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Bending of cantilever beam

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Am a new user of Comsol 5.2a. My design is a fixed-free cantilever beam with a tip mass. I want to find the maximum thickness that can be given for a tip mass without the beam bending. Can anyone help me with the simulation?. Thanks in advance.

5 Replies Last Post Sep 12, 2017, 7:18 a.m. EDT
NDN UNIST/Mechanical Engineering

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Posted: 7 years ago Aug 17, 2017, 2:24 a.m. EDT
It maybe useful for u
www.youtube.com/watch?v=k-4bjO1Cq-4&list=PLC7C49A0F0814EF1E
It maybe useful for u https://www.youtube.com/watch?v=k-4bjO1Cq-4&list=PLC7C49A0F0814EF1E

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Posted: 7 years ago Aug 17, 2017, 2:58 a.m. EDT
These videos are based on resonant frequency. But I need to find the bending of cantilever beam due to a tip mass.
These videos are based on resonant frequency. But I need to find the bending of cantilever beam due to a tip mass.

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

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Posted: 7 years ago Aug 17, 2017, 7:47 a.m. EDT
Updated: 7 years ago Aug 17, 2017, 7:48 a.m. EDT
Hi

I assume you mean under gravity load ?
In such a case your tip mass will always bend a little, so you should probably state tip not to bend more than ...

That is an typically an optimisation problem: you define the beam shape width and length, the material, the tip mass value and then you set as parameter the beam thickness and measure the tip motion and loop back to optimise the thickness until you reach the tip bending limit value you want.

A simpler way is just to do a parametric sweep of the same model, with the beam thickness as parameter, you define a start stop, step range and you monitor the tip deviation by i.e. a point integration of one of the tip points. Once plotted out you can easily read out the thickness value for a given deflection.

There are also some other "engineering" rule of thumb ways (rough approximation, but often quite OK), as for a simple tip loaded beam the first eigenfrequency f0 is roughly :
2*pi*f0 = sqrt(k/m) = sqrt(g_const/Dz)
where k[N/m] is the beam stiffness, m[kg] the tip load mass (assumed to be greater than the beam mass) g_const is the gravity constant 9.18[m/s^2] and Dz is the maximum tip displacement in [m]

Then one can optimise the first eigenfrequency to be above this limit deduced by the formula above

--
Good luck
Ivar
Hi I assume you mean under gravity load ? In such a case your tip mass will always bend a little, so you should probably state tip not to bend more than ... That is an typically an optimisation problem: you define the beam shape width and length, the material, the tip mass value and then you set as parameter the beam thickness and measure the tip motion and loop back to optimise the thickness until you reach the tip bending limit value you want. A simpler way is just to do a parametric sweep of the same model, with the beam thickness as parameter, you define a start stop, step range and you monitor the tip deviation by i.e. a point integration of one of the tip points. Once plotted out you can easily read out the thickness value for a given deflection. There are also some other "engineering" rule of thumb ways (rough approximation, but often quite OK), as for a simple tip loaded beam the first eigenfrequency f0 is roughly : 2*pi*f0 = sqrt(k/m) = sqrt(g_const/Dz) where k[N/m] is the beam stiffness, m[kg] the tip load mass (assumed to be greater than the beam mass) g_const is the gravity constant 9.18[m/s^2] and Dz is the maximum tip displacement in [m] Then one can optimise the first eigenfrequency to be above this limit deduced by the formula above -- Good luck Ivar

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Posted: 7 years ago Aug 23, 2017, 5:36 a.m. EDT
As am not familiar with the steps kindly send me the .mph file for the same. Thanks in advance.
As am not familiar with the steps kindly send me the .mph file for the same. Thanks in advance.

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Posted: 7 years ago Sep 12, 2017, 7:18 a.m. EDT
Hi I dint know how to start .can you please send me the file with these steps(optimization). So that i can proceed. Thanks.
Hi I dint know how to start .can you please send me the file with these steps(optimization). So that i can proceed. Thanks.

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