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This book shows impressively how complex mathematical modeling of
materials can be applied to technological problems. Top-class
researchers present the theoretical approaches in modern mechanics
and apply them to real-world problems in solid mechanics, creep,
plasticity, fracture, impact, and friction. They show how they can
be applied to technological challenges in various fields like
aerospace technology, biological sciences and modern engineering
materials.
This book shows impressively how complex mathematical modeling of
materials can be applied to technological problems. Top-class
researchers present the theoretical approaches in modern mechanics
and apply them to real-world problems in solid mechanics, creep,
plasticity, fracture, impact, and friction. They show how they can
be applied to technological challenges in various fields like
aerospace technology, biological sciences and modern engineering
materials.
Among the variety of wave motions one can single out surface wave
pr- agation since these surface waves often adjust the features of
the energy transfer in the continuum (system), its deformation and
fracture. Predicted by Rayleigh in 1885, surface waves represent
waves localized in the vicinity
ofextendedboundaries(surfaces)of?uidsorelasticmedia. Intheidealcase
of an isotropic elastic half-space while the Rayleigh waves
propagate along the surface, the wave amplitude (displacement) in
the transverse direction exponentially decays with increasing
distance away from the surface. As a
resulttheenergyofsurfaceperturbationsislocalizedbytheRayleighwaves
within a relatively narrow layer beneath the surface. It is this
property of the surface waves that leads to the resonance phenomena
that accompany the motion of the perturbation sources (like surface
loads) with velocities close to the Rayleigh one; (see e. g. , R.
V. Goldstein. Rayleigh waves and resonance phenomena in elastic
bodies. Journal of Applied Mathematics and Mechanics (PMM), 1965,
v. 29, N 3, pp. 608-619). It is essential to note that resonance
phenomena are also inherent to the elastic medium in the case where
initially there are no free (unloaded) surfaces. However, they
occur as a result of an external action accompanied by the
violation of the continuity of certain physical quantities, e. g. ,
by crack nucleation and dynamic propagation. Note that the
aforementioned resonance phenomena are related to the nature of the
surface waves as homogeneous solutions (eigenfunctions) of the
dynamic elasticity equations for a half-space (i. e. nonzero
solutions at vanishing boundary conditions).
Among the variety of wave motions one can single out surface wave
pr- agation since these surface waves often adjust the features of
the energy transfer in the continuum (system), its deformation and
fracture. Predicted by Rayleigh in 1885, surface waves represent
waves localized in the vicinity
ofextendedboundaries(surfaces)of?uidsorelasticmedia. Intheidealcase
of an isotropic elastic half-space while the Rayleigh waves
propagate along the surface, the wave amplitude (displacement) in
the transverse direction exponentially decays with increasing
distance away from the surface. As a
resulttheenergyofsurfaceperturbationsislocalizedbytheRayleighwaves
within a relatively narrow layer beneath the surface. It is this
property of the surface waves that leads to the resonance phenomena
that accompany the motion of the perturbation sources (like surface
loads) with velocities close to the Rayleigh one; (see e. g. , R.
V. Goldstein. Rayleigh waves and resonance phenomena in elastic
bodies. Journal of Applied Mathematics and Mechanics (PMM), 1965,
v. 29, N 3, pp. 608-619). It is essential to note that resonance
phenomena are also inherent to the elastic medium in the case where
initially there are no free (unloaded) surfaces. However, they
occur as a result of an external action accompanied by the
violation of the continuity of certain physical quantities, e. g. ,
by crack nucleation and dynamic propagation. Note that the
aforementioned resonance phenomena are related to the nature of the
surface waves as homogeneous solutions (eigenfunctions) of the
dynamic elasticity equations for a half-space (i. e. nonzero
solutions at vanishing boundary conditions).
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