VIBRATION OF SHEAR-DEFORMABLE BEAMS USING A SPLINE-FUNCTION APPROACH

B-spline functions are used as trial functions in a Rayleigh-Ritz analysis of the free vibration of shear-deformable Timoshenko beams. In a first approach it is demonstrated in numerical applications that when the lateral deflection and the cross-sectional rotation are represented by functions of equal order the calculated natural frequencies are of good accuracy for stocky beams but can overestimate the true frequencies very considerably for slender beams. This is identified as a shear-locking difficulty and consideration of its causes points clearly to the adoption of a new displacement field in which the deflection is represented by a B-spline function which is one order higher than that used to represent the rotation. Numerical results using this new displacement field demonstrate good accuracy for both stocky and slender beams: the shear-locking difficulty is completely eliminated. This has clear significance for the analysis of shear-deformable plates and shells when using B-spline functions.