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the free vibration of the cantilever
Posted 2 apr 2013, 23:15 GMT-4 Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers, Structural Mechanics 12 Replies
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The initial displacement D=1.05mm, is placed on the end of the cantilever beam, to solve the velocity response of the beam end. First, I select space dimension 2D, and add physics Beam, but the simulation result is wrong, when I select space dimension 2D, and add physics Solid Mechanics (solid) , the simulation result also is wrong, the velocity curve is increasing against time. Now I select space dimension 3D, and add physics Beam, but the simulation result is not the same to the experimental result and analytical result. I am confused. Hope some one give me a advice, thank you! Details see attachment.
Attachments:
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first of all I assume that your beam has no (negligible) damping (which could give quite some velocity differences with experimentation).
Then how do you enforce the displacement and then release for the time series analysis for the oscillations ?
if you use a first stationary model and then a time series using the previous case as initial conditions, ensure that the initial conditions are read from the previous statioanry solver case (normally the case when COMSOl generates sa fresh two solver study).
Then for you time series, be sure you have enough time points to resolve your oscillations (>3 steps per periode and you can do an eigenfrequency analysis to get the first frequency quickly) Then go deep into the solver sub-nodes and set the time stepping to "intermediate or strict" and NOT to automatic, to avoid that the internal solver stepping might skip over your rapid oscillation and giving you aliasing
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Good luck
Ivar
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First of all thank you for your enthusiasm and quick reply. You are always very enthusiastic to help others in the discussion forum, to my great admiration. I am new to the COMSOL. In my attachment, I give detail steps to this simulation. First, I select the “stationary” study, and right click “solid mechanics(solid)” select “Initial Values 2” in the “displacement field:” type 1.05mm(Y), then computed and select “time dependent” study. In the study2, “values of dependent variables” I select “Initial values of variables solved for” and in the “Method:” select ‘solution’, in the “Study:” select ‘study1’ then computed.
Your advices are: First, I select “Eigenfrequency ” study, to do an eigenfrequency analysis to get the first frequency then I Select “time dependent” study, but the velocity curve trend is increasing with the time, not attenuation . Maybe my understanding of this sentence is not quite correct “Then go deep into the solver sub-nodes”. Set the time stepping to "intermediate” is very good. Please give me some details such as my attachment, I know that doing so will delay your precious time. Hope to get your reply!
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sorry I was a bit too quick, my intention with the eigenfrequency analysis was to get the value for the fist free mode, this gives you the maximum time steps that should be < 1/(3*f0) where f0 is the first mode. In this way you resolve at least the first mode swinging for your time series (learn to know your model natural behaviour before solving it).
Indeed then as a 2nd study you add TWO solvers, solver1 steady state and solver2 time series with a range() adapted to the value you got from the eigenfrequency study.
For the steady state you either set a boundary prescribed displacement of whatever displacement in mm for your beam tip, and then select in the time series to start from the solver1 - stationary case (and do not forget to disable for this solver the prescribed displacement.
Or you might use a force that is ramped up to get your displacement and then released rapidly (in time)
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Good luck
Ivar
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First of all, I send you many thanks to you! Thank you for your patient detailed and timely explain. The results of the simulation there is a great gap compared with the experimental results and theoretical results. I think maybe there are some mistakes in my sequence steps. Please give some advices and improvements, in my simulation process such as bellows:
First, I make the eigenfrequency analysis and get the first mode frequency 329+6i, so I get the maximum time steps that should be 0.0005[s] < 1/(3*f0)=0.001s.
Study1, I select stationary study type, set a boundary prescribed displacement 1.05mm.
Study2, I select time-dependent study type, and make study1 solution as study2 initial value i.e. selecting “Initial values of variables solved for” and in the “Method:” select ‘solution’, in the “Study:” select ‘study1’ then computed. (Disable for this solver the prescribed displacement)
So I get the displacement vs. time plot as see my attachment,but velocity curve trend not attenuation.
You give me an advice (use a force that is ramped up to get the displacement and then released rapidly (in time)), how to give a force, F= model1,rho*g_constant*(-omrga^2*1.05), is it right? Hope to get your advice.
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The loss factor has been changed from 0.04 to 0.0004, but the simulation result has been not significant change in the plot curve of the disp vs time. Why the velocity response curve is not attenuation? Hoping get your help!
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careful with the damping node, read in details the doc, not all damping settings are compliant with a time series, they work in frequency domain though.
Another way to add a damping, is to add either a boundary load or a point load at the tip with a force of the type
-Damp[Pa*s]*vt
This adds a viscous damping to your system proportional to the velocity "vt" along "Y" (I assume the beam is along X
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Good luck
Ivar
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Words can not express my gratitude to your help. When I see the plot of your simulation result, it's impossible to put into words how I feel. Thank you very much! Your enthusiasm and mastering tips for COMSOL make me admire.
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it's just "applying physics" you will see, with some training, you can manage as well if not even better :)
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Good luck
Ivar
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I saw your model. I have a question about the damping. I'm wondering why the rayleigh damping is diabled when doing the time dependent study? I realized that you add a viscous damping as a edge load. Looking forward to your reply. Thanks a lot.
Regards,
Deng
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if you check the doc you will see its specified that it is not implemented, not all physcis and BC can be used for all combinations of solvers, some are dependent on the frequency spectrum, and that is not known from a time series. Check the theory on the Reyleigh damping
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Good luck
Ivar
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edit:
I saw your model but i still do not understand how you force the study 2 to use the results of study 1.
can you tell me something more about?
Thanks a lot
Dario
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i am new to comsol.I am trying to match the analytical results for eigenfrequency of a simple cantilever beam and its simulation results in comsol.I tried to implement many papers but i am failed to match what i am thinking there is some boundary condition is missing .just one boundary condition is used that is fixed constraint to fix a side .
Kindly help me out i will be very thankful to you .
Thanks in advance .
Khawar
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