Features of wave generation by a source moving along a one-dimensional flexible guide lying on an elastic-inertial foundation

Ерофеев, В. И.; Kolesov, D.A.; Lisenkova, E. E.

doi:10.1134/s1063771016060051

Cited by 7 publications

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“…The first equation of the system describes waves propagating along the string, the second one specifies the dynamics of the elastic-inertial foundation interacting with the string. The dispersion properties of the system under consideration were studied in paper [2].…”

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confidence: 99%

Nonlinear waves in an elastic guide interacting with an elastic-inertial foundation

2018

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This paper deals with the study of the transverse wave propagation in a string resting on an elastic-inertial foundation. A self-consistent dynamic problem is herein considered for a system composed of a one-dimensional flexible guide (string) and an elastic-inertial foundation. As a foundation model the Vesnitsky’s model was chosen. The set of equations is reduced to one fourth-order cubic-nonlinear equation relative to transverse displacements of the string. Depending on the string and the elastic-inertial foundation mass ratio, the evolutionary equation has the following three extreme events: the modified Ostrovsky equation, the Riemann equation with a cubic nonlinearity, the equation for an anharmonic oscillator with a cubic nonlinearity.

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confidence: 99%