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Method for describing large deflection vibration of rubber cylindrical shell

A cylindrical shell, large deflection technology, applied in the field of mechanics

Pending Publication Date: 2021-01-22
DALIAN NATIONALITIES UNIVERSITY
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Problems solved by technology

[0006] In order to solve the problem of establishing a mathematical model to be able to study nonlinear vibrations, the present invention proposes the following technical solutions: a method for describing the large deflection vibration of a rubber cylindrical shell, using the energy principle to give a nonlinear differential equation system describing the motion of a cylindrical shell

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  • Method for describing large deflection vibration of rubber cylindrical shell
  • Method for describing large deflection vibration of rubber cylindrical shell
  • Method for describing large deflection vibration of rubber cylindrical shell

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Embodiment Construction

[0022] 1 Overview of the invention

[0023]At present, there are many studies on the nonlinear vibration of cylindrical shells, but most of them are based on linear constitutive relations. In particular, there are few literature reports on the nonlinear motion of cylindrical shells based on the hyperelastic constitutive relation. The focus of the present invention's research mainly focuses on the superelasticity of rubber material rather than other properties (such as viscoelasticity etc.), to the rubber cylindrical shell characterized by the constitutive character of incompressible Mooney-Rivlin material, studied its radial simple harmonic excitation Some interesting motions under the law, such as periodic, quasi-periodic and chaos. Section 2 gives the relevant tensor knowledge. In addition, based on Donnell's nonlinear thin shell theory, the governing differential equation describing the motion of the rubber cylindrical shell is given; Section 3 uses the Runge-Kutta method ...

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Abstract

The invention discloses a method for describing large-deflection vibration of a rubber cylindrical shell, belongs to the field of mechanics, aims to solve the problem of establishing a mathematical model to research nonlinear vibration, and is characterized in that a nonlinear differential equation set for describing movement of the cylindrical shell is given by utilizing an energy principle, andthe effect is that based on a Donnell nonlinear thin shell theory, a Lagrange equation and a small strain hypothesis, the nonlinear differential equation for describing the large-deflection vibrationof the rubber cylindrical shell is obtained. According to the method, a mathematical model is established and solved, so that the basis of nonlinear vibration research of the thin-wall rubber cylindrical shell is provided, and the motion behavior of the thin-wall rubber cylindrical shell is analyzed through the mathematical model.

Description

technical field [0001] The invention belongs to the field of mechanics and relates to a method for describing large deflection vibration of a rubber cylindrical shell. Background technique [0002] Rubber is a typical hyperelastic material, and some of its important properties (such as high elasticity, large deformation, etc.) are an indispensable part of engineering. Correspondingly, there is a wide range of products composed of these materials, such as tires, gaskets, oil pipes, etc. Due to its excellent mechanical properties, cylindrical shells are widely used in spacecraft, delivery pipes, engine drums and other fields. For thin-shell structures and flexible structures, they produce typical nonlinear responses to perturbation excitations. [1] . In addition, the hyperelastic cylindrical shell has the characteristics of geometric nonlinearity and physical nonlinearity, so it is of great significance to study its nonlinearity, especially the chaotic vibration characteris...

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Application Information

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IPC IPC(8): G06F30/20G06F113/24G06F119/14
Inventor 袁学刚张文正许杰张静
Owner DALIAN NATIONALITIES UNIVERSITY
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