# Discussion Forum

## Problems generating lamb waves in an Aluminum plate

 Topics: Structural Mechanics, MEMS, AC/DC Module, 4.0a
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Rohan Repale

November 22, 2011 12:19pm UTC

Problems generating lamb waves in an Aluminum plate

Hi,
I am trying to generate lamb waves in an Aluminum Plate using a Piezoelectric actuator placed in the center of the plate.
I am pretty sure that the physics involved are solid mechanics and Electrostatics (to apply electric potential to the PZT).
So according to theory, there should be waves generated in the plate because of the electric potential applied to the PZT, which is attached to the Aluminum plate. But I am not getting it, I am unable to couple the two physics. Can someone help !
Also, what BC should be applied to make sure that the deformations in the PZT take effect on the plate.
If it helps, I have attached the file, please take a look

Ivar Kjelberg

November 22, 2011 12:47pm UTC in response to Rohan Repale

Re: Problems generating lamb waves in an Aluminum plate

Hi

I do not have 4.0 and I'm not sure my 4.2a is reading correctly the original model, but I have a few comments:

Solid:
your PZT material isn't really linear isotropic, you must add a 2nd node of linear Elastic material and anisotropic for the PZT material (but this is not enough, see lower)
your device is floating in space, no fixed nodes, you could fix at least one point ans apply a symmetry to the left boundary or "fixed" (careful this would sort your modes to symmetric ones, one need to rerun with antisymmetry BC's, a 2nd time to catch all)

ES:
there is no need to include the full model in ES the aluminium can be dropped, no ?

You are in 2D so you are modelling "per meter depth", be aware (nothing wrong with that)

The main point is: there is no PZT link effects (ES V => PZT forces => solid strain => ES V changes) in solid+ ES you have to write them out yourself
You should rather use PZD physics to have this made precooked by COMSOL (not sure which modules adds PZD though, MEMS certainly, check the COMSOL matrix)

--
Good luck
Ivar

Rohan Repale

November 22, 2011 1:47pm UTC in response to Ivar Kjelberg

Re: Problems generating lamb waves in an Aluminum plate

Ok,

So I added another linear elastic material model and assigned it to the solid, making and isotropic and the default one automatically got assigned to PZT, and I made it anisotropic

Secondly I added, fixed BC to the left wall of solid and PZT (I am not sure about PZT ,correct me if I am wrong)

Yeah about running the full model in ES, I know, I forgot to remove the solid, I did that

I am not really sure wht u meant by per meter depth, my geometry is in mm

So are you suggesting that for PZT link effects, I should use 'Piezoelectric devices' module?

Thanks,
Rohan

November 22, 2011 2:40pm UTC in response to Rohan Repale

Re: Problems generating lamb waves in an Aluminum plate

If this is the cross section, how is it possible to identify lamb modes?

Rohan Repale

November 22, 2011 2:52pm UTC in response to Niranjan Thontadarya

Re: Problems generating lamb waves in an Aluminum plate

Hi Niranjan,
actually ,as of now, I am more concerned with generating lamb waves, rather than the modes. I can obviously switch to 3D once I get the hang of what I am doing
As of now, I am applying, electric potential and computing for displacement (solid.disp) . let me know, if this the right approach towards it

November 23, 2011 8:08am UTC in response to Rohan Repale

Re: Problems generating lamb waves in an Aluminum plate

Is this something like what you are trying to get?? Thoseare antisymmetrical lamb modes if im right.

www.iaeng.org/publication/WCECS2011/WCECS2011_pp166-171.pdf

Guessing from that, lamb modes are possible in comsol...

Rohan Repale

November 23, 2011 1:16pm UTC in response to Niranjan Thontadarya

Re: Problems generating lamb waves in an Aluminum plate

Yes It is possible, but I am not sure how, and which mode, I should be gettting by my approach.

Rohan Repale

November 23, 2011 1:19pm UTC in response to Ivar Kjelberg

Re: Problems generating lamb waves in an Aluminum plate

HI Ivar,
According to your suggestion, I switched to 'Electromechanics' physics module which is added new to the 4.2a version and redesigned the model considering all the BCs as suggested. Hopefully there were no errors, Can you take a look and see If I am going right?
Thanks a lot

Rohan Repale

November 23, 2011 1:21pm UTC in response to Ivar Kjelberg

Re: Problems generating lamb waves in an Aluminum plate

HI Ivar,
According to your suggestion, I switched to Electromechanics physics module which is added new to the 4.2a version and redesigned the model considering all the BCs as suggested. Hopefully there were no errors, Can you take a look and see If I am going right?
Also can you tell me how to plot 1D plot from the surface plot, thank you.

Glenston Miranda

January 10, 2012 12:35pm UTC in response to Ivar Kjelberg

Re: Problems generating lamb waves in an Aluminum plate

Hi

I do not have 4.0 and I'm not sure my 4.2a is reading correctly the original model, but I have a few comments:

Solid:
your PZT material isn't really linear isotropic, you must add a 2nd node of linear Elastic material and anisotropic for the PZT material (but this is not enough, see lower)
your device is floating in space, no fixed nodes, you could fix at least one point ans apply a symmetry to the left boundary or "fixed" (careful this would sort your modes to symmetric ones, one need to rerun with antisymmetry BC's, a 2nd time to catch all)

ES:
there is no need to include the full model in ES the aluminium can be dropped, no ?

You are in 2D so you are modelling "per meter depth", be aware (nothing wrong with that)

The main point is: there is no PZT link effects (ES V => PZT forces => solid strain => ES V changes) in solid+ ES you have to write them out yourself
You should rather use PZD physics to have this made precooked by COMSOL (not sure which modules adds PZD though, MEMS certainly, check the COMSOL matrix)

--
Good luck
Ivar

Hi Ivar,

Im trying to do that same thing a little different.
I'm exciting a point source using a single sine pulse and thereafter checking for
the lamb waves in the steel surface.

Am i applying the right boundary conditions.
Is my physics right?
Acoustic Structure should be fine i'm guessing.

I've attached a mph file for your further review.
Could you please have a look at it as i have been struggling with it for weeks now!!

Thanks a lot for your time and effort!

Regards
Glenston

Ivar Kjelberg

January 10, 2012 1:17pm UTC in response to Glenston Miranda

Re: Problems generating lamb waves in an Aluminum plate

Hi

I'm not equipped with an acoustic module so I cannot open your file.
In general: using point constraints is rather nasty (stress concentration effects) but if you are not interested in the stress, and you can ignore what is happening in the vicinity of your point load, then the rest should be rather correct.

You have the choice:i.e. use a harmonic solver (harmonic development of the time based equations) that is much simpler (computational wise) than a sinus time excitation.

The best is to check the physics equations of COMSOL and that of the Lamb wave theory and see how they match, this to help you select the correct physics

--
Good luck
Ivar

Rohan Repale

January 10, 2012 1:35pm UTC in response to Glenston Miranda

Re: Problems generating lamb waves in an Aluminum plate

Hi Glenston,
I tried opening your model, but I couldn't, So I will simply tell you, how I was able to generate lamb waves using point-force model.

I used Solid Mechanics module on a 2D cross-sectional aluminum plate, with small thickness, and considerably large width.

The only boundary condition, I applied is the edge fixed constraint BC, on the edge opposite to the application of the force (that is opposite to the direction of wave propagation)

The mesh size is considerably small (smaller the better) with minimum element size = 1/10th of lambda.

The study used is time-dependent, with period = 1/freq and time step = 1/10th of period

Results must be checked for solid.mises (Von-Mises Stress)
Simulated result should give two modes (S0 and A0) where S0 precedes A0 in space.
Note: S0 will not be as visible as A0, you will have to play with color range

For further information, please refer to the following paper:
www.ece.cmu.edu/%7Edwg/research/Waves25rev.pdf

Best,
Rohan

Glenston Miranda

January 18, 2012 10:27pm UTC in response to Rohan Repale

Re: Problems generating lamb waves in an Aluminum plate

Hi Glenston,
I tried opening your model, but I couldn't, So I will simply tell you, how I was able to generate lamb waves using point-force model.

I used Solid Mechanics module on a 2D cross-sectional aluminum plate, with small thickness, and considerably large width.

The only boundary condition, I applied is the edge fixed constraint BC, on the edge opposite to the application of the force (that is opposite to the direction of wave propagation)

The mesh size is considerably small (smaller the better) with minimum element size = 1/10th of lambda.

The study used is time-dependent, with period = 1/freq and time step = 1/10th of period

Results must be checked for solid.mises (Von-Mises Stress)
Simulated result should give two modes (S0 and A0) where S0 precedes A0 in space.
Note: S0 will not be as visible as A0, you will have to play with color range

For further information, please refer to the following paper:
www.ece.cmu.edu/%7Edwg/research/Waves25rev.pdf

Best,
Rohan

Hi Rohan,

I went through the paper that you listed in detail and then tried modeling it exactly according to the
specifications in the paper. The metal i have taken is Aluminium with specs that of the paper.
E=70GPa, den=2.7gm/cm^3, v=0.33, thickness=1.59mm and applied force 3.2mm from the y axis.

I've used Structural Mechanics as the Physics and time dependent study.
A point load is used to give the point force as F*sin(wt)*(sin(wt/10))^2 *(t<10*pi/w).
A fixed constraint point as a BC to the origin. The remaining geometry i have used free boundary condition.

I ran this for 100kHz frequency.

My question is it possible to give a frequency sweep in a time dependent study?
If no, is how can u simulate the graphs for the x component of velocity and y component of velocity as a function of frequency?

Ive not quite got the simulations results that 100kHz should be showing compared to the what the paper shows.
Ive attached the model that ive created in 4.2.
Also attached is the pic of the geometry that i have created.
I would be very helpful if you could upload the model that u created.

Thanks a lot for your time and effort.

Regards
Glenston

Glenston Miranda

January 18, 2012 10:31pm UTC in response to Ivar Kjelberg

Re: Problems generating lamb waves in an Aluminum plate

Hi Ivar,

Is it possible to run a frequency sweep using structural mechanics physics and time dependent study?

Regards
Glenston

Ivar Kjelberg

January 19, 2012 7:20am UTC in response to Glenston Miranda

Re: Problems generating lamb waves in an Aluminum plate

Hi

take a look at the main "equations" of your physics when you choose a time solver and when you have a frequency solver (and compare to a steady state solver).

Time solver adds the time derivatives to the equations, (compared to a stationary case)
The frequency sweep solvers replaces the time derivatives by a "omega" (and adds a phase term on the sources)
This represents a harmonic development of the solution.

Consider your FEM with the parallels you probably know better: as when you need to record an analogue signal with a digital DAC: the Nyquist criteria tells you that you need a minimum number of samples (>2) to get a given frequency through your analysis, this corresponds to the FEM meshing and meshing density w.r.t. the dependent variables, and often the gradients of the dependent variables that need to be solved

In the same way when you do digital data analysis like Fourier transforms you work in the time domain or in the frequency domain and you use the "s" parameters to solve your filtering equations or feedback loop calculation, with harmonic developments. This is a closes parallel I can give you for time solving, and frequency sweep harmonic solving (take car it's "analogies" one cannot apply everything 1:1 ;)

So for me mixing both solvers for a simple physics like that seems strange and not really physical

--
Good luck
Ivar

Glenston Miranda

January 25, 2012 8:37pm UTC in response to Ivar Kjelberg

Re: Problems generating lamb waves in an Aluminum plate

Hi

take a look at the main "equations" of your physics when you choose a time solver and when you have a frequency solver (and compare to a steady state solver).

Time solver adds the time derivatives to the equations, (compared to a stationary case)
The frequency sweep solvers replaces the time derivatives by a "omega" (and adds a phase term on the sources)
This represents a harmonic development of the solution.

Consider your FEM with the parallels you probably know better: as when you need to record an analogue signal with a digital DAC: the Nyquist criteria tells you that you need a minimum number of samples (>2) to get a given frequency through your analysis, this corresponds to the FEM meshing and meshing density w.r.t. the dependent variables, and often the gradients of the dependent variables that need to be solved

In the same way when you do digital data analysis like Fourier transforms you work in the time domain or in the frequency domain and you use the "s" parameters to solve your filtering equations or feedback loop calculation, with harmonic developments. This is a closes parallel I can give you for time solving, and frequency sweep harmonic solving (take car it's "analogies" one cannot apply everything 1:1 ;)

So for me mixing both solvers for a simple physics like that seems strange and not really physical

--
Good luck
Ivar

Hi Ivar,

This is very elementary but it still is bothering me.
I used a transient physics and time dependent study.
I gave a sine pulse as the input of the form sin(2*pi*1000000[Hz]*t)*(t<=0.000001).
This works fine for me.

Now i want to use another physics which is not transient so therefore im in the frequency domain right?
My first question is how can i give a pulse as an input ?
In the transient case t was my variable ie time, now i dont know how i can make it work?
By giving the same input as above i dont get the same result as in the transient case.

My second question is a more general question could seem very elementary but have to ask.
If i use frequency domain as a study with giving different frequencies in the frequency sweep.
Are these frequency values going to be used as the frequency of the sine excitation at the application of the excitation with user defined amplitude? Or are the results checked for the steady state response to the frequency values .

I don know if ive made it completely clear.
I'm totally confused.
Any kind of reply will help me a lot !

Thanks a lot for your time and effort!!

Regards
Glenston

Ivar Kjelberg

January 25, 2012 9:02pm UTC in response to Glenston Miranda

Re: Problems generating lamb waves in an Aluminum plate

Hi

you are right that first of all you cannot give a time pulse in harmonic sweep solver, it's a constant driving sinus excitation of a given frequency and of a to be defined amplitude and phase (the latter in option if required)

some physics do not have the time derived equation written up, these cannot be solved in "time". One way to better understand what is happening, is to look at the equations COMSOL uses when you switch the different solver, set up a simple physics model and add a stationary, time and frequency harmonic solver, then look at the physics equation while you switch the solver tab, in stationary there is no d/dt^2 present (we are in a quasi static equation mode, with time dependent they appear, and in harmonic they are replaced by the "omega^2" (it's similar to the Fourier like "s" or "z" functions in data analysis)

Now if you mix some ACDC and mechanical physics you might have a time dependent for one and none for the other, the last version of COMSOL have some new frequency - transient and frequency stationary solver set up, these evaluate a period (no pulse variation) in temporal mode and then apply the rms values to the time decay or transient analysis. Mostly ACDC EM waves and physics are "instantaneous" w.r.t. mechanical vibrations frequencies, or thermal diffusion, (not always fully true in the MEMS dimensions !) so as they have completely different time scales, the ACDC effect is a mean RMS response applied to the slower mechanics or HT.

But one can always imagine a case where you do not find (yet) the full combination desired in the Comsol solvers, in these cases one must decide for the closes, and apply some "good engineering practice" to your results

--
Good luck
Ivar

Ivar Kjelberg

January 26, 2012 2:59pm UTC in response to Ivar Kjelberg

Re: Problems generating lamb waves in an Aluminum plate

Hi

Two important things to make your model work:

as I hadn't open your latest models (I'm not always by my WS, often on travel or in meetings) I hadn't noticed

1) your w for the 2*pi*f is already defined by COMSOL, for the dependent variable 3rd dimension "w"
2) more important, you left the time stepping in "free" mode, you should use "strict" or "intermediate" then you will get far more interesting results ;)

Note the difference in time stepping, you see it in your log file: there are several " - out" without any steps in between, this is not compatible with a sinusoidal BC entry, te default free is for time decaying processes such as diffusion

Rule: if any BC is peridic & you are in time stepping => always use strict or intermediate (never "free")

--
Good luck
Ivar

Glenston Miranda

January 26, 2012 10:03pm UTC in response to Ivar Kjelberg

Re: Problems generating lamb waves in an Aluminum plate

Hi

Two important things to make your model work:

as I hadn't open your latest models (I'm not always by my WS, often on travel or in meetings) I hadn't noticed

1) your w for the 2*pi*f is already defined by COMSOL, for the dependent variable 3rd dimension "w"
2) more important, you left the time stepping in "free" mode, you should use "strict" or "intermediate" then you will get far more interesting results ;)

Note the difference in time stepping, you see it in your log file: there are several " - out" without any steps in between, this is not compatible with a sinusoidal BC entry, te default free is for time decaying processes such as diffusion

Rule: if any BC is peridic & you are in time stepping => always use strict or intermediate (never "free")

--
Good luck
Ivar

Hi Ivar,

I din not quite understand your first suggestion. Could you please elaborate

I have a simple question whats the significance of time stepping and time steps set in the
time edit field.

How does the internal time step have a role to play in the formation of a solution.
Wont manual time stepping with a very small value suffice.?

Thanks a lot for your time and effort.

Regards
Glenston

Glenston Miranda

January 27, 2012 7:45am UTC in response to Glenston Miranda

Re: Problems generating lamb waves in an Aluminum plate

Hi Ivar,

When i wanted to mention the time steps.
I used it referring to the article in the knowledge base

www.comsol.com/support/knowledgebase/1118/
This uses a manual time stepping and is based on the CFL criteria.
Which is right?

Should i be getting a -out for each and every step?
Does that mean my output is right?

Regard
Glenston

Ivar Kjelberg

January 27, 2012 7:59am UTC in response to Glenston Miranda

Re: Problems generating lamb waves in an Aluminum plate

Hi

the first is related to the variable name, you define a parameter "w" but COMSOL uses "w" for the thrd space displacement (dependent variable). You may argue that you are in 2D, but COMSOL works always in 3D so it's dragging internally all variables, also for 3D, even if they are mostly set to "0" (but I do not believe its solving or uneccesary variables)

Try to avoid using COMSOL internal names for your own use, add a letter or a "_" or whatever

Read carefully the doc on the solvers, it's scattered but you have a lot in the user guide and more in the reference guide.

When you define a time step range, these are the values COMSOL will extract from the time stepping it decides (in free mode), but COMSOL might decide by its own to do two steps and extract your values by interpolation in between the two steps. This is mostly OK for diffusion models or critical damped models, but for any periodical signal it's a catastrophy, COMSOL might fully overlook the oscillatory behaviour of a BC condition. therefore you should use "intermediate" or "strict", there Comsol ensure it's taking at least one step inbetween your define time steps, or strict when it takes at least a step AT your defined value (you see that by the - out" log messages).

Depending on the solver BFD, gen-alpha ... COMSOL has different ways to estimate what is reasonably the "next step" via the Jacobian or other resolution parameter (i.e. Newton method ...) This chapter is rather lengthy to explain, and I'm not that comfortable with it, as there are many buttons to tweak and I have not had time to go systematically through them all ;)

COMSOL has a rather good course on solvers, but even a full day is by far not enough to go through all the buttons

--
Good luck
Ivar

Glenston Miranda

January 27, 2012 8:10am UTC in response to Ivar Kjelberg

Re: Problems generating lamb waves in an Aluminum plate

Hi

This will definitely help me a lot.

Thanks a lot again.

Regards
Glenston

Ivar Kjelberg

January 27, 2012 8:27am UTC in response to Glenston Miranda

Re: Problems generating lamb waves in an Aluminum plate

Hi

that KB article is related first of all to RF where the meshing is probably the most delicate, because of the short wavelength of the EM waves (particularly in dense medium.

But the principle remains valid for all FEM (just as for digital signal sampling where most engineers accepted this now, without even thinking),
i,.e. in HT its the heat diffusivity alpha=k/rho/Cp that relates to the CFL number (mesh size time step physical property link), in CFD among others the visosity and Reynolds number for turbulence aspects. In structural p waves its the sqt(E/rho)=c speed of sound that links in material propewrties to the wavelength, hence the mesh density to resolve these ...

--
Good luck
Ivar

Wael Alharbi

March 9, 2012 9:14am UTC in response to Glenston Miranda

Re: Problems generating lamb waves in an Aluminum plate

Hi Glenston

Hope everything went fine with you.

I am working on the same problem, did you find something helpful ?!

Wael

Chengtao Mao

January 3, 2013 5:12pm UTC in response to Rohan Repale

Re: Problems generating lamb waves in an Aluminum plate

Rohan Repale,I just find I have the same problem as you ,could you share your model with me about this issue ,I am exceedly need your help.because I want to do PZT transducer to excite lamb in 3D model.what's more,I need to control the mode of lamb wave.could you help me ?you can send me related materials as more as possible.I am really appreciate your help.you can contact me via maochengtao@shu.edu.cn

God bless you! Thank you!

Elangovan Yedesh Kumar

August 18, 2017 3:25pm UTC in response to Chengtao Mao

Re: Problems generating lamb waves in an Aluminum plate

Hi all, will anyone help me how to perform lamb wave propagation in a isotropic plate in COMSOL? I am a new student learning COMSOL. ? Could any one help me with step by step procedure or any tutorial ?