Description

• Title:
  Pointwise Comparison Principle for clamped Timoshenko beam
• Creator:
  Bartuzel, Grzegorz;
  Fryszkowski, Andrzej
• Description:
  We present the properties of three Green functions for: \roster \item"1." general complex ``clamped beam'' $$ \gather D_{\alpha ,\beta }[y] \equiv y^{\prime \prime \prime \prime} -(\alpha ^{2}+\beta ^{2}) y^{\prime \prime }+\alpha ^{2}\beta^{2}y=f, \\ y(0) =y(1) =y^{\prime }(0) =y^{\prime}(1) =0. \tag{BC} \endgather $$ \item"2." Timoshenko clamped beam $D_{\alpha ,\overline{\alpha }}[y] \equiv f$ with (BC). \item"3." Euler-Bernoulli clamped beam $D_{k(1+i) ,k(1-i)} [ y] \equiv f$ with (BC). \endroster In case 1. we represent solution via a Green operator expressed in terms of Kourensky type system of fundamental solutions for homogeneous case. This condense form is, up-to our knowledge, new even for the Euler-Bernoulli clamped beam and it allows to recognize the set of $\alpha ^{\prime }s$ for which the Pointwise Comparison Principle for the Timoshenko beam holds. The presented approach to positivity of the Green function is much straightforward then ones known in the literature for the case 3 (see \cite{12}).
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2012.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 39, No 2 (June 2012); 335 - 359;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2012.018/8367
• Subject:
  Timoshenko beam;
  Euler-Bernoulli clamped beam;
  Pointwise Comparison Principle;
  nonnegativity of Green function;
  fourth order ODE;
  34B27;
  34B60;
  34L40;
  47E05;
  70J10
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2012.018
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other