Inaug.-diss.--Rostock. / "Literatur": p. 33.

Thesis (P.H.D.)--University of Michigan, 1913. / "Reprinted from the Physical Review, n.s., vol. III., no. 6, June, 1914."

Thesis (M.S.)--University of Wisconsin--Madison, 1937. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 46-47).

Inaug.-diss.--Rostock. / "Literatur": p. 33.

Thesis (M.S.)--University of Wisconsin--Madison, 1968. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.S.)--University of Wisconsin--Madison, 1962. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 164).

Thesis (M.S.)--University of Wisconsin--Madison, 1984. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 113-114).

Frictional vibrations have been induced in a system having an elastically suspended,and viscously damped slider loaded onto a surface driven-at constant velocity. Exact mathematical analysis-of the system reveals a unique value of the driven surface velocity, above which frictional vibrations of the slider cannot exist. Theory suggests that the "critical" value-of the driven surface velocity is dependent upon the damping, load, and stiffness of the suspension, and the friction characteristics-of the rubbing surfaces. Using the approximation that the amplitude of stick of the slider equals the maximum amplitude of vibration, a relationship is developed which predicts the amplitude of vibration at any given value of driven surface velocity. The limiting velocity of this function when the amplitude tends to zero is the critical velocity. Exact and approximate theories are compared for specific practical cases, and reasonable agreement is found. Five systems were investigated experimentally, and displacement-time charts of the slider were obtained at different values of the driven surface velocity. Unstable regions were noted where the slider fluctuated between smooth sliding and frictional vibrations. The experimental data illustrates the existence of a critical velocity of the driven surface, and its dependence upon the degree of damping in the system. The correlation between experimental data and theoretical curves indicates that the developed analytical method could be used to predict the behaviour of systems subject to friction induced vibrations. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Frictional vibrations, which occur when two solid bodies are rubbed together, are analyzed mathematically and observed experimentally. In the mathematical analysis, the non-linear differential equation of motion during the slip period is derived making use of the experimental friction-velocity curve. A qualitative graphical solution of this differential equation of motion is presented to illustrate the general form and behavior of the motion. The experimental friction-velocity curve is then linearized allowing the differential equation of motion to undergo standard analytical solution. The experimental investigations were carried out using unlubricated steel surfaces and six different supporting systems. The experiments were confined to sliding in the negative slope region of the friction curve for the particular surfaces used. The effects of load, stiffness and velocity of the translating surface are considered and the results suggest that the decay of the vibrations, as the speed of the moving surface is increased, corresponds in form to the friction-velocity curve for the surfaces used. Using the original analytical relationship describing the shape of the negative slope region of the friction curve, the theoretical results are altered accordingly. Good correlation is obtained between the analytical results and the experimental observations. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The theory presented describes the physical phenomenon of nonlinear coupling of longitudinal and flexural vibrations when a beam is excited transversely at high frequencies. Equations are derived based on the Bernoulli-Euler theory of flexure, by energy methods, to describe the transverse and the longitudinal vibration of a beam of constant cross-section under plane motion. The initial crookedness of the beam and the longitudinal inertia, accounted for in the theory, give rise to the coupled vibrations. No closed form solution is presented. However, a simple analysis of some of the coupling terms suggests the existence of several coupled vibrations. By the method proposed herein, the frequencies of these vibrations can be established. In particular, the theory predicts two longitudinal coupled vibrations with the frequency ratio 1:2. The agreement between the theory and the experimental results is good. The vibrations predicted exist and the frequency ratio for the predicted longitudinal vibrations was 1:2. Further, the experimental results indicate that there are more longitudinal vibrations than indicated by the theory. A longitudinal coupled vibration at three times the frequency of transverse excitation was recorded. There are indications in the data that coupled flexural vibrations at twice the frequency of transverse excitation exist. A circular plate centrally supported and transversely excited was also tested. Two pronounced resonant radial vibrations were recorded. The frequency ratio was 1:2. Coupled flexural vibrations were not identified. The influence of the longitudinal vibration on the flexural vibration of the beam is examined. The limitations of the theory, of the experiment, and the significance of the resonant strains is discussed. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate