Is it possible to derive the theoretical formulation for rotating cantilever beam as force is a function of rotating speed or displacement.
Suppose 1000 rpm applied, during rotation, the beam vibrating and deflects at some frequency.
Deflection is caused in the beam due to rotational motion, similar to deflection is caused in the beam due to tip excitation, base excitation(force relations are there for this excitation source and FEM simulation is also done for this type of system)
For rotational system, how can i apply a force as a function of rotational speed in the Finite Element Analysis
In the vibration analysis of instruments and similar devices it is occasionally necessary to determine the natural frequencies of systems consisting of a uniform cantilever beam with a tip mass. If the mass be considered to be a point mass concentrated at the tip of the cantilever, the problem is not difficult and the lowest frequency may be obtained with very great accuracy. However, higher frequencies are still hard to find. Finite element programming in MATLAB can be done to find the higher frequencies with great accuracy. A finite element analysis code in MATLAB should be developed to solve the vibration problem of cantilever beam with tip mass at free end.
Raja Velusamy With some assumptions, you can very well formulate the model in any FE package. Use TABLED or Amplitude cards to create frequency dependent loads and solve this problem in frequency domain. For your beam, you can create concentrated loads (make 4-5 approx sections of the beams instead of assuming the CF force acting at the C.G) and a separate load for the tip mass as well. If you are interested in looking for the responses at lower bending frequencies then this assumption would hold good. For all the loads, apply both, the 0 and 90 deg out of phase components.
PS: You did not mention about the source for the lateral excitation of the beam. Is it because of the shape of the beam? Or your base itself is exciting the beam? For a simple beam rotating at any RPM (even close to its natural freqs) won't give any significant response in the lateral directions. This can answer your first question regarding the theoretical formulation. If your query is regarding the deflection of the beam as your initial configuration (self weight+tip mass) and then make it rotate, that can be done with restart analysis + SSD.
Thanks for your answer, Kabir and Pranoy sir. The source for the (tranverse) excitation of the beam is gravitational force of the tip mass while rotating (Flexible beam thickness is 0.1 mm). For this structure, rotating at any RPM (close to its natural freqs) will give response in the transverse direction.
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