Showing papers on "Timoshenko beam theory published in 1969"

Axisymmetric and beam-type vibrations of thin cylindrical shells.

Abstract: : Considerable attention has been devoted in recent years to the use of shell equations for the prediction of the dynamic behavior of thin cylindrical shells as an element in a missile or spacecraft. The complexity involved in the use of the shell equations must be tolerated for problems that require modes having several circumferential waves (e.g., prediction of panel flutter or response to acoustic loading). Moreover the minimum natural frequency usually corresponds to a mode having two or more circumferential waves. For prediction of overall vehicle behavior, however, one is primarily interested in axisymmetric (n = o) and beam-type (n = 1) modes; in these instances the problem can be considerably simplified by considering the cylinder as a bar for n = 0 modes or a compact beam for n = 1 modes. The present paper examines the accuracy of these engineering approximations as compared with exact solutions from Flugge's shell equations and discusses the error in terms of frequency, mode shape, modal forces, and generalized mass. Consideration is given to the effect of shell bending stiffness and the influence of boundary conditions on these parameters. (Author)

Transfer Matrices for Beams Loaded Axially and Laid on an Elastic Foundation

Abstract: Using a modified model of the axially-loaded Timoshenko beam, nine field transfer matrices for the homogeneous case and three field matrices for the non-homogeneous case have been derived, covering thus all the “cases of state” of continuous beams loaded axially and laid on an elastic foundation. The loads and restraints (translatory and rotatory) may be both concentrated and distributed. The matrices make possible a simultaneous treatment of free vibrations, forced vibrations, statics and buckling.

On the coupling of hull vibration and bottom vibration of ships

Abstract: Higher mode vibration of the ship's hull is analysed, where the main hull is assumed to be a uniform beam (bending deflection is neglected) and the bottom, an elastic plate. Coupling effect of vibratory systems (main hull and bottom) is found to be significant. As the mode becomes higher, the natural frequency obtained from the present theory is considerably lower than that from conventional beam theory. In the region above the natural frequency of the bottom plate the new modes are found, which do not appear from the conventional theory. The longitudinal bending rigidity of the bottom has great effect upon the node-frequency relationship especially in the higher mode. The above-mentioned conclusions partially explain the phenomenon observed in the actual ships.

Higher Mode Vertical Vibration of Giant Tanker (1 st Report)

Abstract: For the purpose of clarifying the nature of the hull vertical vibration in the higher mode, the preliminary analysis has been made in which the ship hull is simulated by the two parallel beams model elastically connected. Each beam represents the side shell and the longitudinal bulkhead respectively, and the connecting springs the transverse structural members. The result obtained shows that the relative deformation of longitudinal bulkhead to side shell is remarkable, in the modes higher than 5- or 6-noded mode which means the elastic deformation of the cross section of ship is significant, contrary to the assumption in the beam-theory calculation. As the mode becomes higher than these modes, there appear new modes in which the deflection of the longitudinal bulkhead is out of phase by 180° to that of the side shell.To testify the phenomenon above mentioned, the experiments on full scale ships have been carried out on two 150, 000 D/W class tankers and the following phenomena are observed.(a) The diffence of deflection of longitudinal bulkhead from that of the side shell becomes significant in the modes higher than 4-, 5-noded modes. The difference becomes larger in the higher modes.(b) In the modes higher than 7-, 8-noded, the deflection of the side shell is remarkably different from that supposed from the beam theory. In these modes the deflection of the longitudinal bulkhead is similar to that derived from the beam theory.(c) In the region higher than 10- to 12-noded modes, the deflection of the longitudinal bulkhead as well as that of the side shell becomes very complex and shows no longer the clear nodal point.(d) On the other hand, the phase difference of the deflection is very significant and irregular, possibly due to the effect of damping.* To explain these facts the new theory above-mentioned has been extended and applied to the ship. Calculation of the natural frequency, normal mode and the vibratory response to the sinusoidal exciting force has been made and the results can explain the experimental facts (a) (c) Though the calculation partly explains (d), additional study is necessary.

Static fatigue of acid-etched, soda-lime-silica glass rods,

Abstract: : In studying the strength characteristics of pristine, soda-lime-silica glass using four-point bending, large deflections are imposed on the glass specimens. These large deflections lead to nonlinear relations between load and deflection and the assumptions of simple beam theory are no longer applicable. Without making the simplifying assumptions of simple beam theory, the nonlinear differential equation governing beam deflections in four-point bending was solved using numerical techniques. (Author)

Theoretical aspects of thermomechanical forces in power cables

Abstract: A theoretical treatment of the mechanical forces developed in power cable conductors as a result of temperature changes is presented, using equations based upon classical beam theory. From considerations of flexural rigidity, it is shown that, in most practical cases, such conductors should have very little bending stiffness and possess considerable longitudinal stiffness. It is also proposed that a joint may be effectively represented as a very stiff spring. For single-core cables, the theory is in good agreement with previously published work, under most practical conditions. A brief extension of the analysis to cover the mechanical behaviour of multicore cables is given.