الفهرس | Only 14 pages are availabe for public view |
Abstract Comparison theorems based on domain monotonicity concept of convex boundaries concerning lower and upper bounds for the frequency have been obtained to It is the purpose of this thesis to study the standing gravity waves of small amplitude on the free surface of an inviscid, incompressible, homogeneous liquid filling to a uniform depth, vertical side walls basins of pentagonal, heptagonal and octogonaZ bases. It is required to determine in a reliable manner the fundamental frequency of natural modes of liquid oscillations in these three basins. This has been determined by transforming first to a complex domain and then mapping the domain Dn representing the basin in the Z-plane conformaNy onto the unit disk in the -plane. This conformal mapping reduces the field equations to a two dimensional nonseparable generalized Helmholtz equation associated with Neumann boundary condition on a circle. The required mapping function can be obtained using the well known schwarz-christoffel transformation. Getting an exact solution of the resultant equation is hardly possible, check the calculated frequencies. |