Asymptotic Solutions Of Surface Flexural Waves And Interfacial Gravity Waves Generated By Disturbances

The development and utilization of marine resources have been efective ways tosolve the problem of the lack of the land resources. With the development rangingfrom the shallow to deep waters, advanced technologies are required to exploit seas andoceans so that the construction of very large foating structure (VLFS) is proposed byexperts. The research on the VLFS has been one of the popular topics in the felds ofmarine engineering and academia since the VLFS is not only available to the deep-seawaters but also easy to be maintained, which leads to widespread applications in themarine engineering.The horizontal scale of the VLFS is several kilometers. It is necessary to considerits elastic deformation under the analysis. Then the interaction between VLFS andthe fuid is analyzed as a problem of the fuid–structure with the hydroelastic theory.Moreover, the phenomenon of the pycnocline may occur since the temperature and thesalinity change with the depth of the sea. The two-layer fuid model is generally usedto simulate the system.The hydroelastic response of the fuid disturbed by sources with the elastic plate isconsidered in this thesis, containing the stationary two-layer fuid and uniform single-layer fuid systems. With the presence of the surface tension of fuid, the fexural–andcapillary–gravity waves are considered in parallel. Based on some assumptions for anideal fuid, irrotational fow feld, a thin elastic plate, small amplitude waves, and neg-ligible rigid motion, we obtain the integral solutions by the method of Fourier–Laplaceintegral transforms, then use the stationary-phase method and the residue theorem tosimplify the integration solutions into the asymptotic solutions. Under the form of theasymptotic solutions, some of the factors afecting on the waveform is discussed, suchas the location of the disturbance source, the density ratio, the frequency of distur-bance, the velocity of the fuid, the individual performance of the elastic plate and soon.The main work and results of the thesis are outlined as follows: 1) The interaction of water waves with an elastic plate is considered in the cases ofthe impulsive disturbance in the fuid and an external load force on the plate. Theresults show that the solutions of fexural–gravity waves and capillary–gravitywaves can be derived in parallel and the two kinds of waves do not have a fxedperiod and wavelength. The amplitudes of the wave may decrease and fnallytend to zero, as the speed of the observer increases. At the same time, the curvesindicate that the surface motion of the fexural-gravity wave contains the shortfexural and the long gravity waves.2) The evolution of the wave profles is studied based on the infuences in the case ofan oscillating source submerged in the fuid and a surface oscillating disturbanceplaced on the elastic plate. The results show that the wave profles contain thesteady-state and transient components. The steady-state component is the mainpart in the wave motion, while the infuence from the transient component tendsto zero as the time increases.3) In the single-layer fuid of infnite depth, the surface wave motion of the fuidwith a uniform stream covered with an elastic plate is discussed under the dis-turbance of steady source. The results show that the wave profles consist of thesteady-state and the transient parts. The group velocity of the transient waveis determined by the depth of the fuid, the thickness of the elastic plate andthe elastic modulus. Through the group velocity curves, we can observe thatthe inertial term of the elastic can be ignored, since it has very slight efectson the location of the stationary-phase points. The asymptotic solution of thetransient wave is related to the value of the Froude number, and can be solvedwith the method of the stationary phase. In terms of the steady-state wave, therelationship of the velocity of the fuid and the minimum phase velocity can beapplied to obtain the asymptotic solutions. The gravity wave in the downstreamregion and the fexural wave in the upstream region have diferent period andamplitude, and the period depends on the velocity of fuid.From the work presented in this thesis, we conclude that the wave generated by diferent kinds of disturbance source have diferent nature, while fexural–andcapillary–gravity waves can be considered in parallel. In addition, the efects of thevelocity of the fuid on wave cannot be ignored when there is a current.