Patricio A. A. Laura

Drag on an Oscillating Rod with Longitudinal and Torsional Motion

An analytical expression for the viscous drag on a smooth circular cylindrical rodlike cable oscillating with longitudinal and torsional motion is obtained. Based on a linear damping law, an approximate value for the drag coefficient is also presented. The analysis and con- clusions are useful when dealing with many ocean engineering problems of practical importance. the analysis of many practical problems related to the sea-state excitation of long rods and cable-body systems for salvage, buoy, oil drilling, and towing operations, an expression for the viscous drag force acting on the longi- tudinal rod or cable is required. It has been shown that the inclusion of this term can have a pronounced effect on the tension in the rod or cable and subsequent response of the system. For example, the propagation and attenuation of internal stress waves and snap loads through the cable in a cable lifting system are affected by the external viscous damping.1 The problem is also of considerable interest in offshore oil drilling problems since a similar analysis is usually performed.2 It is a common practice to postulate a linear relationship between the external damping force and the surface velocity of the rod when investigating the longitudinal vibrations based on the wave equation. The solution of this damped wave equation with an arbitrary damping coefficient can show the qualitative effects of external damping. However, the magnitude and frequency dependence of the damping coefficient can significantly alter the nature of the solution. The purpose of this investigation is to formulate an analyti- cal expression for the viscous drag on a smooth circular cylindrical rodlike cable oscillating with longitudinal and torsional motion. An examination of the hypothesis of the linear damping law will be made and the damping coefficient estimated.

Study of Small‐Amplitude Vibrations of Clamped Rectangular Plates Using Polynomial Approximations

By means of the Galerkin method, an analysis is made of the vibration of a rectangular plate whose edges are clamped. Plate deflections are represented by a simple polynomial expression. This requires a minimum amount of labor. A complete table of frequencies is presented. Accurate but very simple frequency equations are derived for the first four modes of vibration.

Application of Complex‐Variable Theory to the Determination of the Fundamental Frequency of Vibrating Plates

This study deals with the determination of the fundamental frequency of vibration of plates of complicated shape. The method makes use of conformal mapping and variational techniques. In the case of a square plate, the results obtained are in good agreement with the exact values. Numerical results are also presented for a circular plate with two flat sides and several plates of regular polygonal shape.

Analytical and experimental investigation on vibrating circular plates with stepped thickness over a concentric circular region

Transverse vibrations of the structural elements described in the title are studied for the case where the edges are elastically restrained against translation and rotation. Since finding an exact solution is a difficult task, it was considered convenient to approximate the response of the plate in the case of free, axisymmetric vibrations by means of a summation of simple polynomial coordinate functions that satisfy the governing boundary conditions. The Ritz method is used in order to generate the frequency equation. The natural frequency coefficients are optimized by minimizing each eigenvalue with respect to an undetermined exponential parameter included in each coordinate function.

Fundamental Frequency of Vibration of Rhombic Plates

The present study deals with the determination of the fundamental frequency of vibration of simply supported rhombic plates. The results are tabulated and compared with values already available in the literature.

Vibrating circular plates with stepped thickness over a concentric circular region: a general, approximate solution

Natural frequencies corresponding to axi‐ and antisymmetric modes of vibration of the structural elements described in the title are studied using the optimized Rayleigh–Ritz approach. It is assumed that the plates are elastically restrained against translation and rotation. The plate amplitude is approximated in terms of polynomial coordinate functions that satisfy the boundary conditions, each one containing an undetermined exponential parameter that allows for the minimization of the eigenvalues under investigation.

Unsteady heat conduction in plates of polygonal shape

Abstract This paper deals with an unsteady heat-conduction problem in a plate of regular polygonal shape using conformal mapping techniques. The classical approach to an exact solution of the Fourier heat equation is the separation of variables technique. For more complicated boundaries, e.g. a hexagonal plate, it is convenient to transform the given shape onto a unit circle where the boundary conditions can be identically satisfied. However, the transformed partial differential equation can only be satisfied approximately. Two “weighted-residuals” techniques are used to solve it, and solutions are obtained for several polygonal shapes. The method can be extended easily in the case of some doubly connected regions of technical importance, e.g. the graphite brick of a gas cooled nuclear reactor.

Transverse vibrations of a beam elastically restrained at one end and with a mass and spring at the other subjected to an axial force

Abstract This paper deals with the exact solution of the title problem. The classical theory of vibrations of beams is used and a tabulation of eigenvalues is presented as a function of some of the governing mechanical parameters. The problem is of basic interest in several areas of engineering, specially to nuclear reactor systems designers since in many instances pumps or other electromechanical arrangements are placed at the end of a clamped beam.

Dynamic Stress and Displacements in a Two‐Material Cable System Subjected to Longitudinal Excitation

This paper deals with the analysis of the dynamic stresses and displacements in a cable subjected to longitudinal excitation simulating ocean‐wave motion. The cable is considered to be made up of two segments of different materials and different physical dimensions. External damping due to fluid action and internal damping due to viscoelastic material properties are considered. The payload mass attached to the end of the cable is considered to be attached to a rigid foundation by an elastic spring and dashpot. This model covers a large number of possible oceanographic applications ranging from salvage recovery of objects immersed in the ocean sediments to suspension of instrumentation packages from buoy systems. Numerical results are presented for a hypothetical system consisting of the payload attached to a steel‐nylon elastic cable exposed to sinusoidal excitation at the upper end. Forcing frequencies approaching the second natural frequency are shown to cause forces in the steel portion which are signi...

Acoustic Detection of Structural Failure of Mechanical Cables

The mechanical cable is one of the most important components in many ocean engineering systems. The present letter describes preliminary research on suitable methods to detect internal failure of the cable prior to complete breakage.