139 research outputs found
An existence result for a nonlinear transmission problems
Let and be open bounded subsets of of
class such that the closure of is contained in
. Let be a function in and let
and be continuous functions from to
. By exploiting an argument based on potential theory and on the
Leray-Schauder principle we show that under suitable and completely explicit
conditions on and there exists at least one pair of continuous
functions such that where the last equality is attained in certain weak sense. In a simple
example we show that such a pair of functions is in general
neither unique nor local unique. If instead the fourth condition of the problem
is obtained by a small nonlinear perturbation of a homogeneous linear
condition, then we can prove the existence of at least one classical solution
which is in addition locally unique
Eigenfrequency correction of Bloch-Floquet waves in a thin periodic bi-material strip with cracks lying on perfect and imperfect interfaces
We analyse an asymptotic low-dimensional model of anti-plane shear in a thin
bi-material strip containing a periodic array of interfacial cracks. Both ideal
and non-ideal interfaces are considered. We find that the previously derived
asymptotic models display a degree of inaccuracy in predicting standing wave
eigenfrequencies and suggest an improvement to the asymptotic model to address
this discrepancy. Computations demonstrate that the correction to the standing
wave eigenfrequencies greatly improve the accuracy of the low-dimensional
model
Frictionless Motion of Lattice Defects
Energy dissipation by fast crystalline defects takes place mainly through the
resonant interaction of their cores with periodic lattice. We show that the
resultant effective friction can be reduced to zero by appropriately tuned
acoustic sources located on the boundary of the body. To illustrate the general
idea, we consider three prototypical models describing the main types of
strongly discrete defects: dislocations, cracks and domain walls. The obtained
control protocols, ensuring dissipation-free mobility of topological defects,
can be also used in the design of meta-material systems aimed at transmitting
mechanical information
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