823 research outputs found
Surface acoustic waves in rotating orthorhombic crystals
The propagation of surface (Rayleigh) waves over a rotating orthorhombic
crystal is studied. The crystal possesses three crystallographic axes, normal
to the symmetry planes: the half-space is cut along a plane normal to one of
these axes, the wave travels in the direction of another, and the rotation
occurs at a uniform rate about any of the three axes. The secular equation for
the surface wave speed is found explicitly; in contrast to the non-rotating
case, it is dispersive (frequency-dependent). Both Coriolis and centrifugal
accelerations appear in the equations of motion: none can be neglected in favor
of the other, even at small rotation rates
Rayleigh waves and surface stability for Bell materials in compression; comparison with rubber
The stability of a Bell-constrained half-space in compression is studied. To
this end, the propagation of Rayleigh waves on the surface of the material when
it is maintained in a static state of triaxial prestrain is considered. The
prestrain is such that the free surface of the half-space is a principal plane
of deformation. The exact secular equation is established for surface waves
traveling in a principal direction of strain with attenuation along the
principal direction normal to the free plane. As the half-space is put under
increasing compressive loads, the speed of the wave eventually tends to zero
and the bifurcation criterion, or stability equation, is reached.
Then the analysis is specialized to specific forms of strain energy functions
and prestrain, and comparisons are made with results previously obtained in the
case of incompressible neo-Hookean or Mooney-Rivlin materials. It is found that
these rubber-like incompressible materials may be compressed more than "Bell
empirical model" materials, but not as much as "Bell simple hyperelastic"
materials, before the critical stretches, solutions to the bifurcation
criterion, are reached. In passing, some classes of incompressible materials
which possess a relative-universal bifurcation criterion are presented
Rayleigh waves in anisotropic crystals rotating about the normal to a symmetry plane
The propagation of surface acoustic waves in a rotating anisotropic crystal
is studied. The crystal is monoclinic and cut along a plane containing the
normal to the symmetry plane; this normal is also the axis of rotation. The
secular equation is obtained explicitly using the "method of the polarization
vector", and it shows that the wave is dispersive and decelerates with
increasing rotation rate. The case of orthorhombic symmetry is also treated.
The surface wave speed is computed for 12 monoclinic and 8 rhombic crystals,
and for a large range of the rotation rate/wave frequency ratio
Stoneley waves and interface stability of Bell materials in compression; Comparison with rubber
Two semi-infinite bodies made of prestressed, homogeneous, Bell-constrained,
hyperelastic materials are perfectly bonded along a plane interface. The
half-spaces have been subjected to finite pure homogeneous predeformations,
with distinct stretch ratios but common principal axes, and such that the
interface is a common principal plane of strain. Constant loads are applied at
infinity to maintain the deformations and the influence of these loads on the
propagation of small-amplitude interface (Stoneley) waves is examined. In
particular, the secular equation is found and necessary and sufficient
conditions to be satisfied by the stretch ratios to ensure the existence of
such waves are given. As the loads vary, the Stoneley wave speed varies
accordingly: the upper bound is the `limiting speed' (given explicitly), beyond
which the wave amplitude cannot decay away from the interface; the lower bound
is zero, where the interface might become unstable. The treatment parallels the
one followed for the incompressible case and the differences due to the Bell
constraint are highlighted. Finally, the analysis is specialized to specific
strain energy densities and to the case where the bimaterial is uniformly
deformed (that is when the stretch ratios for the upper half-space are equal to
those for the lower half-space.) Numerical results are given for `simple
hyperelastic Bell' materials and for `Bell's empirical model' materials, and
compared to the results for neo-Hookean incompressible materials
Surface waves in orthotropic incompressible materials
The secular equation for surface acoustic waves propagating on an orthotropic
incompressible half-space is derived in a direct manner, using the method of
first integrals
Rayleigh waves in symmetry planes of crystals: explicit secular equations and some explicit wave speeds
Rayleigh waves are considered for crystals possessing at least one plane of
symmetry. The secular equation is established explicitly for surface waves
propagating in any direction of the plane of symmetry, using two different
methods. This equation is a quartic for the squared wave speed in general, and
a biquadratic for certain directions in certain crystals, where it may itself
be solved explicitly. Examples of such materials and directions are found in
the case of monoclinic crystals with the plane of symmetry at . The
cases of orthorhombic materials and of incompressible materials are also
treated
The explicit secular equation for surface acoustic waves in monoclinic elastic crystals
The secular equation for surface acoustic waves propagating on a monoclinic
elastic half-space is derived in a direct manner, using the method of first
integrals. Although the motion is at first assumed to correspond to generalized
plane strain, the analysis shows that only two components of the mechanical
displacement and of the tractions on planes parallel to the free surface are
nonzero. Using the Stroh formalism, a system of two second order differential
equations is found for the remaining tractions. The secular equation is then
obtained as a quartic for the squared wave speed. This explicit equation is
consistent with that found in the orthorhombic case. The speed of subsonic
surface waves is then computed for twelve specific monoclinic crystals
Surface waves in deformed Bell materials
Small amplitude inhomogeneous plane waves are studied as they propagate on
the free surface of a predeformed semi-infinite body made of Bell constrained
material. The predeformation corresponds to a finite static pure homogeneous
strain. The surface wave propagates in a principal direction of strain and is
attenuated in another principal direction, orthogonal to the free surface. For
these waves, the secular equation giving the speed of propagation is
established by the method of first integrals. This equation is not the same as
the secular equation for incompressible half-spaces, even though the Bell
constraint and the incompressibility constraint coincide in the isotropic
infinitesimal limit
Elastic interface acoustic waves in twinned crystals
A new type of Interface Acoustic Waves (IAW) is presented, for single-crystal
orthotropic twins bonded symmetrically along a plane containing only one common
crystallographic axis. The effective boundary conditions show that the waves
are linearly polarized at the interface, either transversally or
longitudinally. Then the secular equation is obtained in full analytical form
using new relationships for the displacement-traction quadrivector at the
interface. For Gallium Arsenide and for Silicon, it is found that the IAWs with
transverse (resp. longitudinal) polarization at the interface are of the
Stoneley (resp. leaky) type
Finite-amplitude inhomogeneous plane waves of exponential type in incompressible elastic materials
It is proved that elliptically-polarized finite-amplitude inhomogeneous plane
waves may not propagate in an isotropic elastic material subject to the
constraint of incompressibility. The waves considered are harmonic in time and
exponentially attenuated in a direction distinct from the direction of
propagation. The result holds whether the material is stress-free or
homogeneously deformed
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