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The orthogonality properties among the eigenfunctions for a gyroscopic system are derived for a stiffness operator that is not positive definite. The derivatives of the eigenvalues with respect to certain parameters in the system are then obtained. The results are applied to a spinning disk in contact with a stationary load system, which contains such parameters as friction force, transverse mass, damping, stiffness, and the analogous pitching elements, to predict the effects of these parameters and the stiffening of the disk due to the centrifugal force on the natural frequencies and stability of the spinning disk. The results obtained provide a theoretical understanding for previously reported observations based on numerical solutions.

This paper describes the modeling, theoretical formulation, and eigenvalue analysis for a combined system of a spinning flexible disk and a pair of head and suspension systems that contact the disk at opposing points on its two sides. In the analytical model a constant friction force between the sliders and disk and the slider pitch motion, as well as its transverse motion, are taken into account. From the eigenvalue analysis it is found that pitch stiffness and moment of inertia of the heads induce instability above the critical rotation speed similarly to the transverse stiffness and mass. This instability can be effectively stabilized by increasing the external damping which is spinning with the disk. It is also found that the friction force makes all forward modes unstable over the entire rotational speed range. The friction induced instability can be effectively suppressed by increasing the transverse stiffness and mass and it can be stabilized by the pitch damping and the external damping. The characteristics of instability due to the friction force qualitatively agree well with experimental results reported previously.

In this paper, we study the planar deformation of a thin elastic wire inside a tubular housing with clearance. The center line of the tube is assumed to be in the shape of a planar circular arc. The wire is under longitudinal compression at the ends. This mechanics problem can be found in the stent deployment procedure commonly adopted in treating patients with coronary artery diseases. The tube and the wire are meant to model the patient's artery and the thin guidewire used in endovascular surgery, respectively. When the leading end of the guidewire encounters a blockage in the artery, the total length of the guidewire inside the artery varies as the wire undergoes bending deformation through the pushing at the other end. As a consequence, the leading end of the guidewire may not move forward the same distance that it is pushed in by the surgeon from the input end. It is also found that there exists a range of pushing force magnitude, in which one force magnitude may correspond to three different deformation patterns. Therefore, a deformation pattern jump may occur simply by adjusting the direction of the input force while holding the magnitude of the force constant. All these mechanics problems add more challenges to the surgeon's delicate tasks in performing the surgery effectively. Ó 2007 Elsevier Inc. All rights reserved.

In a previous paper (Chen and Bogy, 1992) we studied the effects of various load parameters, such as friction force, transverse mass, damping, stiffness and the analogous pitching parameters, of a stationary load system in contact with the spinning disk on the natural frequencies and stability of the system when the original eigenvalues of interest are well separated. This paper is a follow-up investigation to deal with the situations in which two eigenvalues of the freely spinning disk are almost equal (degenerate) and strong modal interactions occur when the load parameters are introduced. After comparing an eigenfunction expansion with the finite element numerical results, we find that for each of the transverse and pitching load parameters, a properly chosen two-mode approximation can exhibit all the important features of the eigenvalue changes. Based on this two-mode approximation we study the mathematical structure of the eigenvalues in the neighborhood of degenerate points in the natural frequency-rotation speed plane. In the case of friction force, however, it is found that at least a four-mode approximation is required to reproduce the eigenvalue structure. The observations and analyses presented provide physical insight into the modal interactions induced by various load parameters in a spinning disk-stationary load system.