Buckling of circular, annular plates of continuously variable thickness used as internal bulkheads in submersibles

This paper deals with the determination of the critical load in the buckling of isotropic, circular annular thin plates whose thickness varies slightly according to an exponential law.The outer edge of the plate is elastically restrained against rotation while the inner boundary is free. Classical small-deflection theory is used. An hidrostatic pressure acting in the middle plane is considered.The eigenvalues of the problem are obtained by means of an analytical approach based on the optimized Rayleigh-Ritz method. It is shοwnι that the results are in good agreement from an engineering viewpoint, with those available in the literature.     

Analytical and experimental investigation on transverse vibrations of solid, circular and annular plates carrying a concentrated mass at an arbitrary position with marine applications

This investigation arose from the practical necessity of placing a centrifugal pump rigidly attached to a thin, circular cover plate of a water tank in a medium size ocean vessel. Due to lack of space, it was necessary to locate the system off—center of the circular configuration. It was considered necessary to calculate the fundamental frequency of the coupled system.The first part of the present study is concerned with the determination of the fundamental frequency of vibration of a circular plate carrying a concentrated mass at an arbitrary position, using a variational approach.Numerical results are obtained for the stated problem for several combinations of the intervening geometric and mechanical parameters.An experimental investigation is also performed in the case of clamped plates.Based on the results for solid circular plates, the fundamental frequency of annular plates with a free inner edge and a concentrated mass is also obtained.Circular plates are fundamental structural elements in ocean engineering applications: from off-shore platforms to underwater acoustic transducers. In a great variety of circumstances, they must carry operational systems in an eccentric fashion. Since the dynamic performance is always of interest, one must know at least some of the basic dynamic parameters.     

Unsteady thermoelastic analysis of a circular disk with a hot central core and subjected to adiabatic conditions

The unsteady thermoelastic analysis of a cooling circular disk or cylinder which is originally at uniform temperature is a classical problem of the theory of thermal stresses. More recent studies consider the case of composite structural configurations. The present paper deals with a situation which, apparently, has not been previously considered: unsteady thermal stresses caused by the presence of a hot, central nucleus. The temperature field is obtained in terms of a Fourier–Bessel expansion and then, radial and tangential stresses are evaluated analytically. The problem is of basic interest in mechanical and naval engineering systems.     

The interaction of surface water waves with submerged breakwaters

This paper concerns the behaviour of nonlinear regular waves interacting with rectangular submerged breakwaters. A new series of experimental results is presented and compared with numerical calculations based upon a Boundary Element Method (BEM) that utilises multiple fluxes to deal with the discontinuities encountered at the corners of the domain. Specifically, comparisons concern both the spatial water surface profiles at various times and the spatial evolution of the harmonics generated by the breakwaters, the latter being an important focus for the paper. The BEM is shown to accurately model both the water surface profile and the harmonic generation, provided the breakwater width is sufficient to ensure that flow separation is not a controlling influence. Furthermore, evidence is provided to confirm that reflection from rectangular submerged breakwaters is fundamentally a linear phenomenon.     

Coupled-dynamic analysis of floating structures with polyester mooring lines

A theory and numerical tool are developed for the coupled-dynamic analysis of a deepwater floating platform with polyester mooring lines. The formulas allow relatively large elongation and nonlinear stress–strain relationships, as typically observed in polyester fibers. The mooring-line dynamics are based on a rod theory and the finite element method (FEM), with the governing equations described in a generalized coordinate system. The original rod theory [Nordgren, R.P., 1974. On Computation of the Motion of Elastic Rods. Journal of Applied Mechanics, 41, 777–780] is generalized to allow larger elongation and nonlinear stress–strain relationship. The dynamic modulus of polyester is modeled following an empirical regression formula suggested by [Bosman, R.L.M., Hooker, J., 1999. The Elastic Modulus Characteristic of Polyester Mooring Ropes. In: Proceedings of the Offshore Technology Conference, OTC 10779. Houston, Texas], in which the axial stiffness is not constant, but depends on loading conditions. Two case studies, the static and dynamic behavior of a tensioned buoy and a classic spar with polyester mooring lines, are conducted. The time-domain simulation results are systematically compared with those from the original rod theory. The effects of large elongation and nonlinear stress–strain relations are separately assessed. It is seen that the mean offset, motions, and tension with polyester lines can be different from those by original rod theory with linear elastic lines.