69(3), 283–291 (2002)Ĭallister, W.D.: Material Science and Engineering An Introduction. Towfighi, S., Kundu, T., Ehsani, M.: Elastic wave propagation in circumferential direction in anisotropic cylindrical curved plates. Rokhlin, S.I., Chimenti, D.E., Nagy, P.B.: Physical Ultrasonics of Composites. Sorohan, Ş, Constantin, N., Găvan, M., Anghel, V.: Extraction of dispersion curves for waves propagating in free complex waveguides by standard finite element codes. Schwab, F., Knopoff, L.: Surface-wave dispersion computations. Schöpfer, F., et al.: Accurate determination of dispersion curves of guided waves in plates by applying the matrix pencil method to laser vibrometer measurement data. Sasso, M., Mancini, E., Dhaliwal, G.S., Newaz, G.M., Amodio, D.: Investigation of the mechanical behavior of CARALL FML at high strain rate. Cambridge University Press, Cambridge (1987) Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T., Chipperfield, J.R.: Numerical Recipes: The Art of Scientific Computing. Modified Newton Raphson method - Find root of x2+y2-50,x3+圓-20 with Initial guesses 2,-1 using Modified Newton Raphson method (Multivariate Newton. Press, F., Harkrider, D., Seafeldt, C.A.: A fast, convenient program for computation of surface-wave dispersion curves in multilayered media. Packo, P., Uhl, T., Staszewski, W.J.: Generalized semi-analytical finite difference method for dispersion curves calculation and numerical dispersion analysis for Lamb waves. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. Pavlakovic, B., Lowe, M., Alleyne, D., Cawley, P.: Disperse: a general purpose program for creating dispersion curves. Nayfeh, A.H., Chimenti, D.E.: Propagation of guided waves in fluid-coupled plates of fiber-reinforced composite. 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Harb, M.S., Yuan, F.G.: A rapid, fully non-contact, hybrid system for generating lamb wave dispersion curves. Hora, P., Červená, O.: Determination of lamb wave dispersion curves by means of Fourier transform. Appl. Keywordsīellini, C., Di Cocco, V., Iacoviello, F., Sorrentino, L.: Performance evaluation of CFRP/Al fibre metal laminates with different structural characteristics. This study provides valuable insights into the impact of fiber orientation angle on elastic wave dispersion relations in CARALL composites and could inform future research on composite material design and optimization. However, the sensitivity of the other modes to the angle is negligible. The results indicate that the difference in fiber orientation angle significantly affects the shift in phase velocity between the primary symmetric mode and the horizontal shear mode. The stiffness matrix approach is used to determine the dispersion curves, and the “Dispersion Calculator” computer program is employed in the analysis. The overall configuration of the CARALL composite is s, where the angle parameter is varied between 0° and 90°. The material consists of 14 layers, where the layers are constructed from aluminum alloy and carbon/epoxy resin fibers. The CARALL composite is made up of multiple plies of carbon fiber and aluminum plies bonded together. ![]() Newton's method is an extremely powerful technique-in general the convergence is quadratic: as the method converges on the root, the difference between the root and the approximation is squared (the number of accurate digits roughly doubles) at each step.The purpose of this study is to present a parametric analysis of how the fiber orientation angle affects elastic wave dispersion relations in the case of the CARALL composite. ![]() This x-intercept will typically be a better approximation to the function's root than the original guess, and the method can be iterated. The idea of the method is as follows: one starts with an initial guess which is reasonably close to the true root, then the function is approximated by its tangent line (which can be computed using the tools of calculus), and one computes the x-intercept of this tangent line (which is easily done with elementary algebra). Animation of Newton's method by Ralf Pfeifer ()
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