Vibroscope method for determination of cross-sectional area of glass and carbon fibres – Theory and further development

Accurate determination of cross-sectional area of glass and carbon fibres by the vibroscope method is examined. Complete derivations of the central frequency solutions are presented, to make these derivations accessible in modern scientific literature. The effect of non-zero bending stiffness is included. The influence of shape of fibre cross-sectional area is analysed. Only small deviations in cross-sectional areas are found due to fibre shape, allowing for the use of the vibroscope method for fibres with non-circular cross-sectional areas. Two correction factors are introduced for the effect of volume change and area change of a tensioned fibre, allowing determination of the cross-sectional area of the non-tensioned fibre. A model plot of the vibroscope equation is presented, showing the numerical effect of the corrections on the fibre cross-sectional area depending on the applied tension force. The relations shown by the model plot have implications for the experimental settings of the vibroscope method.