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Initial‐boundary value problems in linear viscoelasticity on the half‐space
Author(s) -
Mark J.,
Meister E.
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670181502
Subject(s) - mathematics , mathematical analysis , laplace transform , fourier transform , boundary value problem , viscoelasticity , laplace transform applied to differential equations , physics , thermodynamics
After deriving the linear hereditary constitutive laws for viscoelasticity, deducing frequency representation and the correspondence principle to linear elastodynamics the weak form of the equations of motion and their decomposition into pseudo‐wave equations are stated. Applying a Laplace transform in the time domain the Green's tensor is constructed by means of a spatial distributional Fourier transform. A detailed discussion of the four main initial‐boundary value problems with prescribed displacement and traction components on the plane { x 3 = 0} leads to half‐space representations by inverse Fourier integrals. Finally some asymptotic behaviour of the solution in the original time domain is deduced.