Abstract
Abstract A generalized solution methodology based on piecewise linear vector fields has been proposed for piecewise linear systems with boundaries for both displacement and time. In this paper, this methodology is applied in analyzing dynamic responses of torsional vibration through bilinear spring stiffness with changing hysteretic torque in the rotating machinery system, which has boundaries for both displacement and velocity. For asymmetric torque with hysteresis, two cases exist when restoring torque changes smoothly and discontinuously. Period-one and period-two solutions are sought in two cases and compared with ones obtained by the numerical method. Our present method can be applied to dynamic responses of piecewise linear systems having velocity and displacement boundaries.
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