Spectral Collocation Method for dispersion curves plotting

Calculate guided wave dispersion curves for orthotropic (anisotropic) laminates.

Description

The MATLAB-based script for calculation of dispersion curves for composite plates as the case of multilayer orthotropic media using (Pseudo-)Spectral Collocation Method.

Paper

A. A. Bryansky, S. V. Panin, Dispersion curves calculation for all-CFRP sandwich composite using Spectral Collocation Method, Acta Astronautica (2025). DOI

Files

SCM_SL.m - Spectral Collocation Method script for a single-layer case

SCM_ML_HCS - Spectral Collocation Method script for a multilayer case (example for honeycomb sandwich composite)

chebdiff.m - function for creation of the Chebyshev differentiation matrices

balance2.m and gcg.m - functions required for balancing algorithm (look Important links).

SM_HC.m - function for calculation of the stifness matrix for honeycomb core

SM_orthotropic.m - function for calculation of the stiffness matrix for orthotropic materials (skin sheets)

SM_isotropic.m - function for calculation of the stiffness matrix for isotropic materials (adhesive layers)

Literature

1. F. Hernando Quintanilla, M. J. S. Lowe, R. V. Craster, Modeling guided elastic waves in generally anisotropic media using a spectral collocation method, J. Acoust. Soc. Am. 137.3 (2015) 1180-1194. DOI
2. F. Hernando Quintanilla, M. J. S. Lowe, R. V. Craster, The symmetry and coupling properties of solutions in general anisotropic multilayer waveguides, J. Acoust. Soc. Am. 141(1) (2017) 406-418. DOI
3. M. Mekkaoui, S. Nissabouri, H. Rhimini, Towards an Optimization of the Spectral Collocation Method with a New Balancing Algorithm for Plotting Dispersion Curves of Composites with Large Numbers of Layers, J. Appl. Comput. Mech. 10(4) (2024) 801-816. DOI
4. I. Zitouni, H. Rhimini, A. Chouaf, Comparative study of the spectral method, DISPERSE and other‎ classical methods for plotting the dispersion curves in‎ anisotropic plates, J. Appl. Comput. Mech. 9(4) (2023) 955-973. DOI
5. A. Huber, M. G. Sause, Classification of solutions for guided waves in anisotropic composites with large numbers of layers, J. Acoust. Soc. Am. 144(6) (2018) 3236-3251. DOI

Important links:

Dispersion Calculator by Armin Huber

About balancing algorithm for eigenvalue problem: BALANCE2 Balancing generalized eigenvalue problem (requires GCG Generalized conjugate gradient method)

Thanks to

• Dr. Armin Huber, German Aerospace Center (DLR), Augsburg, Germany
• Prof. Pavel Utkin, Harbin Institute of Technology, Harbin, China
• Abir Rous (woah!)