Discontinuous self‐excited systems: An asymptotic analysis

摘要

AbstractIn this paper we derive a uniformly valid asymptotic approximation of the periodic solution of a self‐excited system given by the differential equationand β1,β2, are positive constants. By uniformly valid asymptotic approximation we mean that no secular terms are present. Our procedure makes use of a nonlinear change of independent variable that transforms the problem from one in which the discontinuities are ϵ dependent to one in which the discontinuities are ϵ independent. We obtain an asymptotic approximation up to order ϵ of the periodic solution and an asymptotic approximation up to order ϵ2of the period. Some comparisons between our asymptotic results and numerically derived results are given. Application of our technique to other examples of self‐excited systems is discussed. The equationis investigated