Yazar
Erbay, Hüsnü Ata, Rajagopal, K. R., Saccomandi, G., Şengül, Y.
Basım Tarihi
2023-10
Basım Yeri
-
Sage
Konu
Dispersive transverse waves, Implicit constitutive theory, Improved Boussinesq equations, Strain-limiting model, Traveling wave solutions
Tür
Süreli Yayın
Dil
İngilizce
Dijital
Evet
Yazma
Hayır
Kütüphane
Özyeğin Üniversitesi
Demirbaş Numarası
1081-2865
Kayıt Numarası
7119ddc6-5526-4235-b333-c44c02109b7a
Lokasyon
Natural and Mathematical Sciences
Tarih
2023-10
Notlar
Istituto Nazionale di Alta Matematica "Francesco Severi" ; Gruppo Nazionale per la Fisica Matematica ; Instituto Nazionale di Fisica Nucleare
Örnek Metin
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
