When i compare natural frequencies extracted from ansys workbench with exact solution, there is significant difference between the third modes.also, the natural frequency of the third mode is equal to the natural frequency of fourth mode extracted from ANSYS Workbench. Who can I solve this problem?
Hi Morteza,
Can you describe what is the "exact solution"? What is your boundary conditions? Why do you think the third mode frequency can not be equal to fourth mode frequency?
Best Regards...
Dear Mr Yalcin,
Cantilever beam is a beam with on end free and one end fixed.
Exact solution is the solution by the basic formula to find the result.in the other words, it is a solution of a problem by the methods that every ones of a field knows it . it is a theoretical solution of a problem by the formula.
answer of your last question: To get a proper solution of a problem, it is important that the exact solution, Finite element analysis (here, it is solved by ANSYS), and experimental analysis results be equal together with good approximation. The errors depends on the field you have working on.
Regards,
Morteza,
Can you try to model as a one beam element? You should use hard sizing of the edge with one number of division. Afterward, can you compare the results? On the other hand, whats your difference between the theoritical and ansys results as a percentage?
Best Regards...
You can find the Timoshenko beam element stiffness and mass matrices below:
https://mediatum.ub.tum.de/doc/1072355/file.pdf
It looks like you determine the theoretical solution based on Bernoulli-Euler beam model (you call it 'exact solution' in your questions, actually it is a approximate solution if it is), while the finite element simulation uses Timoshenko beam model or more accurate elasticity model (based on your FE model). You could try to get the solution of a cantilever beam with a large length (large length/width ratio). For the long beam, the results should be very close, otherwise there are some mistakes somewhere. And then you could get the solution for the short beam. If the error for natural frequencies is big, the Timoshenko beam model or even the elasticity model should be used to determine the theoretical solution, and the Bernoulli-Euler beam model is not accurate enough to solve this case.
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