Bilinear Systems with Initial Gaps Involving Inelastic Collision: Forced Response Experiments and Simulations

Kohei Noguchi, Akira Saito, Meng Hsuan Tien, Kiran D'Souza

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this paper, the forced response of a two degrees-of-freedom (DOF) bilinear oscillator with initial gaps involving inelastic collision is discussed. In particular, a focus is placed upon the experimental verification of the generalized bilinear amplitude approximation (BAA) method, which can be used for the accurate estimation of forced responses for bilinear systems with initial gaps. Both experimental and numerical investigations on the system have been carried out. An experimental setup that is capable of representing the dynamics of a 2DOF oscillator has been developed, and forced response tests have been conducted under swept-sine base excitation for different initial gap sizes. The steady-state response of the system under base excitation was computed by both traditional time integration and BAA. It is shown that the results of experiments and numerical predictions are in good agreement especially at resonance. However, slight differences in the responses obtained from both numerical methods are observed. It was found that the time duration where the DOFs are in contact with each other predicted by BAA is longer than that predicted by time integration. Spectral analyses have also been conducted on both experimental and numerical results. It was observed that in a frequency range where intermittent contact between the masses occurs, super-harmonic components of the excitation frequency are present in the spectra. Moreover, as the initial gap size increases, the frequency band where the super-harmonic components are observed decreases.

Original languageEnglish
Article number021001
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Issue number2
Publication statusPublished - 1 Apr 2022


  • Dynamics
  • nonlinear vibration


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