• Corpus ID: 238744419

Variational setting for cracked beams and shallow arches

@inproceedings{Gutman2021VariationalSF,
  title={Variational setting for cracked beams and shallow arches},
  author={Semion Gutman and Junhong Ha and Sudeok Shon},
  year={2021}
}
We develop a rigorous mathematical framework for the weak formulation of cracked beams and shallow arches problems. First, we discuss the crack modeling by means of massless rotational springs. Then we introduce Hilbert spaces, which are sufficiently wide to accommodate such representations. Our main result is the introduction of a specially designed linear operator that ”absorbs” the boundary conditions at the cracks. We also provide mathematical justification and derivation of the Modified… 

Figures from this paper

Equations of motion for cracked beams and shallow arches
Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that ”absorbs” the boundary conditions at the cracks. Then the

References

SHOWING 1-10 OF 16 REFERENCES
Multi-cracked Euler-Bernoulli beams: Mathematical modeling and exact solutions
Localized flexibility models of cracks enable one for simple and effective representation of the behavior of damaged beams and frames. Important applications, such as the determination of closed-form
One-dimensional theory of cracked Bernoulli-Euler beams
Abstract The differential equation and associated boundary conditions for a nominally uniform Bernoulli-Euler beam containing one or more pairs of symmetric cracks are derived. The reduction to one
Parameter identification for weakly damped shallow arches
Abstract The paper considers shallow arches under weak damping with hinged and clamped boundary conditions. A self-contained presentation of the existence, uniqueness, and regularity of the solutions
DYNAMICS OF TRANSVERSELY VIBRATING BEAMS USING FOUR ENGINEERING THEORIES
Abstract In this paper, the full development and analysis of four models for the transversely vibrating uniform beam are presented. The four theories are the Euler–Bernoulli, Rayleigh, shear and
Exact closed-form solution for the vibration modes of the Euler-Bernoulli beam with multiple open cracks
Abstract In this study, exact closed-form expressions for the vibration modes of the Euler–Bernoulli beam in the presence of multiple concentrated cracks are presented. The proposed expressions are
NATURAL FREQUENCIES OF A BEAM WITH AN ARBITRARY NUMBER OF CRACKS
In this article a new technique is proposed for calculating natural frequencies of a vibrating beam with an arbitrary finite number of transverse open cracks. The main feature of this method is
Analysis of the effect of cracks on the natural frequencies of a cantilever beam
Abstract A method of analysis of the effect of two open cracks upon the frequencies of the natural flexural vibrations in a cantilever beam is presented. Two types of cracks are considered:
A class of integro-differential equations incorporating nonlinear and nonlocal damping with applications in nonlinear elastodynamics: Existence via time discretization
A general model for the description of, e.g., an extensible beam is studied, incorporating weak, viscous and strong as well as Balakrishnan–Taylor damping. Convergence of a sequence of approximate
Uniform attractor of shallow arch motion under moving points load
  • S. Gutman, J. Ha
  • Mathematics
    Journal of Mathematical Analysis and Applications
  • 2018
Abstract We study the long time behavior of arches and membrane-like structures in the strong damping case. Our main goal is to incorporate moving points load, and to establish the existence of a
Detection of localised damage in plane circular arches by frequency data
The possibility to detect the structural damage affecting a narrow zone of a doubly hinged plane circular arch by means of a few measured natural frequencies is considered. Such localised damage
...
1
2
...