We have discovered a forerunning mode transition as the periodic wave changing the state of a uniform continuous waveguide. The latter is represented by an elastic beam initially rested on an elastic foundation. Under the action of an incident sinusoidal wave, the separation from the foundation occurs propagating in the form of a transition wave. The critical displacement is the separation criterion. Under these conditions, the steady-state mode exists with the transition wave speed independent of the incident wave amplitude. We show that such a regime exists only in a bounded domain of the incident wave parameters. Outside this domain, for higher amplitudes, the steady-state mode is replaced by a set of local separation segments periodically emerging at a distance ahead of the main transition point. The crucial feature of this waveguide is that the incident wave group speed is greater than the phase speed. This allows the incident wave to deliver the energy required for the separation. The analytical solution allows us to show in detail how the steady-state mode transforms into the forerunning one. The latter studied numerically turns out to be periodic. As the incident wave amplitude grows the period decreases, while the transition wave speed averaged over the period increases to the group velocity of the wave. As an important part of the analysis, the complete set of solutions is presented for the waves excited by the oscillating or/and moving force acting on the free beam. In particular, an asymptotic solution is evaluated for the resonant wave corresponding to a certain relation between the load's speed and frequency.
|Number of pages||14|
|Journal||Journal of the Mechanics and Physics of Solids|
|Early online date||02 Feb 2015|
|Publication status||Published - 01 May 2015|
- Beams and columns
- Numerical algorithms
- Transition waves
FingerprintDive into the research topics of 'Forerunning mode transition in a continuous waveguide'. Together they form a unique fingerprint.
- Faculty of Business and Physcial Sciences, Department of Mathematics - Professor of Mathematical Modelling, Royal Society Wolfson Research Merit Award Holder
Person: Teaching And Research, Other