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Step response and resonant frequency

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Dear sir,
I am modelling a piezoresistive pressure sensor. I want to now study the structure when a step load is applied , meaning pressure is applied on the top surface all of a sudden in full magnitude. How can i do this ?

Also i am trying to find the resonant frequency of the same structure. I have run the eigenfrequency analysis but i'm still not clear as to which of these eigen frequencies is the resonance frequency ?

Thanking you in advance,
Vijay


5 Replies Last Post 29.06.2012, 07:24 GMT-4
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 26.06.2012, 02:08 GMT-4
Hi

all frequencies are the resonant frequencies, but if you apply a pressure change over the full thin membrane you excite mostly the fundamental mode (first mode)

to apply a step pulse, use the "smooth" Step() operator (definition functions) and vary the rise time as a parameter, start slowly then increase the steepness.

--
Good luck
Ivar
Hi all frequencies are the resonant frequencies, but if you apply a pressure change over the full thin membrane you excite mostly the fundamental mode (first mode) to apply a step pulse, use the "smooth" Step() operator (definition functions) and vary the rise time as a parameter, start slowly then increase the steepness. -- Good luck Ivar

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Posted: 1 decade ago 26.06.2012, 06:55 GMT-4
Dear sir,
Thank you for your reply. You have mentioned that only the first mode will be present as it is a thin membrane. But in my structure the membrane is thick (0.21mm) , and its side is (0.75mm) because it will be used for a very high pressure application (400 bar). So in this case is calculating the 1st eigen frequency sufficient?

Also i'm still not very clear about applying a step load on the structure. I need to apply a sudden pressure on the top surface. For this you have asked me to use the "smooth" step function but i am unable to understand a few things. Should i now run a time dependant analysis ?? And also should i make the pressure applied a step function ?
Plz explain this process clearly.

Thanking you in advance,
Vijay
Dear sir, Thank you for your reply. You have mentioned that only the first mode will be present as it is a thin membrane. But in my structure the membrane is thick (0.21mm) , and its side is (0.75mm) because it will be used for a very high pressure application (400 bar). So in this case is calculating the 1st eigen frequency sufficient? Also i'm still not very clear about applying a step load on the structure. I need to apply a sudden pressure on the top surface. For this you have asked me to use the "smooth" step function but i am unable to understand a few things. Should i now run a time dependant analysis ?? And also should i make the pressure applied a step function ? Plz explain this process clearly. Thanking you in advance, Vijay

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 26.06.2012, 13:20 GMT-4
Hi

indeed if you are looking for a transient (sudden pressure rise) you should work with a time dependent solver, and deine a step function "Definitions - Function - Step" node check the advanced smothing rise time, and plot the function until you are happy with the shape.

Then in the boundary load, select pressure, and write p0*step1(t[1/s]), where p0 is you nominal pressure jump you define as a Global - Parameter

Then go to the time stepping solver and set the time steps such that oyu ahve a minimum 3-5 steps during the step function rise time.

Now you have still two options: in the main structural (solid) physics node, checl the inertial tems and set to Quasi static. This will remove the sencond time derivatives and you solver will etter converge, but you will not see the details of the turn on transients oscillations, check that your solver converges, that the mesh is OK, the time stepping to, and that you are happy with the turn on time (start slower 0.1 sec perhaps, then make it faster 0.001[s] ?). Then finally turn back on the Inertial terms in the main physics node and solve again, it could be vise to use a time stepping then sufficiently short that you have at least 5-10 time steps per funcamental frequency periode (i.e. frst mode 200 Hz => time stepping <1/(10*20) in seconds, and ensure that this is still about 3x shorter than your rise step time). the convergence now might be very long as there are many steps to calculate, but if you do not have enough time steps you will not get the ringing of the pressure pulse turn on.

You can also improve the solver response if you add some damping, but its difficult to know which value to use, and note that isotropic damping will not work in time domain, check you doc.

--
Good luck
Ivar
Hi indeed if you are looking for a transient (sudden pressure rise) you should work with a time dependent solver, and deine a step function "Definitions - Function - Step" node check the advanced smothing rise time, and plot the function until you are happy with the shape. Then in the boundary load, select pressure, and write p0*step1(t[1/s]), where p0 is you nominal pressure jump you define as a Global - Parameter Then go to the time stepping solver and set the time steps such that oyu ahve a minimum 3-5 steps during the step function rise time. Now you have still two options: in the main structural (solid) physics node, checl the inertial tems and set to Quasi static. This will remove the sencond time derivatives and you solver will etter converge, but you will not see the details of the turn on transients oscillations, check that your solver converges, that the mesh is OK, the time stepping to, and that you are happy with the turn on time (start slower 0.1 sec perhaps, then make it faster 0.001[s] ?). Then finally turn back on the Inertial terms in the main physics node and solve again, it could be vise to use a time stepping then sufficiently short that you have at least 5-10 time steps per funcamental frequency periode (i.e. frst mode 200 Hz => time stepping

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Posted: 1 decade ago 29.06.2012, 03:41 GMT-4
Dear Sir,

Thank you for your reply. I wanted to clarify a few more things. I am trying to get a sudden response so why should i use smooth step function ? Can i do it without using step ? I am getting the same response using smooth step function as i get when i do not apply any step function and directly apply the load.

Secondly I am trying to find the resonant frequency in a different model ( not the same one in which i am using a step response ). Is the resonant the same as 1st eigen frequency ?? I don't understand which of the eigen frequencies is the resonant frequency ?

Thanking you in advance ,
Vijay
Dear Sir, Thank you for your reply. I wanted to clarify a few more things. I am trying to get a sudden response so why should i use smooth step function ? Can i do it without using step ? I am getting the same response using smooth step function as i get when i do not apply any step function and directly apply the load. Secondly I am trying to find the resonant frequency in a different model ( not the same one in which i am using a step response ). Is the resonant the same as 1st eigen frequency ?? I don't understand which of the eigen frequencies is the resonant frequency ? Thanking you in advance , Vijay

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 29.06.2012, 07:24 GMT-4
Hi

all or a combination of all of the frequencies are the "resonant frequency".

Mostly the first one is the "predominant" one, but that depends on the excitation. It is very model (shape) dependent and excitation mode dependent.

You can use the mass participation norm to sort the x-y-z direction ones (not yet the rotational ones in COMSOL)

If you do a transient response, with initial values all "0" and then turn on sudden an excitation as a Dirac function you will excite all modes directly related with the load force direction (pressure in your case). If you smoother a bit the rise time you might filter out the highest frequencies and not excite them.

Try with a Dirac, if the time stepper manages to solve its probably OK, but if you have convergence issues try a smoothed impulse, but with a highest possible rise time, to get the correct impulse response. Tuning of the time step is also important, a fine time step and automatic or intermittent would be required.

Using a Dirac impulse means you excite all (to an infinite frequency limit, in theory)


--
Good luck
Ivar
Hi all or a combination of all of the frequencies are the "resonant frequency". Mostly the first one is the "predominant" one, but that depends on the excitation. It is very model (shape) dependent and excitation mode dependent. You can use the mass participation norm to sort the x-y-z direction ones (not yet the rotational ones in COMSOL) If you do a transient response, with initial values all "0" and then turn on sudden an excitation as a Dirac function you will excite all modes directly related with the load force direction (pressure in your case). If you smoother a bit the rise time you might filter out the highest frequencies and not excite them. Try with a Dirac, if the time stepper manages to solve its probably OK, but if you have convergence issues try a smoothed impulse, but with a highest possible rise time, to get the correct impulse response. Tuning of the time step is also important, a fine time step and automatic or intermittent would be required. Using a Dirac impulse means you excite all (to an infinite frequency limit, in theory) -- Good luck Ivar

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