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On wave-like differential equations in general Hilbert space with application to Euler–Bernoulli bending vibrations of a beam

  • Wave-like differential equations occur in many engineering applications. Here the engineering setup is embedded into the framework of functional analysis of modern mathematical physics. After an overview, the –Hilbert space approach to free Euler–Bernoulli bending vibrations of a beam in one spatial dimension is investigated. We analyze in detail the corresponding positive, selfadjoint differential operators of 4-th order associated to the boundary conditions in statics. A comparison with free string wave swinging is outlined.

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Author of HS ReutlingenHonegger, Reinhard; Lauxmann, Michael; Priwitzer, Barbara
Erschienen in:Partial differential equations in applied mathematics
Place of publication:Amsterdam
Document Type:Journal article
Publication year:2024
Tag:Euler–Bernoulli (partial) differential equation; Friedrichs extension; Sobolev spaces; boundary conditions; positive selfadjoint differential operators of 4-th order; wave-like differential equations in Hilbert space
Page Number:10
First Page:1
Last Page:10
Article Number:100617
DDC classes:510 Mathematik
Open access?:Ja
Licence (German):License Logo  Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International