Speed Oscillations of a Vehicle Rolling on a Wavy Road

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 q...

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Autor principal:	Walter V. Wedig
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	road models quarter car models limit cycles acceleration speed portraits speed oscillations velocity bifurcations Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/0d6d101183ab4e44846b70d989d3ab75
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spelling	oai:doaj.org-article:0d6d101183ab4e44846b70d989d3ab752021-11-11T15:24:12ZSpeed Oscillations of a Vehicle Rolling on a Wavy Road10.3390/app1121104312076-3417https://doaj.org/article/0d6d101183ab4e44846b70d989d3ab752021-11-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/21/10431https://doaj.org/toc/2076-3417Every 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. They need more power supply in order to overcome the resonance peak. For small damping, the speeds after resonance are unstable. They migrate to lower or supercritical speeds of operation. Stability in mean is investigated.Walter V. WedigMDPI AGarticleroad modelsquarter car modelslimit cyclesacceleration speed portraitsspeed oscillationsvelocity bifurcationsTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10431, p 10431 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	road models quarter car models limit cycles acceleration speed portraits speed oscillations velocity bifurcations Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	road models quarter car models limit cycles acceleration speed portraits speed oscillations velocity bifurcations Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Walter V. Wedig Speed Oscillations of a Vehicle Rolling on a Wavy Road
description	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. They need more power supply in order to overcome the resonance peak. For small damping, the speeds after resonance are unstable. They migrate to lower or supercritical speeds of operation. Stability in mean is investigated.
format	article
author	Walter V. Wedig
author_facet	Walter V. Wedig
author_sort	Walter V. Wedig
title	Speed Oscillations of a Vehicle Rolling on a Wavy Road
title_short	Speed Oscillations of a Vehicle Rolling on a Wavy Road
title_full	Speed Oscillations of a Vehicle Rolling on a Wavy Road
title_fullStr	Speed Oscillations of a Vehicle Rolling on a Wavy Road
title_full_unstemmed	Speed Oscillations of a Vehicle Rolling on a Wavy Road
title_sort	speed oscillations of a vehicle rolling on a wavy road
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/0d6d101183ab4e44846b70d989d3ab75
work_keys_str_mv	AT waltervwedig speedoscillationsofavehiclerollingonawavyroad
_version_	1718435350149332992

Speed Oscillations of a Vehicle Rolling on a Wavy Road

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