ME 3220 Fall 2020

PROJECT

Due: Thursday, December 3, 2020

You must solve both problems described below to receive full points.

Important Note: The project counts for 20% of the final grade.

First Problem (50 Points)

A one degree-of-freedom model of a motor vehicle travelling in the horizontal direction

is shown in Figure 2.17 (Inman, 4th edition) and class notes.

(i) Find analytically the relative vertical displacement of the vehicle as it travels over a

wavy road of the form y(s) Y sin(?s / ?)? , where Y is the amplitude of the wave form,

s is the travelled distance, and 10Y? ? .

(ii) Write a MATLAB program for finding the relative vertical displacement of the

vehicle as it travels over a road bump of the form y(s) Y sin(?s / ?)? and compare the

numerical solution to the analytical solution. (25 points)

(iii) Use the computer program to find numerically and plot the relative vertical

displacement when the vehicle travels over the double step shown below. (25 points)

Parameter values: k = 400 kN/m, m = 1200 kg, ? = 0.5, Y = 0.3 m, ? = 6 m.

Attention: If you answer only question (i), the problem will NOT be graded and it will

count for NOTHING.

Important Note: You need to send me a report and a working MATLAB code that

runs from one starting “run” point

ME 3220 Fall 2020

Second problem (50 points)

Write a MATLAB program that can compute the response of an underdamped spring-

mass system for an arbitrary periodic input.

1. Show that your program can derive the analytical solution for a mass-spring system

governed by the equation ? ?mx cx Kx F t? ? ? , with 1m kg? , 10c kg s? ,

100K N m? , and ? ?F t is the square-pulse function with amplitude 0 10F N? and

period 2 secondsT ?? . We assume that the initial conditions are ? ?0 0.1x m? and

? ?0 3x m s? . (Note: It is the example that we solved in class).

2. Show that your program can derive the solution for any arbitrary periodic force with two examples.

Important Note: You need to send me a report and a working MATLAB code that

runs from one starting “run” point