Dynamic response of the leg of a tension leg platform subjected to an axial, suddenly applied load at one end

This paper deals with the solution of the problem of the dynamic response of the leg of a tension leg platform subjected to an axial, suddenly applied load at one end, considering a highly simplified model but taking into account several complicating factors. The problem is solved by means of a non-harmonic Fourier expansion in terms of eigenfunctions obtained from a non-regular Sturm-Liouville system.     

Natural frequencies of a vibrating repaired panel in an ocean structure

The present work arose from the need of repairing steel plates badly damaged by corrosion in a portion of the structural element of the naval vehicle. The possibility of removing the portion and replacing it by a patch of a composite material was considered. Its dynamic behavior is altered by the introduction of the patch and the prediction of its new behavior is of great interest in many situations. This condition would appear in other real-life situations like as a localized orthotropic effect caused in the panel by a welding procedure or a metallurgical process. The first four natural frequency coefficients of the composite repaired panel with different types of boundary conditions are determined by means of a variational approach. The displacement function is approximated making use of complete sets of beam functions. The eigenvalues have been computed from (225×225) secular determinants. An independent solution is obtained using the finite element method and a reasonably good agreement with the analytical solution is encountered.     

Vibrations of a rectangular plate with a free edge in the case of discontinuously varying thickness

Transverse vibrations of a rectangular plate with three edges elastically restrained against rotation while the fourth is free are studied using (a) an analytical approach based on the optimized Rayleigh-Ritz method and (b) the finite element method. The study was motivated by the necessity of finding out how the lower frequencies of vibration were affected by introducing a step discontinuity in the plate thickness. This variation in the plate thickness was practiced in order to obtain a reduction in the total plate weight.     

Forced vibrations of a clamped-free beam with a mass at the free end with an external periodic disturbance acting on the mass with applications in ships’ structures

An exact, analytical solution is obtained for the title problem which constitutes a classical one although no solution is available in well known textbooks and handbooks normally used by the structural engineer in several fields of technology: ocean and naval engineering, aerospace applications, etc. The authors performed this study motivated by a situation where excessive displacements were noticed in a structural element carrying a relatively small motor at the free end and placed at the engine room of a naval vessel. The Bernoulli-Euler model has been employed.     

Vibrations of a rectangular orthotropic plate with a free edge: a comparison of analytical and numerical results

Transverse vibrations of a rectangular orthotropic plate with a free edge while the others are supported according to four different combinations of boundary conditions are considered in the present paper. The presence of a concentrated mass is also taken into account. In view of the difficulty of satisfying exactly the natural boundary conditions at the free edge, the fundamental frequency of vibration is determined by means of the optimized Rayleigh-Ritz method and a pseudo-Fourier expansion which contains, in its argument, the optimization parameters γ_i. The results are in excellent agreement with those obtained by means of a finite element algorithmic procedure.     

Forced vibrations of a beam elastically restrained against rotation and carrying a spring–mass system

An exact solution for the title problem is obtained in closed form fashion in the case of a Bernoulli–Euler beam. It is assumed that the exciting force is applied to the mass which is elastically mounted on the beam. The mathematical model constitutes a first order approximation to a motor or engine elastically mounted on a structural element. The operation of the machine generates a transverse, sinusoidally varying force. The problem is of basic interest in mechanical, naval and ocean engineering systems from the point of view of the determination of dynamic displacements and stresses; sound radiation calculations, etc. The present problem arose in connection with the mounting of an engine on a structural beam in a small naval vessel and when excessive vibrational level was noted. This study was undertaken in order to understand the physical problem and to correct the mechanical situation