The Nature of Solutions of a Rayleigh‐Type Forced Vibration Equation with a Large Coefficient of Damping

摘要

In this paper, the author considers an approximation to the Rayleigh equation, y¨+Є(13y˙3-y˙)+y=A cosωt, and its equivalent form under the transformation y˙=v,y=Єξ. A cubic function 13v3-v+ξ that appears in the altered equation is replaced by a piecewise linear function. For large Є, the existence of periodic solutions of the approximating equation is demonstrated. Strong orbital stability properties of neighboring solutions is also shown.