In the design of geared rotating systems in engineering practice a variety of configurations are used, and their torsional vibration has been extensively studied. Detailed analyses of the modes and frequencies of vibration of these systems have been given by Ker Wilson and Nestorides. When the rotating system is rigidly supported, standard methods may be used to obtain the characteristics of free vibration and the response to impressed forces, from which the transmissibility of the gear-box may be calculated. However, there are many applications in which the gearbox is flexibly mounted. The simple example of a geared engine with a flexibly mounted crankcase has been considered by Den Hartog and Butterfield. In some epicyclic gear-box assemblies, elastic elements are introduced between the reactive element and the gear-case to increase the capacity for absorbing impulsive loads and as a means of varying the natural frequencies of vibration'. Harmonic forces acting on the rotors excite coupled vibration of the rotating system and the supporting frame, and Ker Wilson has shown how the natural frequencies and modes of the combined system may be determined by Holzer-type tabular methods. This involves a trial-and-error technique which may sometimes be tedious. Vibration of geared systems may also be excited by the motion of the frame supporting the gear-box, and an analysis of the response is necessary in the determination of dynamic loads.

A method of analysis is presented for the interaction between the local and torsional modes of instability of a stiffened panel in compression. Numerical results are produced for the particular case of a panel with Z-section stringers, and the influence of the flange width on the buckling stress is illustrated.

Following on from the LUMINA and HERMES elements discussed in TN’s 11 and 12, this note analyses two further three-dimensional elements outlined in ref. 1. These new elements possess the desirable features of completeness and consequent invariance of the polynomials for the displacement fields. It has been shown in ref. 2 and stated in ref. 1 that third order complete polynomials yielding a second order or parabolic strain distribution fit into a tetrahedron element with 20 nodal points and 60 degrees of freedom, denoted within ASKA as TET 20 (Fig. 1).

The natural frequencies of vibration of a cantilever beam allowing for rotary inertia and shear deformation are obtained by the approximate Ritz method.

The workability of the method is dependent upon the approximating functions chosen for the dynamic displacement curves. A series of characteristic functions representing the normal modes of vibration of cantilever beams in simple flexure is used as the approximating functions for both deflections due to flexure and shear deformation. Good agreement is shown between frequencies obtained by the Ritz method and those resulting from an analytical solution.

The effect upon the natural frequencies of allowing for rotary inertia alone is shown and it is seen to increase rapidly with mode number.

Theoretical data from lifting-surface theory are presented to illustrate

• (i) that the vortex drag factor is closely related to the half-wing spanwise centre of pressure on simple planforms without camber or twist,

• (ii) that lifting-line theory is useless for predicting the spanwise distribution of vortex drag on swept wings,

• (iii) that recent numerical improvements in lifting-surface theory help to reconcile the concepts of wake energy and leading-edge suction in relation to vortex drag.