Acta Mechanica Solida Sinica

, Volume 22, Issue 4, pp 287–294 | Cite as

Nonlinear Flexural Waves in Large-Deflection Beams

  • Shanyuan Zhang
  • Zhifang Liu
  • Guoyun Lu
Article

Abstract

The equation of motion for a large-deflection beam in the Lagrangian description are derived using the coupling of flexural deformation and midplane stretching as a key source of nonlinearity and taking into account the transverse, axial and rotary inertia effects. Assuming a traveling wave solution, the nonlinear partial differential equations are then transformed into ordinary differential equations. Qualitative analysis indicates that the system can have either a homoclinic orbit or a heteroclinic orbit, depending on whether the rotary inertia effect is taken into account. Furthermore, exact periodic solutions of the nonlinear wave equations are obtained by means of the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function m → 1 in the degenerate case, either a solitary wave solution or a shock wave solution can be obtained.

Key words

large-deflection beam nonlinear flexural wave Jacobi elliptic function expansion 

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Copyright information

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

Authors and Affiliations

  • Shanyuan Zhang
    • 1
  • Zhifang Liu
    • 1
  • Guoyun Lu
    • 1
  1. 1.Institute of Applied MechanicsTaiyuan University of TechnologyTaiyuanChina

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