Effective wave propagation along a rough thin-elastic beam |
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| Institution: | 1. Department of Mathematics, University College in Qunfudah, Umm Al-Qura University, Saudi Arabia;2. Institut Elie Cartan de Lorraine, Université de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy, F-54506, France;3. Preparatory Institute for Engineering Studies of Nabeul, Mrezgua 8000 Nabeul, Tunisia;1. State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China;2. Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, PR China;3. Institute of Applied Mechanics, University of Kaiserslautern, P.O. Box 3049, D-67653 Kaiserslautern, Germany;4. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China;5. State Key Laboratory of Mechanical and Control of Mechanical structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China |
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| Abstract: | Two methods for computing the complex-valued effective wavenumber of a rough beam in the context of linear time-harmonic theory are presented. The roughness of the beam is modelled as a continuous random process of known characteristic length and root-mean-square amplitude for either the beam mass or the beam rigidity. The first method is based on a random sampling method, with the effective wave field calculated as the mean of a large ensemble of wave fields for individual realisations of the roughness. The individual wave fields are calculated using a step approximation, which is validated for a deterministic problem via comparison to results produced by an integral equation approach. The second method assumes a splitting of the length scale of the fluctuations and an observation scale, employing a multiple-scale approximation to derive analytical expressions for the effective attenuation rate and phase change. Numerical comparisons show agreement of the results of the random sampling method and the multiple-scale approximation for a wide range of parameters. It is shown that the effective wavenumbers only differ by a real constant between the cases of varying beam mass and rigidity. |
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| Keywords: | Wave attenuation Effective wavenumber Elastic beam in vacuo Step approximation Integral equation Multiple-scale approach |
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