Computer simulation of solitary waves in a common or auxetic elastic rod with both quadratic and cubic nonlinearities

Dinh, T. Bui; Long, Van Cao; Xuan, Khoa Dinh; Wojciechowski, Krzysztof W.

doi:10.1002/pssb.201084221

Cited by 11 publications

(7 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It has been shown that these soliton solutions approximate very well numerical results obtained for various forms of initial pulses. Present considerations confirm the earlier result [20] that special exact solutions can be very useful for predicting more complicated solitary waves obtained by numerical simulations. The simulations showed also that the averaged amplitudes and velocities of solitary waves increase monotonically with the Poisson's ratio.…”

Section: Figuresupporting

confidence: 90%

“…Closing this section it is worth to stress that, as it was found earlier in other systems , both the velocity and amplitude of solitons are increasing functions of Poisson's ratio.…”

Section: Numerical Simulationssupporting

confidence: 52%

“…This is caused by the stronger secondary collision defined in Ref. [20], when the small pulses which have appeared during propagation collide continuously between themselves.…”

Section: Figurementioning

confidence: 98%

See 2 more Smart Citations

Solitary waves in auxetic rods with quadratic nonlinearity: Exact analytical solutions and numerical simulations

Dinh

Long

Wojciechowski

2015

Physica Status Solidi (b)

Self Cite

View full text Add to dashboard Cite

Special soliton analytical solutions are seeked for the so-called double dispersion equation (or Porubov's equation), which describes the propagation of longitudinal waves in an elastic rod. Using the F-expansion method, a new interesting class of traveling solitary waves is obtained. As a byproduct, the results obtained by other authors for some special cases are regained. Some numerical simulations are also performed. Splitting of various initial pulses during propagation into a sequence of solitary waves is considered. The dependence of the amplitude and the velocity of the solitary waves on Poisson's ratio is discussed in detail. Collisions between some obtained solitary waves are also presented. The simulation results are compared with the obtained exact analytical solutions-the latter reflect the perfect balance between the nonlinearity and dispersion. The comparison indicates that the obtained exact solutions are useful for describing more complicated wave fields studied by numerical simulations. It also indicates that the numerical results for auxetic materials are in better agreement with theoretical solutions than in the case of ordinary materials. Furthermore, one can conclude that the Secant pulse generates solitary waves closer to the analytical predictions than a Gaussian pulse. This is similar to the case of variational method, where the Secant trial function is also more proper than the Gaussian one.

show abstract

Section: Figuresupporting

confidence: 90%

“…Closing this section it is worth to stress that, as it was found earlier in other systems , both the velocity and amplitude of solitons are increasing functions of Poisson's ratio.…”

Section: Numerical Simulationssupporting

confidence: 52%

See 1 more Smart Citation

Solitary waves in auxetic rods with quadratic nonlinearity: Exact analytical solutions and numerical simulations

Dinh

Long

Wojciechowski

2015

Physica Status Solidi (b)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Auxetic materials have potential applications, including in the aerospace industry , textile fabrics , and bioprostheses , among others . There has been numerous experimental , theoretical , and simulation studies to investigate the auxeticity of materials. Approximately 70% of the known cubic materials show a negative Poisson's ratio along the

[1 \overset{1}{true} 0]

direction when they are stretched along the [110] direction .…”

Section: Introductionmentioning

confidence: 99%

Auxeticity of face‐centered cubic metal (001) nanoplates

Kim

Kwon

et al. 2015

Physica Status Solidi (b)

View full text Add to dashboard Cite

We present the results of an atomistic study on the Poisson's ratios of face‐centered cubic metal (001) nanoplates under tensile loading. Here, we find that the behavior of the Poisson's ratios of metal nanoplates is strongly dependent on the characteristics of a phase transformation that takes place in their bulk counterparts as well as on the amount of compressive stress induced in the nanoplates. In addition, we discuss the effects of the nanoplate thickness and temperature on the mechanical behavior of the nanoplates. As the thickness decreases, the amount of compressive stress increases. As a result, the metal nanoplates become more auxetic. Higher temperatures cause the phase transformation to occur sooner. Thus, strongly auxetic nanoplates can be obtained by raising the temperature. In addition to investigating the effects of the thickness and temperature, we compare the behaviors of the Poisson's ratios of (001) nanoplates of six different metals. Interestingly, the behaviors of the Poisson's ratios of the metal nanoplates differ, even though their corresponding bulks have similar and positive Poisson's ratios. This is because the six metals exhibit large differences in their surface stresses as well as in the critical strains for the phase transformation.

show abstract

“…In [12][13] authors found soliton solution of non-linear partial differential equations using analytical and numerical methods. The F-expansion method is also one of the most useful methods for finding analytical solutions of non-linear partial differential equations [14].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions of Classical and Fractional KP-Burger Equation and Coupled KdV Equation

Ghosh

Sarkar

Das

2016

CMST

View full text Add to dashboard Cite

Development of new analytical and numerical methods and their applications for solving non-linear partial differential equations (both classical and fractional) is a rising field of Applied Mathematical research because of its applications in Physical, Biological and Social Sciences. In this paper we have used a generalized Tanh method to find the exact solution of KP-Burger equation and coupled KdV equation. The fractional Sub-equation method has been used to find the solution of fractional KP-Burger equation and fractional coupled KdV equations. The exact solution obtained by the fractional sub-equation method reduces to classical solution when the order of fractional derivative tends to one. Finally numerical simulation has been done. The numerical simulation justifies that the solutions of two fractional differential equations reduce to shock solution for KP-Burger equation and soliton solution for coupled KdV equations when the order of derivative tends to one.

show abstract

Computer simulation of solitary waves in a common or auxetic elastic rod with both quadratic and cubic nonlinearities

Cited by 11 publications

References 8 publications

Solitary waves in auxetic rods with quadratic nonlinearity: Exact analytical solutions and numerical simulations

Solitary waves in auxetic rods with quadratic nonlinearity: Exact analytical solutions and numerical simulations

Auxeticity of face‐centered cubic metal (001) nanoplates

Analytical Solutions of Classical and Fractional KP-Burger Equation and Coupled KdV Equation

Contact Info

Product

Resources

About