| Based on linear three-dimensional theory of elasticity, wave equations in transversely isotropic pipe are derived, and are calculated with Legendre orthogonal polynomial approach. To verify the validity of the Legendre orthogonal polynomial approach, the governing equations of wave motion in transversely isotropic pipe are derived, the dispersion equations are calculated by polynomial method,and the dispersion curve of phase velocity are identical with the result from software Disperse,the orthogonal polynomial approach are proven to be feasible . Elastic constants of transversely isotropic pipe changing with fiber volume fraction increasing are calculated according to the micromechanics theory, and dispersion curves of transversely isotropic pipe about different fiber volume fraction are plotted and analyzed in details, velocity variation trend of fundamental modes with fiber volume fraction increasing are analyzed, with the fiber volume content increasing from 0 to 100%, the variation characteristics of the dispersion curves of the first three modes A0, SH0 and S0 at the frequency 0.5MHz. The phase velocity of S0 and A0 increases monotonically throughout the region, but when the fiber volume content is equal to 21%, the phase velocity of SH0 first gradually decreases to 1233.37m/s, and then continuously |
