Wayne State University

ENGINEERIN ME2500

Copyrighted Materials: Chin An Tan and Bongsu Kang, Numerical Methods and
Programming Using MATLAB — Principles & Practice
1. Background
This problem is set up to demonstrate the engineering relevance of root finding methods (solving
a single algebraic equation 𝑓(𝑥) = 0) using simple models of vehicle suspension designs. The
suspension system shown in Figure 1 can be modeled by an equivalent single-degree-of-freedom
(SDOF) mass-spring-damper system. Advanced control of suspension systems is an important
subject in autonomous driving and Advanced Driver-Assistance Systems (ADAS).
A simple NVH (noise, vibration, and harshness) test can be set up to understand the fundamental
characteristics of the suspension system. For instance, a static force over a short duration can be
applied to vehicle bumper to initiate the system to oscillate. Time history data of the transient
vibration of the suspension system can provide engineers with useful information about the
performance of the suspension. Figure 2 shows a typical plot of the suspension displacement as
a function of time (for underdamped system) after an initial force or disturbance is applied.
Understanding the behaviour of this simple model is fundamental for more complicated designs
of vehicle suspensions, with applications to active safety, rollover prevention, and autonomous
driving. This project is also a