Wave Phenomena in Vibroacoustic Systems

Manipulating the scattering of waves can allow engineers to achieve numerous goals, like reducing unwanted noise or eliminating potentially destructive vibrations in structures. In this episode, we talk to Vladislav Sorokin (University of Auckland) and Luke Bennetts (University of Melbourne), two guest editors of the recent Special Issue on Wave Phenomena in Periodic, Near-Periodic, and Locally Resonant Systems about recent advances in research regarding vibroacoustic systems. 

Read all the articles from the special issue here!

Read more from The Journal of the Acoustical Society of America (JASA).
Learn more about Acoustical Society of America Publications.

Music Credit: Min 2019 by minwbu from Pixabay. 

Transcript

ASA Publications (00:25)

Today we'll be discussing a recent joint special issue for JASA and JASA Express Letters, The Special Issue on Wave Phenomena in Periodic, Near-Periodic, and Locally Resonant Systems. With me are two of the editors, Vladislav Sorokin and Luke Bennetts. Thanks for taking the time to speak with me. How are you?

Vladislav Sorokin (00:43)

Thank you, all good, all good.

Luke Bennetts (00:44)

Yeah, hi. Hi, Kat. Hi, everyone. Yeah, very well. Thank you.

ASA Publications (00:48)

So first, just tell us a bit about your research backgrounds.

Vladislav Sorokin (00:51)

Yeah, so basically my research background is actually quite diverse because I have done PhD in nonlinear dynamics. Basically we were considering systems under high-frequency vibrations and then studying nonlinear dynamics of these kind of systems, getting some cool phenomenas, like gas bubbles sinking and heavy particle rising in the fluids which are vibrating. And then I switched to completely different field, which was on basically elastic wave propagation in periodic structures. And now in my research group at the University of Auckland, Wave Dynamic Research Group, we actually do projects which are both on nonlinear dynamics, on periodic structures, metamaterials, and also energy harvesting.

Luke Bennetts (01:36)

Okay, and I am an applied mathematician, trained as a mathematician as a student, moved towards applied problems and, in particular, I started solving what are known as wave scattering problems when I was a graduate student. And I was really drawn to the mathematical aspects of what we call composite media and, in particular, periodic media that we look at in the special issue, and also random media which is the near-periodic media that we discussed in the issue as a step towards… I feel like perhaps I'm a little bit of an imposter acting as an editor for JASA because I’m not an acoustician. But like a lot of applied mathematicians, I like to work in a lot of different application areas and I often end up working with acousticians because they have really interesting problems to solve. So I like scattering problems in acoustics and also elastodynamics.

ASA Publications (02:37)

I mean, that makes it sound like you are an acoustician in a way, but you know, everybody is welcome in acoustics. So how did this special issue come about?

Luke Bennetts (02:41)

Vladislav, myself, and the two other guest editors who are not here today, Nicole Kessissoglou and Alex Skvortsov. We met at the KOZWaves conferences. So KOZWaves is the Australian and New Zealand waves science community that runs a conference every two years. And we really interacted over our common interests in the topic of the special issue. It's a very active area for the KOZWaves community, but we're also aware of lots of excellent work being done internationally. We thought it was appropriate to create the special issue to highlight the latest advances in this area. And also for us to be able to show a bit of leadership from the Australasian side.

ASA Publications (03:37)

Very cool. It's always fun to hear about special issues that arrive from conversations at conferences and such.

Luke Bennetts (03:42)

I would say 90% of research comes from conversations at conferences, like the coffees in between the talks.

Vladislav Sorokin (03:50)

Yes, so we basically were kind of inspired by some of the works done at the conferences, presented at the conferences, and discussions that we had at these conferences. So basically decided why not to have a special issue which will basically share, like show some cool stuff which was done.

ASA Publications (03:50)

Awesome. Okay, so for those of us not in the field, what are periodic or near-periodic vibroacoustic systems, and how are they used to manipulate or control acoustic and elastic waves?

Luke Bennetts (04:19)

So if we think about a standard vibroacoustic system in terms of the waves, it only supports very basic sorts of waves, what we might call “plane waves.” So this essentially means that if you know what the waves are in one location you can predict them in a simple fashion everywhere else in the system. But then we think about adding some structure to the system, and that structure redistributes the waves in different directions, and that is what we call scattering that I referred to in terms of my research earlier. 

Now waves have this special property which is called coherence. That means that they can sum or cancel with one another depending on their relative phasing. And that means that we can use scattering to control the waves. So in particular, if the structure is periodic, then scattering creates another sort of wave, which is known as a “block wave,” which we can control with the geometry of the periodic structure.

Now, I also want comment on the “local resonance” part of the title of the special issue, because that's important, because it means that the scattering by the individual elements of the structure is very strong for certain frequency bands. And that allows us to use the block waves to control low frequencies without having very large overall structures.

Vladislav Sorokin (06:03)

I just want to say that actually, to be honest, these periodic structures and vibroacoustic structures, they're actually all around us in the end. So basically like multi-story buildings and some guideways and pipes and even like the wind turbines, essentially, because they have these blades. They are actually periodic structures. So in principle, the theory which is developed for periodic structures, it can be applied to describe dynamics of these kind of systems. And to be honest, these systems, they have been studied already from this point of view of periodic structures, they have been studied for decades, actually. And basically the idea was yes, can we actually try to utilize this, let’s say, this behavior that was mentioned by Luke, that you can actually get in certain frequency ranges, you can get that okay, the structure will not vibrate at all. Because then you can remove vibrations from the structure if you design it in a nice way. So it actually had been done before. And another application is let's say, like something which is called stiffened plate. So you just have a plate and then you add something like ribs on this plate. And then if you add these ribs in a periodic way, with the proper periodicity, then basically the structure will not be vibrating, this plate will not be vibrating, in some low frequency ranges. And then if you know that, okay, at these frequency ranges you can have, without ridge you will have large vibration and you don’t want to have large vibration, then you just add these ribs to the structure and the structure is not vibrating. 

But actually, if you go even deeper into this topic, and especially if we talk about this thing that was mentioned by[KS1]  Luke about the local resonance side of things, then… Basically structures with local resonances, they have been studied, I don’t know, 100 years ago. So as soon as like Den Hartog came up with his tuned mass dampers, basically just if you have any sort of structure, and you want to remove vibrations in this structure in a certain frequency range, like relatively narrow frequency range, you just add this absorber, and then it will basically take all the energy of vibrations into itself. So the hosting structure will not vibrate, but absorber will vibrate. So essentially metamerials are just structures with many absorbers. And then you get this local resonance due to these absorbers resonating. And then they sort of suck all the energy out of the system. So the system, the hosting system is not vibrating, but the absorbers are vibrating.

So basically the idea is that, what I want to say is that these periodic structures is not something artificial. They're all around us. They have been studied for a relatively long time. But we still try to show some new and interesting things in this special issue related to not only the theory and the methods, but also some new phenomena and so on.

ASA Publications (08:42)

It is really interesting. It sounds like it has many applications within structural acoustics. I could see how it would have applications in architectural acoustics and design and maybe even noise control?

Vladislav Sorokin (08:54)

Yes definitely.

ASA Publications (08:56)

Yeah.  Okay. Very cool. So why is it useful to be able to control acoustic and elastic waves?

Vladislav Sorokin (09:01)

Yeah, so basically, again, as I mentioned in my previous example, let's say you basically one of the very nice examples that will actually work, let's say at the University of Auckland, is trying to reduce noise transmission through walls. So let's say you have a building wall, and you want to reduce, let's say you have a neighbor who is super noisy, and you don't want to hear this noise of your neighbor. So what do you do? You can try to design a wall, basically, to have some kind of periodicity, so that basically it doesn't allow this sound to transmit through the wall, from your neighbor. And in this case, of course, like, you as a person, I don't want to hear any kind of noise from the neighbor. So why not to use this, let's say, band gaps, frequency band gaps, which are inherent for periodic structures, to reduce this noise transmission for the wall. This is one example. 

Another example is, of course, the railway tracks. So this is classical example. Let's say you have a railway tracks. And then let's say in... Maybe not in New Zealand, so much, but let's say maybe in Europe, in which we have a bit closer, maybe dense housing and so on. So houses closer to the railway tracks. You don't want to have vibrations transmitted to the houses around the railway tracks. Let's say you have like, you know, a terminal or something and houses around it. You don't want vibrations to be transmitted to the houses. Again, you can use these periodic structures, such as mass dampers, so, essentially, metamaterials to reduce vibrations transmitted to the surroundings. These are just two quick examples. 

Of course, another example is about noise transmission in ships and aircraft and so on. Basically, these vibration transmission problems are everywhere around us. And if we want to reduce this transmission of vibration or noise from one part of a structure to another structure, of course, we can use these periodic structures or near-periodic structures or local resonance structures for this job, essentially.

ASA Publications (10:57)

That makes a lot of sense  and does sound very useful.

Vladislav Sorokin (11:01)

Yes, yes.

ASA Publications (11:01)

So in your introduction to the special issue, you mentioned this area of research overlaps with the study of acoustic and elastic metamaterials. How so?

Luke Bennetts (11:09)

Metamaterials are very closely related to periodic, near-periodic, and locally resonant systems. Almost synonymous. Metamaterials have been around for several decades now, and it's been very difficult to define them. But I think the most commonly accepted definition of a metamaterial is that it is a composite that's designed to have a response that can't be achieved with a single conventional material. So the classic example of a metamaterial is one that's used for invisibility cloaking. In the context of acoustics… so that would be some sort of metamaterial structure that you could use to bend sound waves around a body, making it acoustically undetectable. So it has to be a metamaterial because the bending of the sound waves requires an unnatural property. So perhaps the easiest one to give you a sense of what that would be, is a negative mass, right, which actually doesn't exist. And what I mean by this is what we call a “negative effective mass,” which depends on frequency. And these sort of properties are created by designing the microstructure of the metamaterial in some very clever fashion. Now the connection with the special issue comes because the microstructure of the metamaterial is usually resonant, and classically comes in periodic arrangements, but it is moving towards loosening that restriction, which is the near-periodic part of the special issue.

ASA Publications (13:05)

Okay, okay, I see. What are some challenges that arise in research involving periodic and near-periodic vibroacoustic systems?

Vladislav Sorokin (13:14)

Yeah, so, basically, I think that there are a lot of challenges actually, unfortunately, because for example, one of the challenges is related to one of the examples that I was mentioning. Basically, in many cases, we're talking about not only, let's say, one kind of waves. So it's not only elastic waves, let's say elastic waves, these are waves in, let's say, plates or in walls or maybe in railway tracks. But we are talking about also acoustic waves. And acoustic waves, these are typically waves which are just propagating through air or maybe through water. So in many cases, we actually have systems in which we want to try to attenuate both types of waves. So both basically acoustic waves, which are, let's say, in air, and also elastic waves in structures. And actually having systems that can attenuate both these types of waves is not easy. Another challenge is let's say if we have, a system which can attenuate vibrations in a very nice way. Let's say we talk about vibrations. So it can attenuate vibrations in a nice way. But is it, let's say, if it's used as a wall in a building, or maybe it's used as some component of maybe a bridge, or maybe it's used as a component of maybe a pipe system. So is it strong enough to do another job? So not only attenuate sound, but let's say to support the weight of a building or support the weight of a bridge or any kind of structure. So basically the case when we try to consider different types of waves propagating in the system, or we try to design the system, which is not only for, let's say, attenuating vibrations, but for some other tasks. This is actually kind of challenging,

Luke Bennetts (14:52)

So there’s another set of challenges that exist in being able to simulate the systems that we're interested in to test new concepts. So we typically model the systems using partial differential equations. It's a very classic approach, and there are lots of software packages out there to solve these sorts of systems. Well, in principle at least, but for the sorts of systems that we're interested in those software packages are usually not very efficient and therefore not that useful to us. So most of the systems that we're interested in are what we call “multi-scale” because in reference to the discussion about metamaterials earlier, they have a microstructure, which is at the scale of an individual period, and then a macro scale, which is the entire system.

We want to be able to solve that full system directly, but that requires special approaches because we have to deal with all of the interactions that are going on with the waves that are being scattered between the microscale elements. We also want analytical approximations because they give rapid solutions, and also they often give more insight into the physics of the problem. But they need new theories and methodologies. And then, just to complicate matters even more, we can add in phenomena like non-linearity or time-bearing media. These are new emerging areas for this research area and they're very much open at the moment.

Vladislav Sorokin (16:47)

Yeah, so basically what Luke says is actually directly related to the practical application that I was mentioning before. Because basically what is happening is that, okay, you design the system on the micro level to attenuate vibrations, but you need to consider the system on the macro level, on the big level, on the global level, if you want to assess the overall performance of a structure. Let's say if you want to see how it can support the weight or do the overall job that it's designed to do.

And actually the thing about nonlinearity that Luke mentioned, basically nonlinearity is not something artificial. Actually all systems around us, they're actually nonlinear. All real systems are nonlinear. It just, when we study them, we can do linear approximation, but sometimes this linear approximation doesn't really work because, let's say, vibrations are a bit large or maybe structure is very thin. So basically, let's say, the last thing that was mentioned by Luke about considering nonlinear phenomena in periodic systems and near-periodic systems and locally resonant systems. It's also basically because we need to do it for applications because in many applications when we have a structure, it actually exhibits a bit of nonlinear behavior.

Luke Bennetts (17:56)

Yeah, what Vlad said is of course absolutely right. Everything is nonlinear and everything is time-varying, in some sense. I’ve given you the perspective of a mathematician, which is... but those phenomena don't appear in the equations, then they don't really exist.

ASA Publications (18:14)

Right, right, some articles in the special issue with new concepts and new phenomena in this field of study. Can you share some examples of these innovations?

Vladislav Sorokin (18:24)

Yes, so maybe the easiest would be just to relate to this problem that I have already mentioned about trying to mitigate both acoustic and elastic wave transmission. Abd basically one of the papers, they consider the two-dimensional metamaterial that was actually, that was composed of two different materials, they're called phases. And then basically they propose some, what is called topology, basically design of this metamaterial that in the end was able to do the job. So in the end they obtained not only the dispersion curves to get some insight into the behavior of this metamaterial, but they also get the actual forced response of a finite system composed of this metamaterial. And then basically we demonstrate that yes, it's all good. We can actually attenuate both acoustic and elastic waves. And this is cool, actually. 

Maybe another example is another paper in which we tried to use another cool phenomenon, which is actually called acoustic black hole phenomenon. Basically, the way…  there is like acoustic black hole, it's a thing that can trap all vibrations inside. So basically, if you have, let's say, a wall with this acoustic black hole and you excite the wall, then all the vibrational energy will go into this acoustic black hole and then you can put some damping material so that essentially will dissipate all vibrational energy. And basically what they have done, they have tried to make it like periodic, like a wall which has periodic acoustic black holes, and showed that yes, it can actually work. So this was also very interesting, I think.

Luke Bennetts (19:55)

I’d like to comment on some concept I'm very excited about. It’s called “rainbow trapping.” And now this addresses a really fundamental problem in acoustics, across all wave science, really, which is that in many applications, you want to have a broadband response. That is, you want to be able to control a broad range of wave frequencies. So you might want to do that to filter out broad ranges of frequencies for noise suppression, for example, or you might be interested in harvesting the energy of acoustic waves across a broad range of frequencies.

The thing is, most new concepts are narrow-band, and this applies to periodic media. So with periodic media, essentially, we can do anything that we like to a wave, but over a narrow range of frequencies. The concept of rainbow trapping generalizes what we're able to do with periodic media and gives us the ability to control broadband ranges of frequencies. So the concept is really quite simple. It takes us from the periodic medium to a near-periodic medium. And it does so by gradually varying the properties of the periodic medium. And in doing so, we are able to localize the wave energy to specific regions of space. Now, up to the point that we had the special issue, these rainbow trapping concepts have really only been applied in one dimension. That is to say that the grading of the periodic medium have been done in one direction only. Now there's a paper that appears in the special issue by Ellouzi et al., and it generalizes the concepts to two dimensions, and it does that by taking a disc with grooves in it, and they vary the grooves in an annular fashion with radial distance from the center, and they show that by doing that they are able to create this rainbow trapping effect, a broadband response, where they are able to localize the energy of some incoming waves at selected annular regions in the disk.

ASA Publications (22:42)

Well, that's so cool. 

Luke Bennetts (22:43)

Very cool. Yeah.

ASA Publications (22:47)

It sounds very useful. So in your introduction, you mentioned that f”urther research progress demands new and improved methods for analysis of periodic and locally resonant vibroacoustic systems.” Were there any particular developments of note that appeared in this special issue?

Luke Bennetts (23:00)

Yeah, I mentioned direct numerical simulations earlier, and there is a paper by Ganesh and Hawkins that appears in the special issue in which they consider two-dimensional problems involving vast numbers of what we call discrete, penetrable scatterers, which are embedded in the background acoustic medium. So this could be bubbles in an acoustic fluid, for instance. Ganesh and Hawkins, they developed a three-stage algorithm, and it cleverly combines different existing methods, and it allowed them to run simulations involving up to hundreds of thousands of scatterers, which is really a new benchmark for the field.

Vladislav Sorokin (23:51)

Yes, so maybe I can also briefly mention something regarding this nonlinear behavior and so on. Because basically, the truth is that if we talk about actually modeling something and the methods, then of course, unfortunately, okay, we said that yes, all systems around us are actually nonlinear, and linear is just approximation. But the problem is that modeling nonlinear systems is very complicated. It's actually, computationally, it's very difficult and so on. So basically what people have done, and several papers on the special issue what that have done, they have proposed some relatively simple models to describe the behavior of these nonlinear periodic and near-periodic systems. And actually they showed that, for example, let’s say, a very simple mass-spring model can be used to study the response of these kind of acoustic metamaterials and elastic metamaterials. And then using these models, you can actually design these acoustic and elastic metamaterials, so just periodic structures, so that you get the behavior that you want to get. So this is actually also very nice in terms of methods. Because modeling these nonlinear phenomena and nonlinear structures is very complicated, so we need some more simple kind of models, and some were proposed in this special issue. And then using these models, we can actually design the structures as we wish, utilize this nonlinear behavior and nonlinear phenomena to achieve what we want—let’s say reduced vibrations in a certain frequency range.

ASA Publications (25:17)

Okay, okay, totally. Where do you see this field of research going in the future?

Vladislav Sorokin (25:21)

Yeah, so maybe I can just very quickly give a few thoughts. So basically, not sure whether I should, say, start with this, but basically, of course, now it's a hot topic, all these things related to neural networks and artificial intelligence. So of course, like a lot of people already and definitely in the future, we will be trying to use neural networks and artificial intelligence to basically model the dynamic behavior of these kind of structures, especially if we talk about complicated and complex structures, maybe some nonlinear resonators inside or maybe some nonlinear phenomena that we want to utilize for attenuating vibrations in the structures or acoustic waves. So definitely neural networks and artificial intelligence will be used. I'm not sure that I'm a big fan of it myself, but let's call it like this, but two of my PhD students, they’re actually working on this currently, and it's definitely a big field. 

And of course, as I mentioned at the start, regarding the challenges, trying to design the structure, not only for vibration attenuation or sound attenuation, but also for some other purposes, let's say to be strong, to be able to support some weight or whatever, it's another important thing. So basically like trying to design a structure for multipurposes for many, many different purposes. This is definitely another future target and another future direction for this field. Also potentially trying, okay, we'll talk about, and maybe for JASA, we are talking about acoustic waves and elastic waves. But let's say if we talk about something that I again mentioned at the start. I was talking about buildings. In buildings, we care not only about sound isolation, vibration isolation, but also thermal isolation. So obvious kind of extension would be to try to consider, okay, can we design a wall or a window or whatever, that can basically reduce the vibrations and sound transmission, but also reduce the thermal transmission. So basically increase thermal insulation of these walls. So multitasking, multipurposing of these kind of periodic structures is, I think is the future.

ASA Publications (27:29)

Ooh, yeah, yeah. Well, I have to say, this is not an area of research that I knew much about… Although it seems like the concepts have relevance in a lot of areas, and as you've been talking about it, I do feel like I'm a little familiar with some of these ideas. To our listeners, if you found this discussion interesting, there are a bunch of articles in this special issue. So the collection page is shared in the show notes. And Vladislav and Luke, thank you again for taking the time to speak with me and have a great day.

Vladislav Sorokin (27:55)

Thank you so much. It was a pleasure.

Luke Bennetts (27:55)

Thank you, Kat. Pleasure.

 [KS1]This was not actually transcribed by the AI, so this is what I got. I may have missed a couple words, though. I’ll need Vladislav to confirm.