Wave Theory of Impact and Professor Yury Rossikhin Contribution in the Field (A Memorial Survey)

Shitikova, Marina V.

doi:10.1007/s11665-018-3824-6

Cited by 3 publications

(2 citation statements)

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“…This peculiarity of the 3 g ( À t 0 =t i )-function allowed Rabotnov [36] to name it as the fractional exponential function. It is convenient to rewrite the operators entering in relationships (26) and (27) in the form…”

Section: Problem Formulationmentioning

confidence: 99%

“…However, emphasis in solving dynamic problems of viscoelastic bodies and structures subjected to impact loads was made by the research team [16,18,26] headed by Professor Yury Rossikhin [27]. For the analysis of impact response of structures, two approaches are used for modeling the contact force: (1) a linear viscoelastic buffer in the form of a linear spring-fractional derivative dashpot combination (the fractional derivative Maxwell model in Rossikhin and Shitikova [26,28] or the fractional derivative standard linear solid model in Rossikhin and Shitikova [29]) and (2) generalized Hertz contact law [30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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Impact response of a thin shallow doubly curved linear viscoelastic shell rectangular in plan

Shitikova

2022

Mathematics and Mechanics of Solids

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In this paper, we consider the problem on a transverse impact of a viscoelastic sphere upon a viscoelastic shallow doubly curved shell with rectangular platform, the viscoelastic features of which are defined via the fractional derivative standard linear solid models; in so doing, only Young’s time-dependent operators are preassigned, while the bulk moduli are considered to be constant values, since the bulk relaxation for the majority of materials is far less than the shear relaxation. Shallow panel’s displacement subjected to the concentrated contact force is found by the method of expansion in terms of eigen functions, and the sphere’s displacement under the action of the contact force, which is the sum of the shell’s displacement at the place of contact and local bearing of impactor and target’s materials, is defined from the equation of motion of the material point with the mass equal to sphere’s mass. Within the contact domain, the contact force is defined by the modified Hertzian contact law with the time-dependent rigidity function. For decoding the viscoelastic operators involving the problem under consideration, the algebra of Rabotnov’s fractional operators is employed. A nonlinear integro-differential equation is obtained either in terms of the contact force or in the local bearing of the target and impactor materials. Using the duration of contact as a small parameter, approximate analytical solutions have been found, which allow one to define the key characteristics of impact process.

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Section: Problem Formulationmentioning

confidence: 99%