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Thursday, July 11 • 11:00 - 11:20

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This paper is devoted to investigate the travelling wave motions of axially moving continua with time-varying, harmonic support, boundary conditions. In this paper, the time-varying support is assumed to vary harmonically. The wave motions of axially moving continua with different supports have the distinct characteristics. These properties are not only related to the positions of the support, but also to the direction and the speed of the transport and the frequency of harmonic support. We proceed with the study of the travelling wave motions of axially moving continua with the support changes at two ends and between them. The D'Alembert's method and the modal analysis method are applied to axially moving string and beam, respectively. We decompose the wave motion of the axially moving string into the superposition of the forward travelling wave and the backward travelling wave. With the increasing of the transport speed, the forward travelling wave speed increases, the natural frequency and the wavenumber decrease. However, the backward travelling wave speed decreases, the natural frequency and the wavenumber increase. No matter where the harmonic support is set at the output end or the incident end, the string model always exhibits the backward travelling wave property. But a certain position of external excitation can induce resonance. For the axially moving string, the travelling wave is spotted between any two adjacent nodes. There are n stationary nodes and n+1 travelling wave intervals when the frequency of harmonic support is between the interval of the nth and n+1th natural frequencies. In contrast to the string model, there are only n+1 travelling wave intervals but no certain stationary nodes under the aforesaid frequency with respect to the axially moving beam.


Miroslav Janota

Ph.D., Czech Technical University in Prague
avatar for Vadym Kruts

Vadym Kruts

Senior researcher, G.S. Pisarenko Institute for Problems of Strength of the National Academy of Sciences of Ukraine


Thursday July 11, 2019 11:00 - 11:20 EDT
St-Laurent 4
  T07 Struct. dyn. & nonlin. vib., RS01 Modal analysis

Attendees (2)