Closed-form analytical expressions are obtained for the response of a weakly bilinear oscillator to harmonic forcing. Bilinear systems are used to model cracked beams and rotors; the bilinear oscillator considered here is a lightly damped mass-spring assembly. The spring is linear except that its stiffness is slightly higher when the displacement of the mass is negative. The response is obtained for three ranges of forcing frequencies: far from resonances, and near primary and superharmonic resonances. The difference between the two linear stiffness coefficients is used as the small parameter, ϵ, in a modified perturbation analysis. Of all the behavior analyzed, the response near a super-harmonic resonance of order 2 is the most markedly affected by the weak bilinearity. These results provide insight into the observed behavior of cracked structural members and shafts.

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