Role of topographical disturbances on hydroelastic response of a floating membrane over a slippery bottom

Abstract

Some disruptions occur at the bottom of the sea due to underwater explosions and natural disasters (e.g. tsunamis, submarine earthquakes, landslides, rock and asteroid falls, drastic changes in weather conditions, etc.). The current paper aims to study how a transitory ground disturbance affects the membrane deflection in a viscous fluid over a porous slippery bottom at a finite water depth in the presence of a floating elastic membrane. Three types of ground disturbance are considered such as $H_0(x)=\delta (x)$, $H_0(x)=e^{(-x^2/2)}$ and $H_0(x)=e^{-|x|}$ Kundu et al. [Waves generated on running stream due to a disturbance on sea bed. Int J Appl Comput Math. 2020;6(2):1–17.] and Maiti and Mandal [Waves generated by bottom disturbance in an ice-covered ocean. Int J Appl Mech Eng. 2007;12(2):477–486.]. The Stokes stream function and wave potential boundary value problems are used to formulate this problem. The membrane deflection is obtained as infinite integrals using the Fourier, and Laplace transforms. These integrals are then evaluated using the steepest descent method. The effects of the bottom slip parameter, the fluid's viscosity, and the floating membrane's tension and mass on the membrane deflection are analyzed. The study reveals that the amplitude of the membrane deflection decreases, and the oscillatory pattern of the deflection curve is changed by reducing the value of viscosity. Furthermore, the membrane's deflection amplitude decreases with an increase in the values of mass and tension of the floating membrane. Moreover, the slippery bottom plays a vital role in reducing the amplitude of the membrane deflection.

Keywords:

• Viscous fluid
• bottom disturbance
• laplace and fourier transforms
• steepest descent method
• floating elastic membrane
• membrane deflection
• porous slippery bed

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

H.B. gratefully acknowledges the financial support from SERB, Department of Science and Technology, Government of India through the “CRG” project, Award No. CRG/2022/006698.