TY - GEN
T1 - A perturbation method for the forced response of a weakly bilinear oscillator
AU - Bayly, Philip V.
N1 - Publisher Copyright:
© 1995 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 1995
Y1 - 1995
N2 - 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 offorcing frequencies: far from resonances, and near primary and superharmonic resonances. The difference between the two linear stiffness coefficients is used as the small parameter, e, in a modified perturbation analysis. Of all the behavior analyzed, the response near a superharmonic 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.
AB - 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 offorcing frequencies: far from resonances, and near primary and superharmonic resonances. The difference between the two linear stiffness coefficients is used as the small parameter, e, in a modified perturbation analysis. Of all the behavior analyzed, the response near a superharmonic 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.
UR - http://www.scopus.com/inward/record.url?scp=85103468301&partnerID=8YFLogxK
U2 - 10.115/DETC-1995-0313
DO - 10.115/DETC-1995-0313
M3 - Conference contribution
AN - SCOPUS:85103468301
T3 - Proceedings of the ASME Design Engineering Technical Conference
SP - 727
EP - 735
BT - 15th Biennial Conference on Mechanical Vibration and Noise - Vibration of Nonlinear, Random, and Time-Varying Systems
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 1995 Design Engineering Technical Conferences, DETC 1995, collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium
Y2 - 17 September 1995 through 20 September 1995
ER -