Publications

Conference Proceedings of the Society for Experimental Mechanics Series

Allen, Matthew S.; Ginsberg, Jerry H.

Many systems can be approximated as linear with coefficients that vary periodically with time. For example, an anisotropic shaft rotating at constant speed on anisotropic bearings can be modeled as periodically time varying (PTV). Similar models can be obtained for wind turbines, some mechanisms, etc... However, the vast majority of modal analysis algorithms and techniques apply only to linear time invariant (LTI) systems. In this paper, two methods are demonstrated by which the free response of a periodically time varying system can be exactly parameterized by an LTI system. The parameters of the LTI representation can then be identified using standard techniques. The analysis techniques are demonstrated on a simple system, representing a rotor mounted on an anisotropic, flexible shaft, supported by anisotropic bearings. They are then applied to synthetic response data for a system with parameters that vary only weakly with time, as might be encountered when attempting to detect small cracks in a rotating shaft. These examples demonstrate the methods' ability to characterize the anisotropy of the shaft, even when both the shaft and supports are anisotropic.

Allen, Matthew S.; Massad, Jordan M.; Field, Richard V.

Abstract not provided.

American Society of Mechanical Engineers, Micro-Electro Mechanical Systems Division, (Publications) MEMS

Allen, Matthew S.; Sumali, Hartono S.; Epp, David E.

The responses of micro-cantilever beams, with lengths ranging from 100-1500 microns, have been found to exhibit nonlinear dynamic characteristics at very low vibration amplitudes and in near vacuum. This work seeks to find a functional form for the nonlinear forces acting on the beams in order to aide in identifying their cause. In this paper, the restoring force surface method is used to non-parametrically identify the nonlinear forces acting on a 200 micron long beam. The beam response to sinusoidal excitation contains as many as 19 significant harmonics within the measurement bandwidth. The nonlinear forces on the beam are found to be oscillatory and to depend on the beam velocity. A piecewise linear curve is fit to the response in order to more easily compare the restoring forces obtained at various amplitudes. The analysis illustrates the utility of the restoring force surface method on a system with complex and highly nonlinear forces. Copyright © 2006 by ASME.