dynamics

University of Hertfordshire School of Engineering & Technology 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. Vehicle data

Total mass, M = 1200 kg Pitch Moment of Inertia of M about CG, IP = 1800 kg.m

2

Roll Moment of Inertia of M about CG, IR = 750 kg.m

2

Front suspension distance from CG, a = 1.0 ; Rear suspension distance from CG, b = 1.1 m Passenger seat from CG, d = 0.6 m from front suspension.

Rear view CG is symmetrical with each tyre distance from CG, b = 0.6 m Wheel mass both front and rear each, m = 30 kg each. Front suspension stiffness each, K1 = 16 kN/m Rear suspension stiffness each, K2 = 18 kN/m All four damping suspension dashpots each, c = 5.4 kNs/m Tyre stiffness, k = 150 kN/m each.