IDEAS home Printed from https://ideas.repec.org/a/wly/jnlamp/v2020y2020i1n7360794.html

Nonlinear Hydroelastic Interaction among a Floating Elastic Plate, Water Waves, and Exponential Shear Currents

Author

Listed:
  • Ping Wang
  • Yongyan Wang
  • Xintai Huo

Abstract

Nonlinear hydroelastic interaction among a floating elastic plate, a train of deepwater waves, and a current which decays exponentially with depth is studied analytically. We introduce a stream function to obtain the governing equation with the dynamic boundary condition expressing a balance among the hydrodynamic, the shear currents, elastic, and inertial forces. We use the Dubreil‐Jacotin transformation to reformulate the unknown free surface as a fixed location in the calculations. The convergent analytical series solutions for the floating plate deflection are obtained with the aid of the homotopy analysis method (HAM). The effects of the shear current are discussed in detail. It is found that the phase speed decreases with the increase of the vorticity parameter in the opposing current, while the phase speed increases with the increase of the vorticity parameter in the aiding current. Larger vorticity tends to increase the horizontal velocity. In the opposing current, the horizontal velocity under the wave crest delays more quickly as the depth increases than that of waves under the wave trough, while in the aiding current case, there is the opposite effect. Furthermore, the larger vorticity can sharpen the hydroelastic wave crest and smooth the trough on an opposing current, while it produces an opposite effect on an aiding current.

Suggested Citation

  • Ping Wang & Yongyan Wang & Xintai Huo, 2020. "Nonlinear Hydroelastic Interaction among a Floating Elastic Plate, Water Waves, and Exponential Shear Currents," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:7360794
    DOI: 10.1155/2020/7360794
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2020/7360794
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2020/7360794?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Shijun Liao, 2012. "Homotopy Analysis Method in Nonlinear Differential Equations," Springer Books, Springer, number 978-3-642-25132-0, March.
    2. Wang, P. & Lu, D.Q., 2016. "Nonlinear hydroelastic waves traveling in a thin elastic plate floating on a two-layer fluid," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 700-710.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ping Wang & Yongyan Wang & Chuanqi Su & Yanzhao Yang, 2017. "Nonlinear Hydroelastic Waves Generated due to a Floating Elastic Plate in a Current," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    2. Yu, Qiang & Xiao, Junfeng & Zhao, Kaiqi, 2026. "On accurate closed-form Coiflet solutions of nonlinear Korteweg–de Vries–Burgers equation for shallow water wave by a time-integration wavelet homotopy method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 458-482.
    3. S. S. Motsa, 2014. "On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. S. S. Motsa, 2014. "On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Gohar Rehman & Qura Tul Ain & Muhammad Zaheer & Liulei Bao & Javed Iqbal, 2019. "An Analysis Of Two-Dimensional Flow Through A Water Reservoir Using Mathematical Approach," Environmental Contaminants Reviews (ECR), Zibeline International Publishing, vol. 2(1), pages 11-13, October.
    6. Zhang, Danjin & Ren, Meirong & Qian, Youhua, 2025. "Homotopy homoclinic orbit and global dynamics analysis of the double-excited Duffing–van der Pol system," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    7. Sandile S. Motsa & Zodwa G. Makukula, 2017. "On a Bivariate Spectral Homotopy Analysis Method for Unsteady Mixed Convection Boundary Layer Flow, Heat, and Mass Transfer due to a Stretching Surface in a Rotating Fluid," Journal of Applied Mathematics, John Wiley & Sons, vol. 2017(1).
    8. Ping Wang, 2015. "The Nonlinear Hydroelastic Response of a Semi‐Infinite Elastic Plate Floating on a Fluid due to Incident Progressive Waves," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    9. T. Gandhimathi & S. Eswaramoorthi & K. Loganathan & Nirmith Kumar Mishra, 2023. "Mathematical Modeling of MHD Flow of CNTs/Ag Nanoparticles Past a Heated Stretchy Surface with Nonuniform Heat Sink/Source and Thermal Radiation Impacts," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    10. F. A. Hendi & B. S. Kashkari & A. A. Alderremy, 2016. "The Variational Homotopy Perturbation Method for Solving ((n × n) + 1) Dimensional Burgers’ Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2016(1).
    11. Shu-Li Mei, 2013. "HAM‐Based Adaptive Multiscale Meshless Method for Burgers Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:7360794. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3197 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.