1 Ocak 2023 Dergi makalesi Açık Erişim

Baysal, Onur; Hasanov, Alemdar; Kumarasamy, Sakthivel

DataCite XML

<?xml version='1.0' encoding='utf-8'?>
<resource xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://datacite.org/schema/kernel-4" xsi:schemaLocation="http://datacite.org/schema/kernel-4 http://schema.datacite.org/meta/kernel-4.1/metadata.xsd">
  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/270120</identifier>
  <creators>
    <creator>
      <creatorName>Baysal, Onur</creatorName>
      <givenName>Onur</givenName>
      <familyName>Baysal</familyName>
      <affiliation>Univ Malta, Dept Math, Msida, Malta</affiliation>
    </creator>
    <creator>
      <creatorName>Hasanov, Alemdar</creatorName>
      <givenName>Alemdar</givenName>
      <familyName>Hasanov</familyName>
      <affiliation>Kocaeli Univ, Dept Math, Altunsehir Str,Ayazma Villalari,22 Bahcecik Basisk, TR-41030 Izmit, Kocaeli, Turkiye</affiliation>
    </creator>
    <creator>
      <creatorName>Kumarasamy, Sakthivel</creatorName>
      <givenName>Sakthivel</givenName>
      <familyName>Kumarasamy</familyName>
      <affiliation>Indian Inst Space Sci &amp; Technol IIST, Dept Math, Trivandrum, India</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Determination Of Unknown Shear Force In Transverse Dynamic Force Microscopy From Measured Final Data</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2023</publicationYear>
  <dates>
    <date dateType="Issued">2023-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/270120</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1515/jiip-2023-0021</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;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&lt;/p&gt;
&lt;p&gt;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),&lt;/p&gt;
&lt;p&gt;subject to the homogeneous initial conditions and the boundary conditions&lt;/p&gt;
&lt;p&gt;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),&lt;/p&gt;
&lt;p&gt;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&lt;/p&gt;
&lt;p&gt;J(F) = 1/2 parallel to Phi g - u(T)parallel to(2)(L2(0,l))&lt;/p&gt;
&lt;p&gt;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.&lt;/p&gt;</description>
  </descriptions>
</resource>