Hydroelastic analysis of surface gravity wave interacting with elastic plate resting on a linear viscoelastic foundation
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ORIGINAL PAPER
Hydroelastic analysis of surface gravity wave interacting with elastic plate resting on a linear viscoelastic foundation Saeed Rashidi‑Juybari1 · Alireza Fathi1 · Hamed Afrasiab1 Received: 20 January 2020 / Accepted: 18 August 2020 © Sociedade Brasileira de Engenharia Naval 2020
Abstract This article investigates the interaction between a surface gravity wave that propagates over an elastic plate based on linear viscoelastic foundation. The plate is considered to be thin and infinite and is modeled based on the Euler–Bernoulli beam theory. Static and dynamic boundary conditions are applied to the Laplace equation of the fluid domain. The dispersion relation of the wave–plate system is derived and ratio of surface wave amplitude and plate deflection is proposed. Considering dimensionless dispersion relation, two modes of propagating wave are attained. Problem is analyzed for two cases of presence and absence of viscous damping coefficient in the foundation of the elastic plate. It is shown that flexural rigidity of the submerged plate has considerable effect on wave decay and plate vibration. It is illustrated that shallowness has noticeable effect on the wave propagation frequency and a critical shallowness demarcates damped or overdamped excitation of the elastic plate based on the viscoelastic foundation. Moreover, effects of flexural rigidity of the plate, foundation stiffness coefficient, and foundation viscous coefficient on phase and group velocities of wave are discussed in the present study. Keywords Wave–plate interaction · Viscoelastic seabed · Linear water waves · Euler–bernoulli beam theory · Flexural rigidity · Dispersion relation Abbreviations x Direction of wave propagation h Mean water depth Φ Velocity potential t Time ∇ Laplacian operator η Surface wave amplitude ζ Surface wave amplitude g Gravity acceleration ω Frequency of propagating wave ℜ Real part of complex number i Unit imaginary number ηo Surface wave amplitude at the conventional origin A, B Arbitrary constants γ Dimensionless spring-restoring force μ Shallowness τ Dimensionless thickness Ωs Surface mode dimensionless frequency vPS Surface mode phase velocity of wave
vgS Surface mode group velocity of wave y Direction of water depth Pb Pressure applied on the viscoelastic bottom ρ Fluid density El Flexural rigidity of plate ρb Density of plate d Thickness of plate k* Stiffness of plate’s foundation c* Viscous damping coefficient of plate’s foundation ϕ Spatial velocity potential e Euler’s number k Wave number ζ0 Wave number Ω Dimensionless frequency ξ Dimensionless damping ratio γb Dimensionless elasticity-restoring force ε Dimensionless flexural rigidity Ωb Bottom mode dimensionless frequency vPb Bottom mode phase velocity of wave vgb Bottom mode group velocity of wave
* Saeed Rashidi‑Juybari [email protected] 1
Department of Mechanical Engineering, Noshirvani University of Technology, 47148‑71167 Babol, Iran
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1 Introduction Hydroelastic analy
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