FREE TRANSVERSE VIBRATIONS OF ANISOTROPIC BEAMS.

A uni-directional composite has high Young's modulus in the fiber direction but low shear modulus. This allows large shear strains and so invalidates some of the assumptions of engineering beam theory; in particular, the sectional loadings cannot be assumed to be related to a linear stress distribution. A theory for anisotropic materials which relates the deflection of a beam to the stress pattern is considered. This allows the calculation of corrections to the natural frequencies derived by standard beam theory. It appears that the Euler-Bernoulli theory with a shear correction similar to that of the Timoshenko theory gives adequately accurate results.