Insights on the continuous representations of piecewise-smooth nonlinear systems: limits of applicability and effectiveness

Saunders, B. E.; Vasconcellos, R.; Kuether, R. J.; Abdelkefi, A.

doi:10.1007/s11071-021-06436-w

Insights on the continuous representations of piecewise-smooth nonlinear systems: limits of applicability and effectiveness

Journal Article · Thu Apr 22 00:00:00 EDT 2021 · Nonlinear Dynamics

DOI:https://doi.org/10.1007/s11071-021-06436-w· OSTI ID:1781561

Saunders, B. E. ^[1]; Vasconcellos, R. ^[2]; Kuether, R. J. ^[3]; ^[1]

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

Dynamical systems subject to intermittent contact are often modeled with piecewise-smooth contact forces. However, the discontinuous nature of the contact can cause inaccuracies in numerical results or failure in numerical solvers. Representing the piecewise contact force with a continuous and smooth function can mitigate these problems, but not all continuous representations may be appropriate for this use. Here, five representations used by previous researchers (polynomial, rational polynomial, hyperbolic tangent, arctangent, and logarithm-arctangent functions) are studied to determine which ones most accurately capture nonlinear behaviors including super- and subharmonic resonances, multiple solutions, and chaos. The test case is a single-DOF forced Duffing oscillator with freeplay nonlinearity, solved using direct time integration. This work intends to expand on past studies by determining the limits of applicability for each representation and what numerical problems may occur.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); Coordination for the Improvement of Higher Education Personnel of Brazil (CAPES); National Council for Scientific and Technological Development (CNPq)

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1781561

Report Number(s):: SAND--2021-4573J; 695564

Journal Information:: Nonlinear Dynamics, Journal Name: Nonlinear Dynamics Vol. 107; ISSN 0924-090X

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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chaotic responses
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