Author
Erbay, Hüsnü Ata, Rajagopal, K. R., Saccomandi, G., Şengül, Y.
Publication Date
2023-10
Publication Place
-
Sage
Subject
Dispersive transverse waves, Implicit constitutive theory, Improved Boussinesq equations, Strain-limiting model, Traveling wave solutions
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
1081-2865
Record ID
7119ddc6-5526-4235-b333-c44c02109b7a
Library Location
Natural and Mathematical Sciences
Date
2023-10
Notes
Istituto Nazionale di Alta Matematica "Francesco Severi" ; Gruppo Nazionale per la Fisica Matematica ; Instituto Nazionale di Fisica Nucleare
Sample Text
It is well known that propagation of waves in homogeneous linearized elastic materials of infinite extent is not dispersive. Motivated by the work of Rubin, Rosenau, and Gottlieb, we develop a generalized continuum model for the response of strain-limiting materials that are dispersive. Our approach is based on both a direct inclusion of Rivlin–Ericksen tensors in the constitutive relations and writing the linearized strain in terms of the stress. As a result, we derive two coupled generalized improved Boussinesq-type equations in the stress components for the propagation of pure transverse waves. We investigate the traveling wave solutions of the generalized Boussinesq-type equations and show that the resulting ordinary differential equations form a Hamiltonian system. Linearly and circularly polarized cases are also investigated. In the case of unidirectional propagation, we show that the propagation of small-but-finite amplitude long waves is governed by the complex Korteweg–de Vries (KdV) equation.
DOI
10.1177/10812865231188931
