J.A. Reyes

Vibration frequencies for a uniform beam with one end spring-hinged and subjected to a translational restraint at the other end

Abstract The purpose of the present study is to deal with the free vibration of a beam hinged at one end by a rotational spring and subjected to the restraining action of a translational spring at the other end. The eigenfrequencies for the fundamental mode are presented for different values of the parameters K R L / EI and K T L 3 / EI , where KR and K T are the stiffness constants of the springs.

Analysis of a cable-like system suddenly stopped at one end

The problem investigated is that of a spring and Hookean bar system, with a mass attached at the other end, moving axially with a constant velocity, Vo. A dynamic stress field results if the free end of the spring is suddenly stopped. Determination of these dynamic stresses has been accomplished by following a one dimensional wave approach. The model adopted constitutes a first order approximation to a type of cable system commonly used in ocean engineering applications. A severe sudden loading condition results when the situation previously described arises. The problem is also interesting from an applied mathematics viewpoint since it requires expansion of the displacement function in a series of non-orthogonal functions.

Vibrations of rings of variable cross section

Abstract The present paper deals with the determination of the lower natural frequencies of vibration of rings of variable cross-sectional area using three approximate schemes: • —using polynomial coordinate functions in the angular coordinate in order to approximate the fundamental mode shape • —expanding the ring response in terms of a sinusoidal truncated series • —by means of a finite element algorithm. When using the first two procedures the Ritz method is applied in order to obtain the frequency equation. In general very good agreement is obtained between the eigenvalues predicted by the three approaches.

Dynamic behavior of a cable-payload system suddenly stopped at one end

A one-dimensional wave approach is used to determine dynamic stresses in a rod which has a mass attached to it at one end, moving axially at a constant velocity, when the free end of the rod is suddenly stopped. Within the inherent limitations of the model, the analysis is also valid in the case of a rotating shaft with a disk at one end when the other end of the rod is suddenly fixed. This problem arises in many practical situations and is also interesting from an applied mathematics viewpoint since it involves expansion of the displacement function in a series of non-orthogonal functions on a given interval.

A comparison of analytical and numerical solutions in heat conduction problems

Abstract This paper deals with a comparison of analytical and finite element results in two types of steady state diffusion problems: (a) determination of solutions in domains of complicated boundary shape, and (b) analysis diffusion-type problems in nonhomogeneous media.

Some practical considerations on vibrating timoshenko beams

Abstract The present study deals with two types of considerations which are of practical importance when dealing with vibrating, simply supported Timoshenko beams: (1) range of validity of the theory, taking as a basic geometric-mechanical parameter the ratio: radius of gyration of the cross-section/beam length; and (2) the position of the supports at the beam ends.

Analysis of a type of dynamic problem by a simulation approach

Mechanical cables are used in a multitude of engineering applications: towing, remotecontrol, ocean bottom search and survey, salvage recovery operations and a large variety of mechanical systems. The present investigation deals with a basic dynamic model which represents a severe operational requirement in most cable systems. Consider a rod AB moving with constant velocity V o in the direction AB with an attached mass M at B. The end A is suddenly brought to rest. Following a one dimensional wave approach one can find the solution in terms of a series of non-orthogonal functions. If additional complexities come into play-e.g., a segmented cable system, several masses attached to the cable, damping, etc.-it is convenient to make use of an approximate method. It is shown in the present paper that the simulation method can be used to advantage in a great variety of problems typified by the previous example.