Forerunning mode transition in a continuous waveguide |
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| Institution: | 1. School of Mechanical Engineering, Tel Aviv University, P.O. Box 39040, Ramat Aviv 69978 Tel Aviv, Israel;2. The Shamoon College of Engineering, Beer-Sheva 84105, Israel;3. Institute of Mathematics and Physics, Aberystwyth University, Ceredigion, SY23 3BZ Wales, UK;1. State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, PR China;2. CAPT, HEDPS and IFSA Collaborative Innovation Center of MoE, Peking University, Beijing 100871, PR China;3. State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, PR China;4. Department of Mechanics and Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200444, PR China;5. State Key Laboratory for Mechanical Behavior of Materials, Xi''an 710049, PR China;6. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai, 200072, PR China;1. School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore;2. Institute of High Performance Computing, A⁎STAR, Singapore 138632, Singapore;1. Mechanical and Aerospace Engineering Department, Sapienza Universityof Rome, Via Eudossiana 18, Roma 00184, Italy;2. Faculty of Science and Technology, Free University of Bozen-Bolzano, P.zza Università 5, Bolzano 39100, Italy;1. Mechanical Engineering Department, University of California, Santa Barbara, CA 93106, USA;2. Materials Department, University of California, Santa Barbara, CA 93106, USA;3. Laboratoire PPMD, ESPCI Paris Tech, 10, Rue Vauquelin, 75231 Paris, France;4. School of Engineering, University of Aberdeen, King’s College, Aberdeen AB24 3UE, Scotland, UK;5. INM – Leibniz Institute for New Materials, Campus D2 2, 66123 Saarbrücken, Germany |
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| Abstract: | 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. |
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| Keywords: | Delamination Dynamics Beams and columns Transition waves Numerical algorithms |
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