Samsonov, A. M. Nonlinear strain waves in elastic waveguides. (English) Zbl 0806.73018 Jeffrey, A. (ed.) et al., Nonlinear waves in solids. Lectures presented at the CISM course, held in Udine, Italy, September 13-17, 1993. Wien: Springer-Verlag. CISM Courses Lect. 341, 349-382 (1994). Strain wave propagation in nonlinearly elastic waveguides is considered. The general idea is how, starting from the first principles, to reduce the initial highly nonlinear elastic wave problem governed by coupled p.d.e. to the only one “double dispersion” equation, describing longitudinal strain waves in a one-dimensional waveguide, e.g., in a rod. The problem of wave motion in a rod, having slowly varying cross-section or elastic moduli is solved. Special attention is paid to nonlinear dissipative waves, corresponding to the wave motion in a rod embedded into an active or a dissipative medium.For the entire collection see [Zbl 0791.35001]. Cited in 44 Documents MSC: 74J10 Bulk waves in solid mechanics 35Q72 Other PDE from mechanics (MSC2000) Keywords:double dispersion equation; Abel equation; rod; slowly varying cross- section; dissipative waves PDFBibTeX XMLCite \textit{A. M. Samsonov}, CISM Courses Lect. 341, 349--382 (1994; Zbl 0806.73018)