natural freq. for beam with non-uniform cross-section
natural freq. for beam with non-uniform cross-section
(OP)
Hi,
I would like to model a cantilever beam in a program like MathCAD that I can modify quickly. It seems silly using FEA (Nastran) to model this type of system just to get the first few modes and mode shapes.
I have been able to do this for a simple uniform beam using the flexural matrix and mass matrix, obtaining the eigenvalues and eigenvectors. However, I am having a hard time figuring out the best way to tackle the non-uniform cantilever beam. The example I am working is a section of pipe, coupling, another section of pipe (diff. schedule), and a large mass at the free end. I need to model the details b/c the solution needs to be very accurate. PLEASE HELP!! Thanks in advance.
I have attached a schematic.
I would like to model a cantilever beam in a program like MathCAD that I can modify quickly. It seems silly using FEA (Nastran) to model this type of system just to get the first few modes and mode shapes.
I have been able to do this for a simple uniform beam using the flexural matrix and mass matrix, obtaining the eigenvalues and eigenvectors. However, I am having a hard time figuring out the best way to tackle the non-uniform cantilever beam. The example I am working is a section of pipe, coupling, another section of pipe (diff. schedule), and a large mass at the free end. I need to model the details b/c the solution needs to be very accurate. PLEASE HELP!! Thanks in advance.
I have attached a schematic.





RE: natural freq. for beam with non-uniform cross-section
In theory, a distributed parameter model would be the most accurate. Unless you are familiar with solving coupled PDE's then FEA is the easiest.
Although, if it were me, the first thing I would start with is lumping the pipe sections and then solve the lumped parameter system.
From here you can get a "feel".
Then move on to the PDE modeling.
Fe
RE: natural freq. for beam with non-uniform cross-section
Fe
RE: natural freq. for beam with non-uniform cross-section
But if you already have an FEA program...
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RE: natural freq. for beam with non-uniform cross-section
Anyway, Rayleigh Ritz is another good approach for this sort of problem, it depends on whether you'd rather use iteration (Holzer) or differentiation(R-R).
Holzer is probably better suited to mathcad
Cheers
Greg Locock
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