It is known that in the calculation of natural frequencies and modal shapes for a vibrating beam, a value for the shear stress factor K has to be used. What exact value should be used is not known. This note presents the results of an investigation into the effect of various values of K on the natural frequencies.
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References
1.
TimoshenkoS.‘On the correction for shear of the differential equation for transverse vibration of prismatic bars’, Phil. Mag.192141 (Series 6).
2.
NewlinJ. A.TrayerG. W.‘Deflection of beam with special reference to shear deformation’, Naca rep.180, 1924.
3.
MindlinR. D.DeresiewiczS.‘Timoshenko's shear coefficient for flexural vibration of beam’, Proc. 2nd U.S. National Congr. Appl. Mechanics1954.
4.
CowperG. R.‘The shear coefficient in Timoshenko's beam theory’, J. appl. Mech.1966 (June).
5.
RissioneW.WilliamsJ.‘Vibration of non-uniform cantilever beams’, The Engineer1965 (September 24).
6.
DawsonB.GhoshN. G.CarnegieW.‘Modal curves of pre-twisted blading allowing for shear deformation and rotary inertia’, Proc. 12th Congr. Theoretical and Applied Mechanics December 1970 (Sindri, India).
7.
DawsonB.GhoshN. G.CarnegieW.‘Effect of slenderness ratio on the natural frequencies of pre-twisted cantilever beams’, J. mech. Engng Sci.197113 (No. 1).