Flexural vibrations of nonlinearly elastic circular rings

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• 作者：Walter Lacarbonara (1)
  Andrea Arena (1)
  Stuart S. Antman (2)
  
  1. Department of Structural and Geotechnical Engineering ; Sapienza University of Rome ; 00184聽 ; Rome ; Italy
  2. Department of Mathematics ; Institute for Physical Science and Technology ; and Institute for Systems Research ; University of Maryland ; College Park ; MD聽 ; 20742-4015 ; USA
  
• 关键词：Nonlinear flexural vibrations ; Circular rings ; Nonlinearly elastic constitutive laws ; Backbone curves and surfaces ; Softening and hardening response ; Nonlinear normal modes
• 刊名：Meccanica
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：50
• 期：3
• 页码：689-705
• 全文大小：873 KB
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• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Civil Engineering
  Automotive and Aerospace Engineering and Traffic
  Mechanical Engineering
  
• 出版者：Springer Netherlands
• ISSN：1572-9648

文摘

This paper treats free nonlinear flexural vibrations of circular elastic rings in the context of a geometrically exact formulation accounting for the effects of nonlinear material behavior. A direct asymptotic approach based on the method of multiple scales is used to investigate such vibrations. It is shown that the flexural motions are softening for linearly elastic rings, in agreement with previous results in the literature, while there are nonlinearly elastic rings for which the motions are hardening. There are thresholds in the nonlinear constitutive laws separating softening from hardening behaviors.