A high-order approach for modelling transient wave propagation problems using the scaled boundary finite element method

2013 ◽  
Vol 97 (13) ◽  
pp. 937-959 ◽  
Author(s):  
D. Chen ◽  
C. Birk ◽  
C. Song ◽  
C. Du
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
High Order ◽  
Transient Wave ◽  
Transient Wave Propagation ◽  
Scaled Boundary Finite Element ◽  
Element Method

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

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Yu Liu ◽  
Andrew J. Dick
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Geometric Nonlinearity ◽  
Material Nonlinearity ◽  
Transient Wave ◽  
One Dimensional ◽  
Transient Wave Propagation ◽  
1D Model ◽  
Element Method

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.

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