0
Research Papers

Numerical Analysis of Transient Wave Propagation in Nonlinear One-Dimensional Waveguides by Using the Spectral Finite Element Method

[+] Author and Article Information
Yu Liu, Andrew J. Dick

Nonlinear Phenomena Laboratory,
Department of Mechanical Engineering and Materials Science,
Rice University,
Houston, TX 77005

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 26, 2013; final manuscript received July 12, 2014; published online April 2, 2015. Assoc. Editor: Carmen M. Lilley.

J. Comput. Nonlinear Dynam 10(5), 051003 (Sep 01, 2015) (10 pages) Paper No: CND-13-1233; doi: 10.1115/1.4028015 History: Received September 26, 2013; Revised July 12, 2014; Online April 02, 2015

In this paper, transient wave propagation in nonlinear one-dimensional (1D) waveguides is studied. A complete nonlinear (CN) 1D model accounting for both axial and transverse displacements is developed and geometric and material nonlinearities are separately modeled. The alternating frequency-time finite element method (AFT-FEM) is implemented for this complete 1D model. Numerical simulations are conducted and the response behaviors for axial and transverse motions are analyzed. Comparison of the responses for the geometrically nonlinear (GN) model with a corresponding linear model supports predictions made from the previous analytical studies that the geometric nonlinearity has limited influence on the response of transient transverse waves in the intermediate strain regime. On the contrary, strong nonlinear behavior appears in the response for the materially nonlinear (MN) models. Depending on the local nonlinear property of the material in the intermediate strain regime, the amplitude of the response can be significantly influenced and additional dispersion can be introduced into the response. An exploration of the interaction between the geometric nonlinearity and the material nonlinearity for a rod model in a large strain regime is also conducted and the responses are analyzed by using time-frequency analysis. The competing effect of the geometric nonlinearity and the material nonlinearity can result in a pseudolinear response in a strong nonlinear system for a given range of impact loading.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Nonlinear constitutive relationship for an aluminum alloy

Grahic Jump Location
Fig. 2

Simulation conditions for a rod subject to an axial impact load

Grahic Jump Location
Fig. 3

Simulation conditions for a beam subject to a transverse impact load

Grahic Jump Location
Fig. 4

Impact force profile

Grahic Jump Location
Fig. 5

Spectrum of the impact force

Grahic Jump Location
Fig. 6

Comparison of the linear and nonlinear velocity responses of the GN rod model at location A. (a) The complete response. (b) The nonlinear component Vd.

Grahic Jump Location
Fig. 7

Comparison of the linear and nonlinear velocity responses of the GN beam model at location B. (a) The complete response. (b) The nonlinear component Vd.

Grahic Jump Location
Fig. 8

Comparison of the linear and nonlinear velocity responses of the GN beam model at location C. (a) The complete response. (b) The nonlinear component Vd.

Grahic Jump Location
Fig. 11

Comparison of the linear and nonlinear velocity responses of the MN beam model at location C. (a) The complete response. (b) The nonlinear component Vd.

Grahic Jump Location
Fig. 10

Comparison of the linear and nonlinear velocity responses of the MN beam model at location B. (a) The complete response. (b) The nonlinear component Vd.

Grahic Jump Location
Fig. 9

Comparison of the linear and nonlinear velocity responses of the MN rod model at location A. (a) The complete response. (b) The nonlinear component Vd.

Grahic Jump Location
Fig. 13

STFT results of different rod models at the observation location A when the impact load magnitude F = 3000 kN. Response for (a) the GN rod model, (b) the MN rod model with α = −111, and (c) the CN rod model combined with α = −111 is compared to the case of linear rod model (dotted black contour line)

Grahic Jump Location
Fig. 12

The predicted responses at the observation location A when the impact load magnitude F = 3000 kN for the GN rod model, the MN rod model with α = −111, the CN rod model combined with α = −111, and the linear rod model

Grahic Jump Location
Fig. 14

Phase velocity versus magnitude and frequency when α = 20

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In