Nonlinear Longitudinal Bulk Strain Waves in Layered Elastic Waveguides
We consider long longitudinal bulk strain waves in layered waveguides using Boussinesq-type equations . The equations are developed using lattice models , and this is viewed as an extension of the Fermi–Pasta–Ulam problem . We describe semianalytical approaches to the solution of scattering problems in delaminated waveguides, and to the construction of the solution of an initial value problem in the class of periodic functions, motivated by the scattering problems.
Unable to display preview. Download preview PDF.
- Askar, A.: Lattice Dynamical Foundations of Continuum Theories: Elasticity, Piezoelectricity, Viscoelasticity, Plasticity. World Scientific, Singapore (1985). https://doi.org/10.1142/0192
- Fermi, E., Pasta, J., Ulam, S.: Studies of Nonlinear Problems. Los Alamos Scientific Laboratory Report No. LA-1940, 1955. Lect. Appl. Math. 15, 143–155 (1974)Google Scholar
- Il’yushina, E.A.: Towards formulation of elasticity theory of inhomogeneous solids with microstructure. Doctoral dissertation, PhD Thesis, Lomonosov Moscow State University (1976) (in Russian)Google Scholar
- Johnson, R.S.: A Modern Introduction to the Mathematical Theory of Water Waves. Cambridge University Press (1997). https://doi.org/10.1017/cbo9780511624056
- Khusnutdinova, K.R.: Wave dynamics of a medium constructed on the basis of a two-row system of particles. Deep Refinement of Hydrocarbon Material, 2, 136–145 (1993) (in Russian)Google Scholar
- Maugin, G.A.: Nonlinear Waves in Elastic Crystals. Oxford University Press (1999)Google Scholar
- Ostrovsky, L.A.: Nonlinear internal waves in a rotating ocean. Okeanologiya 18, 119–125 (1978).Google Scholar
- Pelinovsky, E.N.: On the soliton evolution in inhomogeneous media. Appl. Mech. Techn. Phys. 6, 80–85 (1971)Google Scholar
- Porubov, A.V.: Amplification of Nonlinear Strain Waves in Solids. World Scientific (2003). https://doi.org/10.1142/5238