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Speed oscillations of a vehicle rolling on a wavy road

Wedig, W. V.


Every driver knows that his car is slowing down or accelerating when driving up or down, respectively. The same happens on uneven roads with plastic wave deformations, e.g., in front of traffic lights or on nonpaved desert roads. This paper investigates the resulting travel speed oscillations of a quarter car model rolling in contact on a sinusoidal and stochastic road surface. The nonlinear equations of motion of the vehicle road system leads to ill-conditioned differential-algebraic equations. They are solved introducing polar coordinates into the sinusoidal road model. Numerical simulations show the Sommerfeld effect, in which the vehicle becomes stuck before the resonance speed, exhibiting limit cycles of oscillating acceleration and speed, which bifurcate from one-periodic limit cycle to one that is double periodic. Analytical approximations are derived by means of nonlinear Fourier expansions. Extensions to more realistic road models by means of noise perturbation show limit flows as bundles of nonperiodic trajectories with periodic side limits. Vehicles with higher degrees of freedom become stuck before the first speed resonance, as well as in between further resonance speeds with strong vertical vibrations and longitudinal speed oscillations. ... mehr

Verlagsausgabe §
DOI: 10.5445/IR/1000140693
Veröffentlicht am 15.12.2021
DOI: 10.3390/app112110431
Zitationen: 3
Web of Science
Zitationen: 2
Zitationen: 3
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Technische Mechanik (ITM)
Publikationstyp Zeitschriftenaufsatz
Publikationsdatum 05.11.2021
Sprache Englisch
Identifikator ISSN: 2076-3417
KITopen-ID: 1000140693
Erschienen in Applied Sciences (Switzerland)
Verlag MDPI
Band 11
Heft 21
Seiten 10431
Schlagwörter road models; quarter car models; limit cycles; acceleration speed portraits; speed oscillations; velocity bifurcations; noisy limit cycles; limit flows of trajectories; Sommerfeld effects; differential-algebraic systems; polar coordinates of roads; covariance equations; stability in mean; supercritical speeds; analytical travel speed amplitudes; Floquet theory applied to limit cycles
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