Abstract
A hydroelastic model is developed to study the interaction of linear long gravity waves with a very large floating flexible plate resting on a viscoelastic foundation, which is based on the Kelvin–Voigt model. Flexural gravity wave blocking occurs for specific values of the compressive force in the absence of viscous damping. During wave blocking, the group velocity vanishes, and mode swapping occurs. Within wave blocking and plate buckling limit in the presence of compressive force, three distinct propagating modes occur in the absence of viscous damping. Moreover, the study reveals that irrespective of the values of viscous damping constant, the blocking/buckling points shift to a higher wavenumber with an increase in the value of elastic foundation constant. On the other hand, the flexural gravity wave modes become complex in the presence of a viscoelastic foundation. The complex wave modes are classified as predominant progressive wave modes and rapidly decaying modes. In the presence of viscous damping, wave blocking does not happen before the buckling limit of the compressive force. However, the phase velocity vanishes, and the group velocity becomes continuous irrespective of the value of non-zero viscous damping at the buckling limit for the compressive force. The detailed behavior of the roots of the dispersion equation and the mode shapes are illustrated through contour plots and by analyzing the roots’ loci. Furthermore, plate deflections are exhibited for different wave and structural parameters.
Highlights
In the last few decades, there have been significant developments in the theory of hydroelasticity
Squire6,7 established that the results for wave–ice interaction problems apply to problems associated with gravity wave interaction with very large floating structures (VLFSs)
By eliminating Φ from Eqs. (1) and (6), the linearized long flexural gravity wave equation in the presence of lateral force, with the floating structure resting on a viscoelastic foundation, is obtained as EI ∂x6 + N ∂x4 + ρid ∂t2∂x2 ρ ∂2η
Summary
In the last few decades, there have been significant developments in the theory of hydroelasticity. Under the assumption of linearized water wave theory and small amplitude structural response, Das et al. examined the blocking dynamics of flexural gravity waves in the presence of a compressive force in a two-layer fluid having a floating elastic plate covered surface and an interface. The loci of the dispersion relation roots are demonstrated graphically for different limiting values of the compressive force, including the threshold of blocking and buckling limit as discussed in the study of Das et al. in the presence of a viscoelastic foundation for different elastic foundation values and viscous damping constants.
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