Showing papers on "Rotary inertia published in 1974"

A dynamic analysis of unstable crack propagation and arrest in the DCB test specimen

Abstract: A simple analytical model is developed to accompany experimental work on rapid crack propagation and arrest in the DCB test specimen. The present work extends the beam-on-elastic foundation model used previously by taking account of shear deformation and of both translational and rotary inertia. Crack speeds predicted with the model are found to be in good agreement with the constant-speed behavior observed experimentally. It is demonstrated that kinetic energy makes an important contribution to maintaining unstable crack propagation and to crack arrest.

Initially Stressed Mindlin Plates

Abstract: Equations of motion for a transversely isotropic plate in a general state of nonuniform initial stress where the effects of transverse shear and rotary inertia are included are derived by two methods. The first method is to perturb the nonlinear equations of elasticity by an incremental deformation. The resulting equations are linearized and integrated through the thickness of the plate to obtain the plate equations. The second method is to derive nonlinear equations of motion for a thick plate variationally by Hamilton's principle. These equations are then perturbed and suitably linearized to obtain the same equations as were obtained by the first method. A reduced set of equations for a thin plate are also given. Finally, the thick plate equations are solved for a simply supported rectangular plate in a state of uniform compressive stress plus a uniform bending stress both acting in the same direction.

Natural vibrations of systems of elastically connected Timoshenko beams

Abstract: The differential equations governing the flexural vibrations of systems of elastically connected parallel bars are derived considering the effects of rotary inertia and shear deformation. These equations are solved to find the natural frequencies and mode shapes of particular three‐ and two‐beam systems. For the two‐beam system, the present results are compared with the available experimental values.

Axisymmetric vibrations of laminated composite cylindrical shells

Abstract: A refined theory of vibration of laminated composite thick shells is developed. The present theory includes the effects of transverse shear deformation, transverse normal stress and strain, rotary inertia, and higher‐order stiffness terms. Numerical results of natural frequencies under axisymmetric vibrations for graphite‐epoxy composites are evaluated and compared to results obtained from Flugge's theory. A significant difference between these two results is observed for shells having relatively large thickness‐to‐length ratio.

Flexural Vibrations and Timoshenko's Beam Theory

Abstract: This paper is a study of flexural elastic vibrations of Timoshenko beams with due allowance for the effects of rotary inertia and shear. Two independent formulations are developed, one based on the concepts proposed by Timoshenko and the other on the extended Rayleigh-Ritz energy method. The results obtained from the two formulations are matched in order to determine the correcting coefficients in the simplified formulae which are proposed for the frequency of the first two flexural branches. The proposed formulae are shown to achieve greater accuracy in describing the flexural motions. New accurate solutions are offered for several cross-sectional geometries which enable the accuracy of the available methods to be assessed. Correction coefficients are evaluated for several sections and are compared with previous work.

Mechanical automatic torque converter

Abstract: A torque converter that uses the reaction of energy storing devices to mechanically convert a given input angular velocity into an output torque. The torque converter is comprised of an input shaft which delivers an oscillatory motion to an inertia device, such as a flywheel, through connecting rods and lever arms. The inertia device transfers the oscillatory motion to the output shaft through differential gears and overrunning clutches. In the preferred embodiment, two inertia devices mounted on parallel axes with each 90° out of phase provide a smooth, continuous output torque.

Stability analysis of a damped polygenic systems with relocatable mass along its length

Abstract: The stability of a clamped-free rod subjected to a compressive follower force at its tip, and bearing one or two relocatable mass points, is investigated. The outcomes of the calculations either using Euler's beam theory and neglecting damping and rotary inertia or using Rayleigh's beam theory including damping and rotary inertia are compared with each other: An optimal location exists for the mass points in both cases, however, the optimum is less pronounced with Rayleigh's theory including damping and rotary inertia than with Euler's theory neglecting damping and rotary inertia. Hence, one may conclude that for a safe design damping and rotary inertia, of the beam's mass elements as well as of the masspoints, has to be taken into account. The results obtained are of interest in connection with aircraft wings carrying jet engines, with turbine blades having varying cross-sections, etc.

Experimental determination of the principal moments of inertia of the Helios prototype spacecraft

Abstract: The moment of inertia of the Helios Spacecraft about its spin axis was determined by use of a roll-fixture using two sets of crossed flexure pivots as elastic constraints The test procedure entailed measurement of a system oscillation period with each of a set of added moment-of-inertia increments The tare effect of the fixture was determined by a like process and was subtracted from the gross value to yield the spacecraft roll moment of inertia to an estimated accuracy of 02% Lateral moments of inertia (ie, about each of three axes normal to the spin axis) were determined by a gravity pendulum method that makes use of the fact that any physical pendulum has a minimum period of oscillation determined by a particular distance from the axis of rotation to the system center of gravity

Dependence of Plate-Bending Finite Element Deflections and Eigenvalues on Poisson's Ratio

Abstract: only transverse shear and in the analysis the flexural rigidities of the face sheets about their own midplanes have been included. Results for co/o>0 were again computed by omitting the effect of the rotary inertia from the governing differential equations. These results can be generated by redefining the four coefficients A5, A6, A8, and A9 in Eqs. (7) and then computing the roots of Eq. (14) again. For lower frequencies, the values obtained for o)/co0 by dropping the rotary inertia terms and the corresponding values shown in Fig. 2 are essentially the same. This conclusion is in agreement with the one for rectangular sandwich plates and for homogeneous circular plates. Rotary inertia terms would, however, play significant role for higher modes. Figure 3 shows modal shapes for first three modes for which the frequency distribution is given in Fig. 2.

On the Three-dimensional Correction Factors for the Added Mass and the Added Mass Moment of Inertia Related to Manoeuvrability in Shallow Water

Abstract: When we want to estimate the added mass and the added mass moment of inertia of a ship, the strip method which has proved to be very useful for the calculation of ship motion in waves, seems to be suitable, because it is possible to take the hull form of a ship into consideration in detail. However, since the strip method is based on two-dimensional consideration of the flow field around a three-dimensional body, both the added mass and the added mass moment of inertia obtained by the strip method are always excessively large compared with their exact values.Therefore in this paper, the correction factors are introduced separately for the added mass as to the swaying motion, and for the added mass moment of inertia as to the yawing motion in an analogous way to the correction factor for the added mass of the vertical ship hull vibration.Especially, the effect of finite water depth on these correction factors is investigated from the viewpoint of ship's manoeuvrability in restricted waters. As a result, it is found that the correction factors decrease with decrement of the water depth, and that the correction factor for the added mass moment of inertia is smaller than that for the added mass.

Transient Response of Shells of Revolution by Direct Integration and Modal Superposition Methods

Abstract: The results of an analytical effort to obtain and evaluate transient response data for a cylindrical and a conical shell by use of two different approaches: direct integration and modal superposition are described. The inclusion of nonlinear terms is more important than the inclusion of secondary linear effects (transverse shear deformation and rotary inertia) although there are thin-shell structures where these secondary effects are important. The advantages of the direct integration approach are that geometric nonlinear and secondary effects are easy to include and high-frequency response may be calculated. In comparison to the modal superposition technique the computer storage requirements are smaller. The advantages of the modal superposition approach are that the solution is independent of the previous time history and that once the modal data are obtained, the response for repeated cases may be efficiently computed. Also, any admissible set of initial conditions can be applied.