis, Eigenvalues and all what that means and in this article, I will dive into what is frequency response analysis.

## The most important lesson about modal analysis

– Modal analysis helps to determine the modes of vibrations and the frequencies at which those modes are triggered

– Modal analysis doesn’t give you any info about the real deformation that an excitation of one of those modes will actually cause

When you have to do a dynamic analysis, *modal analysis is only the beginning!*

**I think it’s clear:**

Some modes will cause more « resonance » than others (and thus more damage)… so we want to know which ones and we want also to calculate the maximum deformation for each of the modes « triggered ».

Now how do we actually do that?

## Case Study: the utrasonic welding machine

*In this section, I’ll explain to you first what is an ultrasonic welding machine, how it work, and then I’ll show you a full tutorial and analysis about how to actual SIMULATE that by performing a frequency response analysis.*

If you don’t know how it works, here’s the wikipedia definition:

**Ultrasonic welding** is an industrial technique whereby high-frequency ultrasonic acoustic vibrations are locally applied to workpieces being held together under pressure to create a solid-state weld. It is commonly used for plastics, and especially for joining dissimilar materials. In ultrasonic welding, there are no connective bolts, nails, soldering materials, or adhesives necessary to bind the materials together.

And here is a video which shows the principle:

It’s actually vibrating so fast that you don’t see it vibrating! Amazing! :)

But do you hear this noise when it vibrates? This is a noise created by an ultrasonic wave

Now think about it… this part is by nature submitted to high frequency vibrations.

But how do we know that the frequency of vibration won’t excite one of the natural frequencies…causing resonance and unexpected failure??

That’s exactly what** Frequency response analysis** will help us to understand!

## What is frequency response analysis and what’s the difference with modal analysis?

When you do modal analysis, you are asking your part: « Hey, what are the dangerous natural frequencies that make you resonate? »

When you do frequency response, you are not « asking », you are actually testing: « Let’s input a load which will vibrate in a certain defined range of frequencies and let’s see how you actually deform! »

There is a huge difference between the type of results you will get from Modal Analysis and the type of results you will get from Frequency response analysis. What is frequency response analysis?

I decided to create a full video tutorial for you in which I’ll show you:

1- How to make a modal and a frequency response of a ultrasonic welding machine horn

2- How to analyze and understand the results

What I’ll show you in this video took me months to understand, that’s why I thought it may be extremely useful to you as well!

That’s all for today!

**If you like this article, there are 2 things you can do for me:**

1- Help me to share this article on **Linkedin, facebook, twitter** or in your habitual forum to help more people understand frequency response analysis (use the share button on the left of the article).

2- Let me know in the comments what you learned from it and what you would like to learn even further so I can write more on the topic

Thank you for reading!

–Cyprien

If didn’t read the previous article about modal analysis, here it is:

Antti Lehikoinen says

Nice post! :) In electrical engineering, we sometimes also use frequency response functions for stability analysis.

I mean an electrical machine can have an electromechanical resonance frequency in SPEED (rather than angle or displacement), at which it tends to increase the amplitude of the oscillations. If that frequency is close to some of the torsional natural frequencies of the shaft-system, bad things happen :D

Cyprien says

Waouh, I didn’t know about that! Thanks for completing and adding value Antti, as usual ;-)

Vaughan says

Great video, thanks.

One thing I missed in the Modal Analysis, was it performed under a preload of 0.1N/mm?

Cyprien says

Thank you Vaughan! No, no preloading here. I created the load for the frequency response analysis I did after, it wasn’t used for the modal analysis.

Vaughan says

Thanks for the feedback. And I meant 0.1N/mm^2

ALOZ OKEZIE says

I appreciate that you really try to explain things in detail. I am Civil Engineer and we also use some of these FEA tools and often find your posts very helpful.

Cyprien says

Thank you Aloz! I appreciate very much that my articles were useful for you! :)

venkatesan says

Really great post ,

How to know how may mode shapes it takes into account to do frequency response analysis and The the plot we are getting is in which direction and which node because when doing modal analysis mode shapes are different in different frequency .

Warm Regards

Venkat

Cyprien says

Hi Venkat,

Good question, first by doing modal analysis, you can spot the different frequencies of the mode shapes, so you get a range of frequencies which contains your modes. Then, when you do frequency response, you have to choose the frequency range where you will perform the analysis like I did in the video. So if your modal frequencies are in this range and if they resonate with your load (that’s not obvious), you will see peaks at the mode frequencies in your frequency response graph.

The graph plotted in the video is for the maximum displacement. If you want to know at which node of the model it actually happened, you will have to use the post process tools in your software to spot those nodes.

venkatesan says

Hi Cyprien

I have done a modal analysis of my steel bracket and i found no. of frequencies Than i compared with my working frequency and fundamental frequency of steel bracket. The working frequency is very less compared to the fundamental frequency so the bracket is not in the dynamic loading. from dynamic point of view that is safe..

my question is when should i go for harmonic analysis and what should i conclude from that analysis.

Warm Regards

Venkat

Abhishek Soni says

Hi Cyprien,

I really appreciate your efforts for posting this video and it was great learning experience. Could you please explain the direct frequency response as well. I understand what exactly happens but replicating ina video would be great. Look forward to it. Keep up the great work.

Thanks & Regards,

Abhishek

Cyprien says

Thank you Abhishek! Direct Frequency Response is very similar to Modal Frequency Response Analysis in terms of workflow. What is different is the equations used in the solver. Direct response takes more time because it solves mechanical equations in a coupled way. You use direct response when you need to consider damping for example.

sawant singh says

thank you Cyprien for such an informative video..

i have a doubt..that there were a number of natural frequencies between the range 1000 to 2000 hz but the first resonance occurred at 2400 hz !!! why not at every natural frequency when the frequency of pressure load passed through it ( the latter also started from 1000 Hz in increments)? and the natural frequencies given by modal analysis didn’t exactly match with the resonance frequency? does it depend on the increment you gave for pressure load frequency ?

Cyprien says

Hi Sawant, not every resonance frequencies will enter in resonance with the frequency of your loading for a simple reason. The direction of the load for example is involved. Your model may vibrate at 1500 Hz, but not in the same direction than the input loading. In this case, it has no chance to resonate…For your second question you guessed right, if you want more precision, you need more increments!

sawant singh says

thank you

Kris says

That was a great video Cyprien! Thanks for sharing. I have developed similar benchmark analysis, natural frequency and then utilized for frequency response, which for non-resonance range are the same as linear static response. Reviewing frequency response results at resonance I have noticed that displacement value is very sensitive to damping ratio. Could you please shear your experience how to estimate damping ratio for steel structures or perhaps refer to same third party publications reachable online? Will appreciate your response! Thanks!

Cyprien says

Damping ratio depends on the material and the structural system considered…for example for standard bolt structures 0.8 percent, and for welded structures 0.3 percent, while for reinforced concrete structures 5 percent. Damping ratio depends also a lot in which kind of damping you are assuming. In structural engineering viscous damping (related to velocity) is normally used as it is easier to work with. However, for some cases Coulomb damping (friction based) is more realistic. As for a typical value, 5% is correct for concrete structures, being lower for steel structures. Keep in mind that this are just gross estimations and that the real damping ratio depends on a huge number of parameters and complex mechanical interactions, making it only possible to accurately estimate its value experimentally.

You can check those books for more details:– Dynamics of Structures – Ray W.Clough and Joseph Penzien;

– Fundamentals of Vibrations – Leonard Meirovitch;

– Dynamics of Structures – Theory and Applications to Earthquake Engineering – Anil K Chopra.

Kris says

Thanks Cyprien!

Could you please take a look also on my next question?

Since you explained Frequency Response (FR) analysis type very well, I am now wondering what is the difference if one would like to use Transient Stress (TS) analysis (either Super Position or Direct Integration). Could you please let us know what is the major difference and purpose of each?

What may be observed is FR gives us plot Displacement vs Frequency, while TS plots Displacement vs Time, hence if would be hard to observe resonance in TS, therefore what is the purpose. Thanks !

jose manue gil santacruz says

Congratulations for your tutorials Cyprien; were more people like you Engineering world woulb be a less “Dark Ages and Middled Aged Era world” as many want Engireering life remain.

My question is very simple… what would be the external physical real cause that makes the static load to vibrate at such a high frecuency? It is just made to vibrate at high frecuency for Academic explanation and purposes?

Cyprien says

Hi Jose, thanks for your comment!

There are some specific systems that vibrate because of the way they are conceived. Sometimes it’s wanted, like the example of ultrasonic welding that I am talking about in the article. Sometimes, it isn’t wanted…like the vibration of a motor engine while the car is functioning.

Sagar Desai says

Really nice article…..thank you

Dung says

Hi. Could you explain mode superposition method in frequency domain.

Thank you so much

Ziyue says

Great article, thank you for posting!

Ekain San José Garcia says

Thank hoy Cyprien!!!

mohi says

hi.

did any one do this analysis(ultrasonic welding) in ansys workbench or abaqus?

Sakrit says

It is really useful for me. Thank

Yoli says

Great video and information source for frequency response analysis!!

Is the dynamic load applied as sinus function ?

Thank You!

Cyprien says

In my example, yes, but in practice, you can apply a dynamic load with any kind of temporal function!

Faisal says

What I dont get is why the result on y-axis is shown as acceleration or g-loads? Per my understanding, the g-loads are the local force vectors at that point, and you can only get displacement using local stiffness matrix at that point. In this case, calling 1.5g experienced at a location as ‘amplitude’ is wrong isn’it ?