Ok, i have an euler beam having rectangular cross section. but it's shear center axis and neutral axis are different. how can i obtain the equation of motion of this beam for transverse vibrations?
any help??
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First, if it is a solid,
First, if it is a solid, homogeneious section made of isotropic materials, the shear center and neutral axis should be the same. If there are indeed different for some sections, such as thin-walled with different thickness each wall, heterogeneous, or anisotropic, you can the Timoshenko model to set the origin of the coordinate system at any point to establish your EOM. If you stick to an Euler-Bernoullie model, then you need to establish the EOM w.r.t to the shear center. The following paper pointed out the pitfalls associated with use of E-B beam model.
Hodges, D. and Yu, W.: "A Rigorous, Engineering-Friendly Approach for Modeling
Realistic, Composite Rotor Blades," Wind Energy, vol. 10, no. 2, 2007,
pp. 179-193. (pdf)
Wenbin