D.V. Bambill

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

Abstract 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.

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

Abstract 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 γi. The results are in excellent agreement with those obtained by means of a finite element algorithmic procedure.

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.

Natural frequencies of a vibrating repaired panel in an ocean structure

Abstract 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.

Natural vibrations of micro beams with nonrigid supports

The present study aims to provide some new information for the design of micro systems. It deals with free vibrations of Bernoulli–Euler micro beams with nonrigid supports. The study is based on the formulation of the modified couple stress theory. This theory is a nonclassical continuum theory that allows one to capture the small-scale size effects in the vibrational behavior of micro structures. More realistic boundary conditions are represented with elastic edge conditions. The effect of Poisson’s ratio on the micro beam characteristics is also analyzed. The present results revealed that the characterization of real boundary conditions is much more important for micro beams than for macro beams, and this is an assessment that cannot be ignored.

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

Abstract 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

Forced vibrations of a beam elastically restrained against rotation at the ends in the case of a concentrated load

Abstract The title problem is solved using Bernouillis classical theory and by means of the separation of variables technique. Numerical data is presented for the simply supported beam, simply supported - clamped and clamped - clamped situations for the case of a concentrated load which varies sinusoidally with time. Certainly no claim of originality is made by the authors since the problem is of a classical nature but it hoped that the rather complete tabulation of displacements, bending moments and shear forces amplitudes included in the present study will be of practical use to ocean and naval engineers.

Free Vibrations of Beam System Structures with Elastic Boundary Conditions and an Internal Elastic Hinge

The study of the dynamic properties of beam structures is extremely important for proper structural design. This present paper deals with the free in-plane vibrations of a system of two orthogonal beam members with an internal elastic hinge. The system is clamped at one end and is elastically connected at the other. Vibrations are analyzed for different boundary conditions at the elastically connected end, including classical conditions such as clamped, simply supported, and free. The beam system is assumed to behave according to the Bernoulli-Euler theory. The governing equations of motion of the structural system in free bending vibration are derived using Hamiltons principle. The exact expression for natural frequencies is obtained using the calculus of variations technique and the method of separation of variables. In the frequency analysis, special attention is paid to the influence of the flexibility and location of the elastic hinge. Results are very similar with those obtained using the finite element method, with values of particular cases of the model available in the literature, and with measurements in an experimental device.

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.