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attaching a 10mg mass to the free end of a cantilever beam
Posted Jun 21, 2010, 6:50 a.m. EDT 3 Replies
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Hello,
I'm quite new to COMSOL as I am from electronics background. As a first exercise I need to model a suspended mass cantilever beam. The beam dimensions are L = 1000um(excluding the suspended mass), H = 50um, width = 10um. Could anyone please help me how to attach the mass to the cantilever beam? I am familiar with meshing,solving and eigen analysis methods in basic vibration theory.
I'm quite new to COMSOL as I am from electronics background. As a first exercise I need to model a suspended mass cantilever beam. The beam dimensions are L = 1000um(excluding the suspended mass), H = 50um, width = 10um. Could anyone please help me how to attach the mass to the cantilever beam? I am familiar with meshing,solving and eigen analysis methods in basic vibration theory.
3 Replies Last Post Jun 22, 2010, 8:23 a.m. EDT
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Posted:
1 decade ago
Hi
in 2D or 3D there is no easy way to add a "point" rigid body mass, in beam or truss mode they are included as part of the BCs, apart that you can add a small surface/volume, that you give an artificially high density and stiffness. The only other way is to add it by equation, in the weak form and check that all your boundary conditions considered it, including in time and eigenfrequency mode, so that your global equations remain correct.
Point masses are anyhow slightly cumbersome as they make a easily singularities, you should better distribute them over an edge or an area.
Have fun Comsoling
Ivar
in 2D or 3D there is no easy way to add a "point" rigid body mass, in beam or truss mode they are included as part of the BCs, apart that you can add a small surface/volume, that you give an artificially high density and stiffness. The only other way is to add it by equation, in the weak form and check that all your boundary conditions considered it, including in time and eigenfrequency mode, so that your global equations remain correct.
Point masses are anyhow slightly cumbersome as they make a easily singularities, you should better distribute them over an edge or an area.
Have fun Comsoling
Ivar
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Posted:
1 decade ago
Hi,
Many thanks for such fast reply. I have tried to do many things :
1. instead of force excerted by the earth on the mass of 10mg, I have specified in terms of force/area on one of the faces.
2. I have tried force/length option on one of the edge faces.
3. I have tried specifying the initial normal stress component on along the length
4. I have tried specifying the initial shear stress component on along the cross section
5. I have tried to create a composite object - cantilever and a small cube of extremely high density value of such a volume so as to match 10mg load
All these work for static analysis with no problem whatsoever
I have used the following parameters for simulation
density : 2300kg/m3
L = 1000um, H = 50um, W = 10um rectangular cross section
But the problem with eigen frequency analysis is as follows. Irrespective of any force applied, since I am unable to attach the 10mg mass(let us forget about the mass for the time being.), the total mass of the cantilever beam is = density*volume = (2300)*(1000u*50u*10u) = 1.15e-9.
The value of k calculated theoretically is k = 3EI/(L^3) = 59.39 N/m . where I = ((10u)*(50u)^3)/12
Now if I use f = (1/2*pi)sqrt(k/m) i get around 36.16k Hz. But the simulation shows 14.713 kHz. Can you please explain this discrepancy?
Many thanks for such fast reply. I have tried to do many things :
1. instead of force excerted by the earth on the mass of 10mg, I have specified in terms of force/area on one of the faces.
2. I have tried force/length option on one of the edge faces.
3. I have tried specifying the initial normal stress component on along the length
4. I have tried specifying the initial shear stress component on along the cross section
5. I have tried to create a composite object - cantilever and a small cube of extremely high density value of such a volume so as to match 10mg load
All these work for static analysis with no problem whatsoever
I have used the following parameters for simulation
density : 2300kg/m3
L = 1000um, H = 50um, W = 10um rectangular cross section
But the problem with eigen frequency analysis is as follows. Irrespective of any force applied, since I am unable to attach the 10mg mass(let us forget about the mass for the time being.), the total mass of the cantilever beam is = density*volume = (2300)*(1000u*50u*10u) = 1.15e-9.
The value of k calculated theoretically is k = 3EI/(L^3) = 59.39 N/m . where I = ((10u)*(50u)^3)/12
Now if I use f = (1/2*pi)sqrt(k/m) i get around 36.16k Hz. But the simulation shows 14.713 kHz. Can you please explain this discrepancy?
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Posted:
1 decade ago
Hi
Yes as most programmes, eigen mode analysis is done without external forces, and if you define the "mass" through a force it will not be introduced into the equations for eigenfrequency or buckling analysis, you must add the mass as amultiplier to the j*omega term.
To learn how COMSOL does it, use the 2D beam physics and add a mass on a point and go the the equations (Physics - Equation Settings - Point Variables in 3.5, turn on the equations in the Preferences in V4 and click on the node equation icons).
Have fun Comsoling
Ivar
Yes as most programmes, eigen mode analysis is done without external forces, and if you define the "mass" through a force it will not be introduced into the equations for eigenfrequency or buckling analysis, you must add the mass as amultiplier to the j*omega term.
To learn how COMSOL does it, use the 2D beam physics and add a mass on a point and go the the equations (Physics - Equation Settings - Point Variables in 3.5, turn on the equations in the Preferences in V4 and click on the node equation icons).
Have fun Comsoling
Ivar