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A study is made on the parametric stability of open thin-walled beams under axial load. A set of nonlinear equations of stability and the appropriate boundary conditions are obtained using the energy approach. The derived equations are applicable to thin-walled open section of any shape. The effect of longitudinal deformation is taken into account in the derived theory. Using the nonlinear theory, the torsional parametric stability of a beam of a symmetrical 1 section is studied. The principal region of torsional instability is determined. The steady-state amplitude of torsional oscillation when the system is parametrically excited is found. Finally, the transient growth of the torsional motion from the onset of instability to the steady-state oscillation is computed. The effect of viscous damping on the steady-state and transient response is also included in the analysis.

A theory to analyze nonplanar coupled shear walls subjected to lateral loading is presented. The theory is applicable to a pair of shear walls of arbitrary cross-sectional shapes connected by a band of evenly spaced connecting members. The lateral loadings can be completely general and are not restricted to act in certain planes. The theory gives the torsional deformation in addition to the flexural deformations of the structure. A test on a Plexiglas structural modal is carried out to verify the accuracy of the theory.

A study has been made on the parametric excitation of a nonlinear system with hardening springs. In the parametric excitation of linear systems, the only subharmonic predicted is a subharmonic of order 1/2. However, in the parametric excitation of non-linear systems, it is shown that higher order subharmonics can exist, depending both on the amplitude and frequency of the parametric excitation.

A study is made on the parametric torsional stability of an elastic cantilever of rectangular cross section under dynamic axial loading. The coupling between the longitudinal and torsional motions exists due to the “shortening effect.” The problem is so formulated that the stability of torsional vibrations is represented by a Mathieu equation, the stability of which is well known. The effect of longitudinal vibrations on the torsional stability is investigated. The steady-state torsional-vibrational response curves are given analytically, and the effect of longitudinal damping on the boundary of stability and the steady-state response curves is also determined.

In this paper, the equations of motion of a curved and twisted rod are derived from the basic principles of dynamics. The set of equations gives the extensional, flexural and torsional motions of the rod. The coupling among these types of motion due to the curvature and tortuosity of the rod is shown explicitly in the case of a helical spring. By successive simplification of the equations, the equations of motion of a circular ring and those of a straight rod are obtained. In this respect, the derived equations can be considered as a generalization of the elementary theories of rod in extensional, torsional and flexural motion.

A simple pendulum with a hinge of double bilinear hysteretic restraining moment-rotation characteristic under parametric excitation is studied. In contrast with a linear system with viscous damping, a double bilinear hysteretic system leads, in general, to finite response under parametric resonance. The response curves and the conditions under which unbounded response results are given. Further, it is shown that unlike the bilinear hysteretic system, a double bilinear hysteretic system may be shock excited into parametric resonance even when the exciting frequency is outside the parametrically resonant frequency range.

Non-Hodgkin's lymphoma which presents as adrenocortical insufficiency is rare, however, it should be a well-recognised entity because, in addition to specific chemotherapy or radiotherapy, it needs hormonal replacement. We report a patient with diffuse histiocytic lymphoma, who had remission for seven years and relapsed with Addisonian crisis.