Modeling of the dynamics of plane functionally graded waveguides based on the different formulations of the plate theory of I. N. Vekua type

• Published in: Mechanics of advanced materials and structures Vol. 28; no. 5; pp. 506 - 515
• Main Authors: Egorova, Olga V., Kurbatov, Alexey S., Rabinskiy, Lev N., Zhavoronok, Sergey I.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04.03.2021; Taylor & Francis Ltd
• Subjects: analytical dynamics; Dynamic structural analysis; Fields (mathematics); functionally graded materials; Lagrangian formalism; Mathematical analysis; normal waves; phase frequencies; Plate theory; plates; Spatial distribution; Thickness; Thin wall structures; Thin-walled waveguides; Wave dispersion; Wave propagation; Waveguides
• ISSN: 1537-6494; 1537-6532
• DOI: 10.1080/15376494.2019.1578008

The dynamics of elastic functionally graded waveguides with symmetric through-thickness structure is considered on the background of the new formulation of the Nth-order plate theory. The general plate model is based on the Lagrangian formalism of analytical dynamics and the dimensional reduction approach combined with the biorthogonal expansion technique applied to the spatial distribution of the displacement vector field. The use of compact basis is shown, the normal wave propagation in a plane waveguide is modeled, and the convergence is analyzed using the isotropic homogeneous plate as a test example. Finally, the same formulation is used to model the normal wave dispersion in functionally graded plates. The proposed method is a base for the investigation of the effect of uncertainties and for the solution of inverse coefficient problems for functionally graded thin-walled structures.