Generalized point models in acousto-elastic interactions

Research output

Abstract

Vibrations of thin-walled mechanical constructions are often described by accepting approximate models that consider only some types of deformations. This essentially simplifies the analysis excluding the study of wave processes in the interior of the construction. Joints, cracks, reinforcements, etc. are described in the frame of these approximate models by fixing so-called contact conditions. These conditions can be treated as second level boundary conditions (boundary conditions inside usual boundary conditions fixed on the surface of elastic elements). Classical contact conditions allow point models of cracks, joints, attached masses and momentums, and other inhomogeneities to be introduced. However for practical applications accuracy of such models can appear not enough. Several examples when next order terms are significant are to be presented. Technique of self-adjoint operators perturbations in the form of zero-range potentials allows classical point models to be generalized and smaller order corrections to be included. The simplicity of solution construction remains the same as in classical models. The standard procedure of the generalized point models construction and many generalized point models are described in [1]. Some other models are to be presented. References: I.V. Andronov, Generalized point models in structural mechanics.

Original languageEnglish
JournalActa Acustica (Stuttgart)
Volume89
Issue numberSUPP.
Publication statusPublished - 1 May 2003

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interactions
boundary conditions
cracks
Interaction
reinforcement
fixing
inhomogeneity
momentum
operators
perturbation
vibration
Boundary Conditions
Crack

Scopus subject areas

  • Acoustics and Ultrasonics

Cite this

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title = "Generalized point models in acousto-elastic interactions",
abstract = "Vibrations of thin-walled mechanical constructions are often described by accepting approximate models that consider only some types of deformations. This essentially simplifies the analysis excluding the study of wave processes in the interior of the construction. Joints, cracks, reinforcements, etc. are described in the frame of these approximate models by fixing so-called contact conditions. These conditions can be treated as second level boundary conditions (boundary conditions inside usual boundary conditions fixed on the surface of elastic elements). Classical contact conditions allow point models of cracks, joints, attached masses and momentums, and other inhomogeneities to be introduced. However for practical applications accuracy of such models can appear not enough. Several examples when next order terms are significant are to be presented. Technique of self-adjoint operators perturbations in the form of zero-range potentials allows classical point models to be generalized and smaller order corrections to be included. The simplicity of solution construction remains the same as in classical models. The standard procedure of the generalized point models construction and many generalized point models are described in [1]. Some other models are to be presented. References: I.V. Andronov, Generalized point models in structural mechanics.",
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N2 - Vibrations of thin-walled mechanical constructions are often described by accepting approximate models that consider only some types of deformations. This essentially simplifies the analysis excluding the study of wave processes in the interior of the construction. Joints, cracks, reinforcements, etc. are described in the frame of these approximate models by fixing so-called contact conditions. These conditions can be treated as second level boundary conditions (boundary conditions inside usual boundary conditions fixed on the surface of elastic elements). Classical contact conditions allow point models of cracks, joints, attached masses and momentums, and other inhomogeneities to be introduced. However for practical applications accuracy of such models can appear not enough. Several examples when next order terms are significant are to be presented. Technique of self-adjoint operators perturbations in the form of zero-range potentials allows classical point models to be generalized and smaller order corrections to be included. The simplicity of solution construction remains the same as in classical models. The standard procedure of the generalized point models construction and many generalized point models are described in [1]. Some other models are to be presented. References: I.V. Andronov, Generalized point models in structural mechanics.

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