Green-Naghdi theory in application to the problems of hydroelasticity


11:00 AM - 12:00 PM



  • 时间: 11:00 am - 12:00 pm (Beijing Time)
  • 日期: Thursday,May 23, 2024
  • 地点: MB537
  • 主讲人:Dr. Vasily Kostikov (XJTLU)


The Green-Naghdi theory was originally developed by A.E. Green of University of Oxford and P.M. Naghdi of University of California to study the problems of wave-structure interaction. In contrast to the classical approach of perturbation techniques for the long wave equations, the Green-Naghdi theory uses the theory of directed fluid sheets and has its roots in the theory of shells and plates in structural mechanics and three-dimensional continuum model called a Cosserat surface. This approach leads to the set of partial differential equations of the continuum under study, representing the conservation of mass and the integrated momentum, and satisfying the nonlinear boundary conditions exactly. The Green-Nahgdi equations are classified based on the number of functions prescribing the distribution of the vertical velocity along the fluid depth. Since no perturbation or scaling parameters are used in the derivation of these equations, there is no theoretical restriction on the limit to which the theory is applicable.

In my presentation, I will discuss the development of analytical and numerical models for interaction of nonlinear waves with floating and submerged deformable plates in the context of the Level I Green-Naghdi theory. Since the motion and deformation of an elastic structure also modifies the flow field, a comprehensive analysis of the hydroelasticity problems requires the simultaneous consideration of the two-way fluid-structure and structure-fluid interactions. This challenge is addressed by coupling the Green-Naghdi theory with appropriate structural elasticity equations. As a result, an accurate and efficient numerical model is built, that predicts the hydroelastic response of floating and submerged deformable structures (e.g. floating solar panels, ice sheets in marginal ice zones, underwater tunnels).