Property distribution determination for nonuniform composite beams from vibration response measurements and Galerkin's method

This paper presents initial results from a program to develop a "rapid screening test" for determining the in-plane fiber distributions in unidirectionally reinforced composite structures by the use of the vibration response measurements and Galerkin's method. Theoretical models and experimental data are generated on the basis of two methods: (1) the "shifting method," in which the effective length of the beam is changed, and (2) the "added mass method, " in which the mass distribution of the beam is changed. The elastic constants and the density are all assumed to be functions of fiber volume fraction, while the spatial distribution of the fiber volume fraction is assumed to be given by a polynomial function. The concept of an effective density is employed to obtain the appropriate solution to the coefficients of the polynomial function. Results show that the fundamental mode gives rise to better predictions of physical properties than the higher modes do. Art error analysis includes discussion of the errors due to the influences of the mode number, the assumed order of the polynomial in the fiber volume fraction distribution, and the bending-extension coupling effect caused by the unsymmetrical distribution of properties about the beam middle surface.