Investigation of a non-linear suspension in a quarter car model

  • Mahmoud Salem

Student thesis: Doctoral ThesisDoctor of Philosophy


This thesis presents the study of a quarter car model which consists of a two-degree-of-freedom (2 DOF) with a linear spring and a nonlinear spring configuration. In this thesis, the use of non-linear vibration attachments is briefly explained, and a survey of the research done in this area is also discussed. The survey will show what have been done by the researches in this new field of nonlinear attachments. Also, it will be shown that this topic was not extensively researched and is a new type of research where no sufficient experimental work has been applied. As an application, a quarter car model was chosen to be investigated. The aim of the Thesis is to validate theoretically and experimentally the use of nonlinear springs in a quarter car model. Design the new type of suspension and insert it in the experimental set up, built from the ground up in the laboratory.
A novel criterion for optimal ride comfort is the root mean square of the absolute acceleration specified by British standards ISO 2631-1997. A new way to reduce vibrations is to take advantage of nonlinear components. The mathematical model of the quarter-car is derived, and the dynamics are evaluated in terms of the main mass displacement and acceleration. The simulation of the car dynamics is performed using Matlab® and Simulink®. The realization of vibration reduction through one-way irreversible nonlinear energy localization which requires no pre-tuning in a quarter car model is studied for the first time. Results show that the addition of the nonlinear stiffness decreases the vibration of the sprung mass to meet optimal ride comfort standards. As the passenger is situated above the sprung mass, any reduction in the sprung mass dynamics will directly have the same effect on the passenger of the vehicle. The future is in the use of a nonlinear suspension that could provide improvement in performance over that realized by the passive, semi active and active suspension. The use of a quarter car model is simple compared to a half car model or a full car model, furthermore in the more complex models you can study the heave and the pitch of the vehicle. For the initial study of the nonlinear spring the quarter car model was sufficient enough to study the dynamics of the vehicle.
Obtaining an optimum suspension system is of great importance for automotive and vibration engineer involved in the vehicle design process. The suspension affects an automobile’s comfort, performance, and safety. In this thesis, the optimization of suspension parameters which include the spring stiffness and damper coefficient is designed to compromise between the comfort and the road handling. Using Genetic algorithm an automated optimization of suspension parameters was executed to meet performance requirements specified. Results show that by optimizing the parameters the vibration in the system decreases immensely.
Date of Award1 May 2018
Original languageEnglish
SupervisorXianghong Ma (Supervisor)


  • quater car
  • McPherson suspension
  • simulation
  • nonlinear dyamics
  • targeted energy transfer
  • ride comfort
  • genetic algorith optimization

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