Enjilela E., Honarvar F., Sinclair A.

In this paper, a novel numerical method for solving the frequency equation in problems of ultrasonic wave propagation in elastic structures is presented. While the traditional numerical methods are mostly based on finding the zeros of the equation by an iterative find-root algorithm, the new method uses a three-dimensional plot of the frequency equation for obtaining the dispersion curves. In the new method, a three-dimensional representation of the frequency equation is plotted first. The desired dispersion curve is then easily obtained by applying a suitable horizontal cut to this plot in the phase velocity-frequency plane. To demonstrate the advantages of the proposed method, the problems of longitudinal wave propagation in isotropic and transversely isotropic cylinders are numerically solved and the three-dimensional representations of the frequency equation as well as the corresponding dispersion curves are plotted. Simplicity, high speed, low possibility of numerical error, and convenient graphical illustration are among the advantages of this new method.