Dynamic behavior of cracked beams and shallow arches
1
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
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.
Abstract
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.
참고문헌 (10)
- J. M. Ball, "Stability theory for an extensible beam", J. Differential Equations, 14, pp.399~418 (1973)[DOI]
- V. Barbu, "Nonlinear differential equations of monotone types in Banach spaces, Springer Monographs in Mathematics" (2010), Springer
- H. Brézis, "Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert" (1973), North-Holland Publishing Co
- M. N. Cerri, "Detection of localised damage in plane circular arches by frequency data", J. Sound Vibration, 270(1), pp.39~59 (2004)
- E. Emmrich, "A class of integro-differential equations incorpo-rating nonlinear and nonlocal damping with applications in nonlinear elastodynamics: existence via time discretization", Nonlinearity, 24(9), pp.2523~2546 (2011)[DOI]
- S. Gutman, "Parameter identification for weakly damped shallow arches", J. Math. Anal. Appl, 403(1), pp.297~313 (2013)[DOI]
- Semion Gutman, "EQUATIONS OF MOTION FOR CRACKED BEAMS AND SHALLOW ARCHES", Nonlinear Functional Analysis and Applications, 27(2), pp.405~432 (2022), 경남대학교 수학교육과[DOI]
- S. Gutman, "Variational setting for cracked beams and shallow arches", Arch. Appl. Mech, 92, pp.2225~2236 (2022)[DOI]
- J.-L. Lions, "Non-homogeneous boundary value problems and applica-tions. Vol. I" (1972), Springer-Verlag
- R. Temam, "Infinite-dimensional dynamical systems in mechanics and physics" (1997), Springer-Verlag