1 Ocak 2023 Dergi makalesi Açık Erişim

Baysal, Onur; Hasanov, Alemdar; Kumarasamy, Sakthivel

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<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
  <dc:creator>Baysal, Onur</dc:creator>
  <dc:creator>Hasanov, Alemdar</dc:creator>
  <dc:creator>Kumarasamy, Sakthivel</dc:creator>
  <dc:date>2023-01-01</dc:date>
  <dc:description>In this paper, we present a new methodology, based on the inverse problem approach, for the determination of an unknown shear force acting on the inaccessible tip of the microcantilever, which is a key component of transverse dynamic force microscopy (TDFM). The mathematical modelling of this phenomenon leads to the inverse problem of determining the shear force g(t) acting on the inaccessible boundary x = l in a system governed by the variable coefficient Euler-Bernoulli equation
r(A)(x)u(tt) + mu(x)u(t) + (r(x)u(xx) + kappa(x)u(xxt))(xx) = 0, (x, t) is an element of (0, l) x (0, T),
subject to the homogeneous initial conditions and the boundary conditions
u(0, t) = u(0)(t), u(x)(0, t) = 0, (u(xx)(x, t) + kappa(x)u(xxt))(x=l) = 0, (-(r(x)u(xx) + kappa(x)u(xxt))x)(x=l) = g(t),
from the final time measured output (displacement) u(T) (x) := u( x, T). We introduce the input-output map (Phi g)(x) := u( x, T; g), g is an element of G, and prove that it is a compact and Lipschitz continuous linear operator. Then we introduce the Tikhonov functional
J(F) = 1/2 parallel to Phi g - u(T)parallel to(2)(L2(0,l))
and prove the existence of a quasi-solution of the inverse problem. We derive a gradient formula for the Frechet gradient of the Tikhonov functional through the corresponding adjoint problem solution and prove that it is a Lipschitz continuous functional. The results of the numerical experiments clearly illustrate the effectiveness and feasibility of the proposed approach.</dc:description>
  <dc:identifier>https://aperta.ulakbim.gov.trrecord/270120</dc:identifier>
  <dc:identifier>oai:aperta.ulakbim.gov.tr:270120</dc:identifier>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:rights>http://www.opendefinition.org/licenses/cc-by</dc:rights>
  <dc:source>JOURNAL OF INVERSE AND ILL-POSED PROBLEMS 18</dc:source>
  <dc:title>Determination of unknown shear force in transverse dynamic force microscopy from measured final data</dc:title>
  <dc:type>info:eu-repo/semantics/article</dc:type>
  <dc:type>publication-article</dc:type>
</oai_dc:dc>