Generation of the second,fourth, eighth,and subsequent harmonics by a quadratic nonlinear hyperelastic longitudinal plane wave |
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Authors: | J J Rushchitsky S V Sinchilo I N Khotenko |
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Institution: | 1.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine,Kyiv,Ukraine |
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Abstract: | The perturbation (small-parameter) method is used to obtain the first three approximations for the problem of a harmonic longitudinal
plane wave propagating in a quadratic nonlinear hyperelastic material described by the classical Murnaghan model. The subsequent
approximations are discussed. The contribution of each approximation to the overall wave pattern is analyzed. It is shown
that the third approximation corrects the prediction of the evolution of the initial wave profile. Which of the harmonics
dominates depends on the distance traveled by the wave: the second harmonic is generated first, then it transforms into the
fourth harmonic, and finally, as the distance increases, the eighth harmonic shows |
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Keywords: | |
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