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Analytical analysis for vibration of longitudinally moving plate submerged in infinite liquid domain

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Abstract

The vibration of a longitudinally moving rectangular plate submersed in an infinite liquid domain is studied analytically with the Rayleigh-Ritz method. The liquid is assumed to be incompressible, inviscid, and irrotational, and the velocity potential is used to describe the fluid velocity in the whole liquid field. The classical thin plate theory is used to derive mechanical energies of the traveling plate. As derivative of transverse displacement with respect to time in the compatibility condition equation exists, an exponential function is introduced to depict the dynamic deformation of the moving plate. It is shown that this exponential function works well with the Rayleigh- Ritz method. A convergence study shows a quick convergence speed for the immersed moving plate. Furthermore, the parametric study is carried out to demonstrate the effect of system parameters including the moving speed, the plate location, the liquid depth, the plate-liquid ratio, and the boundary condition. Results show that the above system parameters have significant influence on the vibration characteristics of the immersed moving plate. To extend the study, the method of added virtual mass incremental (AVMI) factor is used. The results show good agreement with those from the Rayleigh-Ritz method.

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Authors and Affiliations

  1. Department of Mechanics, Northeastern University, Shenyang, 110819, China

    Yanqing Wang

  2. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, M5S 3G8, Canada

    J. W. Zu

Authors
  1. Yanqing Wang
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  2. J. W. Zu
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Correspondence to Yanqing Wang.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11302046 and 11672071) and the Fundamental Research Funds for the Central Universities (No.N150504003)

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Wang, Y., Zu, J.W. Analytical analysis for vibration of longitudinally moving plate submerged in infinite liquid domain. Appl. Math. Mech.-Engl. Ed. 38, 625–646 (2017). https://doi.org/10.1007/s10483-017-2192-9

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  • DOI: https://doi.org/10.1007/s10483-017-2192-9

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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