Periodic response of piecewise non-linear oscillators under harmonic excitation

Abstract

The method of equivalent linearization has been extended to obtain periodic responses of harmonically excited, piecewise non-linear oscillators. A dual representation of the solution is used to greatly enhance the algebraic simplicity. The stability analysis of the solutions so obtained is carried out by the method of error propagation. These different systems having piecewise non-linearity are considered. Numerical results are compared with those obtained from the simple harmonic balance method and direct numerical integration. The proposed method not only gives better results than harmonic balance but is also capable of including super- and subharmonics.