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Hydroelastic analysis of surface gravity wave interacting with elastic plate resting on a linear viscoelastic foundation

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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.

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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

η o :

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

v PS :

Surface mode phase velocity of wave

v gS :

Surface mode group velocity of wave

y :

Direction of water depth

P b :

Pressure applied on the viscoelastic bottom

ρ :

Fluid density

El :

Flexural rigidity of plate

ρ b :

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

ζ 0 :

Wave number

Ω:

Dimensionless frequency

ξ :

Dimensionless damping ratio

γ b :

Dimensionless elasticity-restoring force

ε :

Dimensionless flexural rigidity

Ωb :

Bottom mode dimensionless frequency

v Pb :

Bottom mode phase velocity of wave

v gb :

Bottom mode group velocity of wave

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Authors and Affiliations

  1. Department of Mechanical Engineering, Noshirvani University of Technology, 47148-71167, Babol, Iran

    Saeed Rashidi-Juybari, Alireza Fathi & Hamed Afrasiab

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  1. Saeed Rashidi-Juybari
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  2. Alireza Fathi
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  3. Hamed Afrasiab
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Rashidi-Juybari, S., Fathi, A. & Afrasiab, H. Hydroelastic analysis of surface gravity wave interacting with elastic plate resting on a linear viscoelastic foundation. Mar Syst Ocean Technol 15, 286–298 (2020). https://doi.org/10.1007/s40868-020-00085-1

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  • DOI: https://doi.org/10.1007/s40868-020-00085-1

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