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Acta Mechanica Solida Sinica

, Volume 22, Issue 3, pp 267–275 | Cite as

Nonlinear dynamics of axially accelerating viscoelastic beams based on differential quadrature

  • Hu Ding
  • Liqun Chen
Article

Abstract

This paper investigates nonlinear dynamical behaviors in transverse motion of an axially accelerating viscoelastic beam via the differential quadrature method. The governing equation, a nonlinear partial-differential equation, is derived from the viscoelastic constitution relation using the material derivative. The differential quadrature scheme is developed to solve numerically the governing equation. Based on the numerical solutions, the nonlinear dynamical behaviors are identified by use of the Poincaré map and the phase portrait. The bifurcation diagrams are presented in the case that the mean axial speed and the amplitude of the speed fluctuation are respectively varied while other parameters are fixed. The Lyapunov exponent and the initial value sensitivity of the different points of the beam, calculated from the time series based on the numerical solutions, are used to indicate periodic motions or chaotic motions occurring in the transverse motion of the axially accelerating viscoelastic beam.

Key words

nonlinear partial-differential equation numerical solution chaos bifurcation differential quadrature 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2009

Authors and Affiliations

  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghaiChina
  2. 2.Department of MechanicsShanghai UniversityShanghaiChina

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