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Analytical modeling of flexible circular submerged mound motion in gravity waves

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Abstract

Submerged flexible mounds are designed to reduce the incident waves’ energy based on their motion, allowing for greater movements by attaching at one side to the bottom. In the present approach, an approximate analytical solution is proposed based on the Fourier transform and Hamilton’s principle to investigate the structural displacements of a submerged mound in waves. Experimental data and image processing techniques are employed to verify the analytical results. Validation is performed using experimental data with different wave heights and finite water depths. Comparison with the available experimental data suggests that the proposed approximate analytical model is an appropriate tool to predict the structural movements accurately.

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Abbreviations

CSS:

Corrected sum of squares

MAE:

Mean absolute error

NRMSE:

Normalized root mean square error

RSS:

Residual sum of squares

SE:

Standard error

D :

Flexible mound equivalent diameter (m)

d :

Deep water depth (m)

E :

Tube Young modulus of elasticity (N m−2)

f:

Functional symbol (–)

f :

Wave frequency (Hz)

g :

Gravitational acceleration (m s−2)

H i :

Incident wave height (m)

H :

Wave height due to the structural displacement (m)

h :

Shallow water depth (m)

L :

Wave length (m)

P :

Internal pressure of tube (Pa)

S :

Beach slope (–)

T :

Wave period (s)

ε :

Tube wall thickness (m)

ρ :

Water density (kg m−3)

G :

Tube shear modulus of elasticity (N m−2)

J :

Tube polar moment of inertia (m4)

I :

Tube moment of inertia (kg m2)

ρ s :

Tube density (kg m−3)

T′ :

Kinetic energy (J)

U :

Potential energy (J)

C :

Speed of wave propagation (ms−1)

u :

Horizontal velocity under the wave (ms−1)

ω :

Angular frequency (s−1)

ƞ :

Water surface elevation (m)

C M :

Inertia coefficient (–)

KC :

Keulegan–Carpenter number (–)

F x :

Inertia forces (N)

u p :

Displacement of structure (m)

φ :

Angle at the center of structure (°)

W :

Non-resistor forces (N)

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Author information

Authors and Affiliations

  1. Department of Civil Engineering, Isfahan University of Technology, PO Box 84156, Isfahan, Iran

    Elham Jafarzadeh, Abdorreza Kabiri-Samani & Bijan Boroomand

  2. Institute of Geophysics, University of Tehran, Tehran, Iran

    Asghar Bohluly

Authors
  1. Elham Jafarzadeh
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  2. Abdorreza Kabiri-Samani
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  3. Bijan Boroomand
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  4. Asghar Bohluly
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Correspondence to Elham Jafarzadeh.

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Jafarzadeh, E., Kabiri-Samani, A., Boroomand, B. et al. Analytical modeling of flexible circular submerged mound motion in gravity waves. J. Ocean Eng. Mar. Energy 9, 181–190 (2023). https://doi.org/10.1007/s40722-022-00248-9

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  • DOI: https://doi.org/10.1007/s40722-022-00248-9

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