Nonlinear Waves in Elastic MediaCRC Press, 31.08.1995 - 256 Seiten Nonlinear Waves in Elastic Media explores the theoretical results of one-dimensional nonlinear waves, including shock waves, in elastic media. It is the first book to provide an in-depth and comprehensive presentation of the nonlinear wave theory while taking anisotropy effects into account. The theory is completely worked out and draws on 15 years of research by the authors, one of whom also wrote the 1965 classic Magnetohydrodynamics. Nonlinear Waves in Elastic Media emphasizes the behavior of quasitransverse waves and analyzes arbitrary discontinuity disintegration problems, illustrating that the solution can be non-unique - a surprising result. The solution is shown to be especially interesting when anisotropy and nonlinearity effects interact, even in small-amplitude waves. In addition, the text contains an independent mathematical chapter describing general methods to study hyperbolic systems expressing the conservation laws. The theoretical results described in Nonlinear Waves in Elastic Media allow, for the first time, discovery and interpretation of many new peculiarities inherent to the general problem of discontinuous solutions and so provide a valuable resource for advanced students and researchers involved with continuum mechanics and partial differential equations. |
Inhalt
Preface | 1 |
Riemann Waves | 67 |
Shock Waves | 81 |
Unsteady SelfSimilar Problems for Small Amplitude | 123 |
TwoDimensional Steady Nonlinear Waves | 153 |
Simplified Equations NonselfSimilar Problems | 163 |
ViscousElastic Medium Motion | 175 |
Finite Amplitude Waves in Weakly Anisotropic Media | 203 |
229 | |
235 | |
Andere Ausgaben - Alle anzeigen
Nonlinear Waves in Elastic Media A.G. Kulikovskii,Elena I. Sveshnikova Eingeschränkte Leseprobe - 2021 |
Nonlinear Waves in Elastic Media A.G. Kulikovskii,Elena I. Sveshnikova Eingeschränkte Leseprobe - 2021 |
Häufige Begriffe und Wortgruppen
A₁ anisotropy asymptotics boundary conditions c₁ c₂ Chapter characteristic velocities coefficients coincide components conservation laws considered const continuum mechanics coordinate system D₁ deformation depend eigenvalues eigenvector elastic media elastic potential equality equations evolutionary conditions evolutionary segments evolutionary shock expression extremum fast Riemann wave fast shock wave fast wave finite follows function incompressible media inequality initial point integral curve interaction intersection isotropic Jouget point linear magnetohydrodynamics matrix medium nonevolutionary nonlinear waves obtained one-dimensional parameter plane plane-polarized quadrant quantity quasilongitudinal wave quasitransverse waves R₁ relations represented satisfied second type Section self-similar self-similar problem shock adiabat shock velocity shown in Figure singular points slow shock wave slow waves small perturbations strain tensor structure symmetrical tangent tensor transverse transverse waves u₁ and u2 u₁-axis u₂ u2-axis variations vector W₁ W₂ wave corresponding wave isotropy waves propagating მე მთ მი