Q1- The body, suspension and engine mounting system of a vehicle may be idealised as a three degree of freedom system consisting of a bar of mass 1400 kg and the centre of mass at G, 1 m from the front and 2 m from the rear ends as shown in the Figure Q1. The suspension system consists of springs and dampers, the front suspension consists of a spring of stiffness of kF = 25 kN/m and damper of damping coefficient cF and the rear with stiffness of kR = 20 kN/m and damping coefficient of cR.

The moment of inertia of the vehicle about point G is1200 kgm2. The engine and its mount is idealised as mass-spring-damper attached to the vehicle at G to isolate the engine vibration transmitted to the vehicle, the engine has a mass of 400 kg, the isolator has stiffness kE= 10 kN/m and damping coefficient of cE.

(a) Draw the free body diagrams and express the system matrix equations of motion in parametric form for the system.

(b) Using the above data and eigen functions in MATLAB, calculate all the mass- normalised modal vectors and associated undamped natural frequencies. Hence sketch the modeshapes illustrating the dynamic behaviour of the system. Use hand calculations wherever possible to verify the results obtained from MATLAB.

(c) The engine produces a sinusoidal excitation force of magnitude 150 N at frequency of 30 Hz, further excitation forces from the road are in the form of unit impulses applied to the front and rear ends of the vehicle, using Modal Analysis calculate the response of the system at the front suspension. using MATLAB plot the response in time domain. Assume damping matrix is proportional to the stiffness matrix with a proportionality factor of 0.02.

(d) Calculate one Frequency Response Function in Inertance form and plot (linear and log (dB)) in the frequency range of interest using MATLAB and comment on its validity.

Q2- Using "youtube or Google" find video or information on "Ground Vibration Testing". Write an account of the technique with some case studies, the following keywords must appear in the report:

Structural Dynamics, Methods of excitation, Sensors, Frequency Response Functions, Modal testing, Natural frequencies, damping and Mode shapes, Aero- elascticity, Flutter, Flight envelope (the length of report must be around 1000 words)