Effects of time delay on the excited nonlinear quarter and half-car models with jumping nonlinearities

Effects of time delay on the excited nonlinear quarter and half-car models with jumping nonlinearities | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Effects of time delay on the excited nonlinear quarter and half-car models with jumping nonlinearities Masahisa Watanabe, Manish D. Shrimali, Awadhesh Prasad This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7332107/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Nonlinear vehicle dynamics are omnipresent and significantly affect driving performance and safety. In particular, jumping vehicles exhibit strong nonlinearity that can cause severe vibrations and steering instabilities. In this study, the dynamics of nonlinear jumping vehicle models with and without a time delay are investigated to understand their general characteristics. Quarter- and half-car models incorporating jumping nonlinearity are employed in which delayed feedback was introduced as an active suspension control. Numerical simulations are performed under periodic and random excitations. The results reveal several novel findings regarding jumping vehicle systems. First, sudden discontinuous transitions from chaotic to nonchaotic dynamics are observed in the bifurcation diagrams of both models. A general relationship between the time period of the periodic motion and forcing period is also identified. This relationship is also validated in a forced Duffing oscillator with a time delay, which exhibits a generic effect. In the presence of a delay, both in-phase and out-of-phase motions occur, particularly between the front and rear, even under simultaneous excitations. From a practical perspective, in-phase motion between the front and rear is undesirable. Thus, achieving out-of-phase motion within a specific range of delay parameters is important for improved ride performance. Quarter-car model Half-car model Chaos Delayed system Out-of-phase motion Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7332107","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":506366439,"identity":"c50e372f-148a-44a5-8731-5d6dd7fd87a8","order_by":0,"name":"Masahisa Watanabe","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABQ0lEQVRIiWNgGAWjYJACZgYDBCeBgb0BWZIHrxbGBrAWngNgCqoYlxYGZC0SCchaMIFu+/GHnwsK6uQZJJKfP/i5wy6PX/L5xQeMPw7L2zMwP/zAIHMHXYvZmRxj6RkGhw0bJNIMG3vPJBdLzs4pNmBIOGzYw8BmLMHA8wxDy4EcBmkegwOM+28nGDbwtjEnbridkyYB1MLYA5QFOu8whpbzzx//5jGos2+QTv/Y+LetPnH/zTNgLfY9DOzfsGq5kWAGtIU5sUE6x7CZt+1w4gYJ9mMgLYk9DDzYbbnxxsyax+BwcoP8m8LZsm3HiyXO5DAbJKSlJ/cc5imWSMDil/Ppj2/z/KmzbeA5vuHj27bqPH5gGD74YGNt297evvHDxx6MEMMGeAxA0QKJr8SeA8RoYX+AxPlBlJZRMApGwSgY1gAAt+VwtVZXx08AAAAASUVORK5CYII=","orcid":"","institution":"Tokyo University of Agriculture and Technology","correspondingAuthor":true,"prefix":"","firstName":"Masahisa","middleName":"","lastName":"Watanabe","suffix":""},{"id":506366440,"identity":"00354406-23bb-43e8-9c63-4bbf2dd871c4","order_by":1,"name":"Manish D. 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In particular, jumping vehicles exhibit strong nonlinearity that can cause severe vibrations and steering instabilities. In this study, the dynamics of nonlinear jumping vehicle models with and without a time delay are investigated to understand their general characteristics. Quarter- and half-car models incorporating jumping nonlinearity are employed in which delayed feedback was introduced as an active suspension control. Numerical simulations are performed under periodic and random excitations. The results reveal several novel findings regarding jumping vehicle systems. First, sudden discontinuous transitions from chaotic to nonchaotic dynamics are observed in the bifurcation diagrams of both models. A general relationship between the time period of the periodic motion and forcing period is also identified. This relationship is also validated in a forced Duffing oscillator with a time delay, which exhibits a generic effect. In the presence of a delay, both in-phase and out-of-phase motions occur, particularly between the front and rear, even under simultaneous excitations. From a practical perspective, in-phase motion between the front and rear is undesirable. 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