Car vibration modelling assignment

Objectives

To investigate and estimate by analysis natural frequencies and mode shapes for bounce, pitch and roll modes.

To estimate the vibration amplitude at the driver seat given a typical road input.

Analysis -

(a) In the following cases neglect damping.

1. Use a simplified 2 DOF free vibration ¼ car-model for bounce, to estimate the natural frequencies and mode shapes. Include the tyres in this model and state any other assumptions used.

2. Use a simplified 2 DOF free vibration ½ car-model for each bounce-pitch and bounce-roll to estimate the natural frequencies and mode shapes. Exclude the tyres in this model and state any other assumptions used.

3. Analyse 3 DOF free vibration ½ car model for bounce. Calculate the resulting natural frequencies and mode shapes by using a numerical method such as Matrix Iteration. State any assumptions used. Repeat this for both pitch and roll.

4. Analyse the full 4 DOF ½ coupled car models for both bounce -pitch and bounce- roll including the tyres. Find the natural frequencies or Eigen values and Eigen Vectors of the resulting matrix by using MATLAB.

(b) For the above case in (a) 4 with damping included and find the response of the car body at the passenger seat if the road input can be approximated by a sine wave of amplitude 10 mm and a frequency of 10 Hz.

Discussion: Compare and discuss your results by the above methods and comment on the accuracy regarding the assumptions that you made.