COMSOL Forums: beam vibration by a shaker

Re: beam vibration by a shaker

Wed, 13 Mar 2013 15:01:40 +0000

Hi

in all generality the "thumb" rules:

2*pi*freq = sqrt(k_stiff / mass) = sqrt(k_rot / Inertia),

and for a beam under gravity load, for the first mode gies about the max deflection

2*pi*freq = sqrt(g_const / Dz_deflection)

I a rather good approximation. So if you add a mas via your attachment to a shaker, it is clesr that you will influence the mode to. That is why one often attach the FULL system to the shaker, or we shake the base and not the directly part of structure itself under test. At least not with any mass of significance w.r.t. the object mass

--
Good luck
Ivar

Re: beam vibration by a shaker

Wed, 13 Mar 2013 09:43:20 +0000

Hello all,

This is a very interesting discussion so far and I am trying to make a vibration model along similar lines.

I work with a similar excitation, but with a metal beam fixed at both ends (with compliant mounts) and a shaker applies vibration at the center of the beam with a static preload to hold it in place. Experimentally, I noticed that the resonances observed are of the entire system (shaker + beam) and not the beam alone. The frequencies I use are in several kilohertz where the shaker dimensions do matter.

So, in most of the discussions above where the shaker was attached to the beam, isn't it an issue to consider? Is there a way to include this non-linearity in the comsol model?

Re: beam vibration by a shaker

Thu, 13 Dec 2012 22:59:43 +0000

Hmm,may I know why? Because from what I understand, Adding tip mass to the structure increases the strain,which eventually increases the deformation. Body load is assigned on the "large" mass attached to the beam and added mass is assigned at the other end of the beam,together with boudary load

Thanks

Re: beam vibration by a shaker

Thu, 13 Dec 2012 22:03:32 +0000

Ok, one more thing to check. Conceptually, if you apply a certain body load and you change the structure by adding mass the deformations should in general be lower and also the voltage.

Re: beam vibration by a shaker

Thu, 13 Dec 2012 10:18:11 +0000

Hi,

thanks for the reply. in the frequency analysis, I've specified a range of frequency, the eigenfrequency lies within that range.

Thanks.

Re: beam vibration by a shaker

Thu, 13 Dec 2012 09:45:46 +0000

The added mass reduces the natural frequency so the voltage may be dropping because the frequency you specified in the frequency domain analysis is no longer close to the beam’s natural frequency.

Re: beam vibration by a shaker

Wed, 12 Dec 2012 11:33:38 +0000

Hi

if you add an "added mass then you must also add a boundary force, as the body load applies ONLY forces to the DOMAIN, not to the added mass that is a separate "fictuous " entitiy do not forget that ;)

--
Good luck
Ivar

Re: beam vibration by a shaker

Wed, 12 Dec 2012 08:32:33 +0000

Hi,

I've applied body load to represent base excitation, and assigned "added mass" BC at the free end of the cantilever ( to represent tip mass). Howver, it shows that the voltage output at the eigenfreq keeps decreasing as the "added mass" increases. I believe by adding the tip mass, the voltage will be increased.

Thanks

Re: beam vibration by a shaker

Mon, 19 Nov 2012 12:19:40 +0000

Hi
Check the doc about frequency domain solving, and look at the equations, you will understand, it solves far quicker in constant regime sinus type excitation

--
Good luck
Ivar

Re: beam vibration by a shaker

Sun, 18 Nov 2012 23:56:40 +0000

Hi

In any case you should not talk about comparing eigenfrequencies, as these do not depend on external forces, only on the material, geometry shapes

And amplitudes depends on damping, which is a delicate issue, often ignored, but essential for any amplitude evaluation, you must add thedamping as specific material property nodes, the only thing is to know what to use as values !

Finally use rather the harmonic development and not the time series, as ou have then all the initial transient behaviour to consider

--
Good luck
Ivar

Hi Ivar,

Thank you for the fast response.

Comparison of eigenfrequencies is regards to existing lab results and, as you say, of course not dependent on external driving.

Obviously you are (also) right about damping - I only consider real physical systems why damping is larger than zero.
I have already obtained experimental damping coefficients for the system at hand - I will look at the implementation of damping coefficients in Comsol as you suggested soon...

Furthermore, I do not understand what you mean by "use rather the harmonic development and not the time series". I have already developed analytical approximate expressions for the steady-state response using perturbation analysis. For these, and relating numerical solution given by a Runge-Kutta solver, I have an estimate for the time period after which the transients are negligible. Thus, I can simulate the system with transients - but as for now, I do not know how to impliment/be able to analyse a time series in Comsol?

Most importantly, I would like you to elaborate on "use rather the harmonic development and not the time series" if possible - and preferably in relation to Comsol.

Kind regards,
Stefan

Re: beam vibration by a shaker

Sun, 18 Nov 2012 18:24:42 +0000

Re: beam vibration by a shaker

Sun, 18 Nov 2012 17:07:33 +0000

Hi everybody.

I have with great interest read this thread.

I would like to simulate the steady-state response of a vertically base-excited cantilever beam.

The driving could e.g. be A*cos(Omega*tau) where A is the amplitude, Omega is the frequency, and tau is time.

(no PZT or multilayer or anything "fancy" - just an isotropic beam of steel).

I can see from this thread, that several challenges occur when modeling a vertically base-excited cantilever beam. I am completely new to Comsol, and have no experience with it what so ever. It has, in this thread, been proposed to add a comparably large rigid body mass. It seems inappropiate in my case - I would definitely prefer only to consider a cantilever which is driven by an external load (i.e. shaker) and that the resulting values (eigenfrequencies, absolute amplitude etc.) are directly comparable with experimental results.

The modeling itself should, I guess, be a very simple task for an experienced user and require a minimum of time. Could anybody please provide my with a working example?

It will of course require subsequent work from me, but I need to start from "steady ground" :)

Help is highly appreciated!

Kind regards,
Stefan

Re: beam vibration by a shaker

Fri, 03 Aug 2012 20:33:43 +0000

Hi

Thanks a lot. you've been really helpful

Re: beam vibration by a shaker

Fri, 03 Aug 2012 12:41:37 +0000

Hi

indeed fixing your block and applying a body load as an acceleration is o good way, in a frequency domain sweep you can get the frequency response too of your system. If you leave a floating potential its as if you have an open circuit, you voltage will be given by the charge build-up and the PZT beam capacity. If you add a CIR physics with an electric impedance of some kind, i.e. representing the entry impedance of your system, then you will see the response and voltage build up of your device in loaded conditions. One way to optimise the energy transfer is to play with the bandpass of your load impedance and the response of the beam

--
Good luck
Ivar

Re: beam vibration by a shaker

Fri, 03 Aug 2012 09:37:45 +0000

Hi

I think I'd better stick with your initial suggestion that is to apply body load. I use steel as the large mass due to its stiffness and aluminum beam. I apply fixed constraint to the faces of the mass except for the one that is attached to the beam.

I'm currently using one physics only that is piezoelectric device. I apply floating potential to the top of the PZT and ground at the bottom of the layer and this is how I extract the voltage generated Do I need to add another physics(i.e electrical circuit) for the impedance?

Thanks

Re: beam vibration by a shaker

Thu, 02 Aug 2012 22:29:46 +0000

Hi

from you image, you should not use fixed and acceleration simulatneously, but you must use two roller conditions on two opposite sides of your sqare mass at right angle to the acceleration direction. Be sure you large mass is "large" compared to the beam, and then get the correct estimate of the true load on the beam

100V is not necessarily that much, you can get a sparck (>1kV) easily with a stressed PZT, but this also depends strongly on the impedance you connect up on your PZT

--
Good luck
Ivar

Re: beam vibration by a shaker

Wed, 01 Aug 2012 08:43:23 +0000

However, by applying prescribed acceleration, the value of voltage is hundreds volts, which is I think is not correct

Re: beam vibration by a shaker

Wed, 01 Aug 2012 08:04:45 +0000

Hi Ivar,

From the attached figure, does my model represent a beam subjected to base excitation? (the beam is attached to a big rigid mass). I've applied body load before to the rigid mass but the output voltage generated is maximum at the fifth eigenfreq. If I changed it to prescribed acceleration and applied it on top of the rigid mass, I can see that the maximum value of voltage is at the first eigenfreq (which is theoretically correct according to my understanding)

thanks

Re: beam vibration by a shaker

Sun, 22 Jul 2012 11:06:18 +0000

Hi

indeed if you apply a prscribed acceleration, your object CANNOT be fixed these are antogonists. What you can do is to apply a body load of the type "material.rho*my_acceleration" and keep the fixed section "fixed".

I'm neither not fully happy as today I have not found a clean way to apply a shaker type PSD on a model, in a simple way. there are several threads about this on the Forum, try a search

--
Good luck
Ivar

Re: beam vibration by a shaker

Sun, 22 Jul 2012 04:44:58 +0000

Hi,
I've tried applying 'prescribed acceleration' to the fixed end of the beam and managed to get the 'voltage vs freq' plot. However, when i do analysis of the beam's deformation at every single frequency, I've found out that the fixed end of the beam moves. It stays fixed only at the natural frequencies. I believe this might be due to 'fixed constraint' is overridden by 'prescribed acceleration'. If 'fixed constraint' overrides 'prescribed acceleration', there will be no output voltage generated.

If I changed the 'prescribed acceleration' to 'body load' of "pzd.rho*acceleration", the fixed end stays fixed throughout the simulation. However, I noticed that the list of eigenfrequencies changed and I'm not sure why.

If I want to plot the voltage distribution at every point accross the length of the beam, should i choose "electric field-Z component"?

Thanks