*How we can mathematically model this beam ?
* calculating the resonant frequency of the beam??
*what will be the DOF of this beam???
If anyone give any reference for doing or understanding the mathematical modeling this structure....I really appreciate your help.
Thank you in advance.
I assume it is okay to approach the round tips of the outside beams by the middle point rectangle and that central connection may be simplified to a spring system (axial/torsional spring connections simplification) which constants you can estimate. Then try to see if you can follow and get inspiration from the publications (and may be contact the authors) of
H.V. Vu, A.M. Ordóñez, B.H. Karnopp Vibration of a double-beam system
J Sound Vib, 229 (2000), pp. 807-822
or
Article Free transverse vibrations of a triple-beam system
You can check the results from the mathematical model with a FE shell model and see if all modes (both outplane as well as inplane modes) are nearly correlated. Also, keep under observation the eventual model differences if shell is Midlin Theory and beam is Euler-Bernoulli, or other possibilities.
Hope others can also contribute here with their view on this.
I like to point to one important thing. If the beams are MEMS and the beam is experiencing large deflection, you should consider vibration of large deflection.
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