A generalized solution methodology based on piecewise linear vector fields is proposed for piecewise linear systems with singular regions or asymmetric restoring forces which vary spatially and temporally. In matrix representation for these systems, state variables in each region can be explicitly expressed as a function of the time the orbit spends between two boundaries or the time when the orbit hits the boundary. The time can be determined by the Brent method, and periodic solutions can then be obtained. Analytical solutions are validated on a system with 3-regions of displacement and 2-regions of time, a circumferential vibration of gear meshing system, by using the newly developed numerical method.
Analysis of Piecewise Linear Systems With Boundaries in Displacement and Time
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 2000; Revised February 2002. Associate Editor: J. P. Cusumano.
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Nakai, M., Murata, S., and Hagio, S. (September 20, 2002). "Analysis of Piecewise Linear Systems With Boundaries in Displacement and Time ." ASME. J. Vib. Acoust. October 2002; 124(4): 527–536. https://doi.org/10.1115/1.1502668
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