Dynamic behavior of cracked beams and shallow arches

We develop a rigorous mathematical framework for studying dynamic behavior of cracked beams and shallow arches. The governing equations are derived from the first principles, and stated in terms of the subdifferentials of the bending and the axial potential energies. The existence and the uniqueness...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society pp. 869 - 890
Main Authors Semion Gutman, 하준홍, 손수덕
Format Journal Article
LanguageEnglish
Published 대한수학회 01.09.2022
Subjects
수학
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Summary:We develop a rigorous mathematical framework for studying dynamic behavior of cracked beams and shallow arches. The governing equations are derived from the first principles, and stated in terms of the subdifferentials of the bending and the axial potential energies. The existence and the uniqueness of the solutions is established under various conditions. The corresponding mathematical tools dealing with vector-valued functions are comprehensively developed. The motion of beams and arches is studied under the assumptions of the weak and strong damping. The presence of cracks forces weaker regularity results for the arch motion, as compared to the beam case. KCI Citation Count: 0
Bibliography:https://jkms.kms.or.kr/journal/view.html?doi=10.4134/JKMS.j210650
ISSN:0304-9914
2234-3008
DOI:10.4134/JKMS.j210650