Generalized factorization method in spatial dynamical mixed problems of elasticity theory (Obobshchennyj metod faktorizatsii v prostranstvennykh dinamicheskikh smeshannykh zadachakh teorii uprugosti). (Russian) Zbl 0588.73014
Moskva: “Nauka”. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 256 p. R. 3.00 (1984).
The eight chapters cover equations applied to elasticity. After chapters on basic properties of such integral equations (30 pp.), factorization of (matrix-) functions which appear as their kernels (18 pp.), and systems of such equations (45 pp.), the author deals with problems in infinite wedges (35 pp.), the use of Fourier transforms (30 pp.), the method of false position (30 pp.), linear systems of one-dimensional equations (15 pp.) and finally, as announced in the first chapter, mixed problems in elastodynamics. There are about 120 references, mainly in Russian.
The book discusses general methods for solving mixed boundary-value problems in the vibration of stampers on semi-infinite elastic media, layered, anisotropic or pure. The contact region may be arbitrary, bounded or unbounded, even wedge-shaped. The range of possible applications is very wide: geophysics and seismology, electroacoustical instruments for surface waves and acoustics in general, dynamics of foundations, even flaw detection. Despite this advertising of applications the book is heavily theoretical and based on a Green function-functional analytic approach with quite detailed calculations throughout, and in the final chapter covers stampers or dies.
The book discusses general methods for solving mixed boundary-value problems in the vibration of stampers on semi-infinite elastic media, layered, anisotropic or pure. The contact region may be arbitrary, bounded or unbounded, even wedge-shaped. The range of possible applications is very wide: geophysics and seismology, electroacoustical instruments for surface waves and acoustics in general, dynamics of foundations, even flaw detection. Despite this advertising of applications the book is heavily theoretical and based on a Green function-functional analytic approach with quite detailed calculations throughout, and in the final chapter covers stampers or dies.
Reviewer: J.J.Cross
MSC:
74B99 | Elastic materials |
74H99 | Dynamical problems in solid mechanics |
74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |
74A55 | Theories of friction (tribology) |
74M15 | Contact in solid mechanics |
45F05 | Systems of nonsingular linear integral equations |
74H45 | Vibrations in dynamical problems in solid mechanics |
35A25 | Other special methods applied to PDEs |