Characterization and interaction of geometric and contact/impact nonlinearities in dynamical systems

Saunders, Brian E.; Vasconcellos, Rui; Kuether, Robert; Abdelkefi, Abdessattar

doi:10.1016/j.ymssp.2021.108481

Characterization and interaction of geometric and contact/impact nonlinearities in dynamical systems

Journal Article · Tue Mar 15 00:00:00 EDT 2022 · Mechanical Systems and Signal Processing

DOI:https://doi.org/10.1016/j.ymssp.2021.108481· OSTI ID:1834129

Saunders, Brian E. ^[1]; Vasconcellos, Rui ^[2]; Kuether, Robert ^[3]; Abdelkefi, Abdessattar ^[1]

New Mexico State Univ., Las Cruces, NM (United States)
Sao Paulo State University (UNESP), Sao Joao da Boa Vista (Brazil)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Here, we study how a contact/impact nonlinearity interacts with a geometric cubic nonlinearity in an oscillator system. Specific focus is shown to the effects on bifurcation behavior and secondary resonances (i.e., super- and sub-harmonic resonances). The effects of the individual nonlinearities are first explored for comparison, and then the influences of the combined nonlinearities, varying one parameter at a time, are analyzed and discussed. Nonlinear characterization is then performed on an arbitrary system configuration to study super- and sub-harmonic resonances and grazing contacts or bifurcations. Both the cubic and contact nonlinearities cause a drop in amplitude and shift up in frequency for the primary resonance, and they activate high-amplitude subharmonic resonance regions. The nonlinearities seem to never destructively interfere. The contact nonlinearity generally affects the system’s superharmonic resonance behavior more, particularly with regard to the occurrence of grazing contacts and the activation of many bifurcations in the system’s response. The subharmonic resonance behavior is more strongly affected by the cubic nonlinearity and is prone to multistable behavior. Perturbation theory proved useful for determining when the cubic nonlinearity would be dominant compared to the contact nonlinearity. The limiting behaviors of the contact stiffness and freeplay gap size indicate the cubic nonlinearity is dominant overall. It is demonstrated that the presence of contact may result in the activation of several bifurcations. In addition, it is proved that the system’s subharmonic resonance region is prone to multistable dynamical responses having distinct magnitudes.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); CAPES; CNPq

Grant/Contract Number:: NA0003525

OSTI ID:: 1834129

Alternate ID(s):: OSTI ID: 1868645

Report Number(s):: SAND--2021-13118J; 701078

Journal Information:: Mechanical Systems and Signal Processing, Journal Name: Mechanical Systems and Signal Processing Vol. 167; ISSN 0888-3270

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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