Project 3: Multiple degree of freedom systems Due date: Tuesday of Week 8 Weighting: N/A Length N/A Objectives This project relates to the course learning outcomes 13, 5, 6 and 8. Question 1 Your project now is to improve the model you developed in Project #2 and again analyse the performance of the monster truck. The first improvement in the model to be evaluated will be inclusion of the unsprung mass of the wheel, axles and the stiffness of the tyres. Assume a typical tyre pressure of N3D. Rim diameter: 0.6m. Tyre width: m. Tyre height: 1.m. Derive or estimate an approximate linear model for the tyres. [*Make an estimate of the tyre properties, again, do not spend time getting 'good numbers' it is your analysis that is important. State clearly how you obtain this, you may use experimentation, measurement of existing tyre deflection on vehicle of known mass, you may derive, accuracy is less important than approach.] Assume again linear suspension elements and analyse the two degree of freedom system clearly stating assumptions and limitations of your model, (you may use Linear modelling equations, Matlab and Simulink). Analysis Your analysis will include:  An evaluation of suspension performance, vibrations and transients. Deliverables - Team Presentation of key findings (10 minutes), due Thursday Week 7 - Team Report, due Tuesday Week 8Minimum scope Your requirement here is to analyse the monster truck as a mechanical system using mathematical modelling and two degree of freedom vibration analysis. Your analysis will include:  Draw mathematical model schematic of a monster truck.  Simplify the model to be a two degree of freedom system (vertical motion only—Assume there is no roll or pitch).  Free vibration response.  Road surface induced vibration. Assume road speeds up to 0 kph. Assume a simplified corrugation shape and a set of realistic road corrugation depths and wavelengths.  Determine resonant frequencies.  Produce plots of magnification factor and transmissibility factor.  Laplace transform of the modelling equations. From these equations develop transfer functions describing the system. Produce a Bode plots for the system. Reflection and discussion Compare with your Bode diagrams with plots of magnification factor and transmissibility factor. Reflect again on the differences, advantages and disadvantages of frequency domain analysis (Laplace, frequency response etc.) verses time domain (simulation, time series output etc.). Reflect on the differences between the single and two degree of freedom models examined so far. Reflect on resonance, magnitude of responses at resonance and controlling resonant amplitudes etc. Question 2 The second improvement in the model to be evaluated will be inclusion of a pitch degree of freedom, then the addition of more translational degrees of freedom. In addition to the information you have from earlier problems you will need to estimate moments of inertia data as best you can from the diagram and mass data. The last part of your task will be to examine performance over a jump ramp as shown in Figure 1 using your simulink model. m 1 m Figure 1 Analysis Your analysis will include:  An evaluation of the natural frequencies and mode shapes for the monster truck suspension.  Simulation over the jump ramp.Minimum scope  Find the natural frequencies and mode shapes assuming linear suspension elements for a mathematical model using just the vehicle body mass and two degrees of freedoms.  Extend your model to include the stiffness of the tyres and convert your model into a three mass model with four degrees of freedom. Again find the find the natural frequencies and mode shapes.  Develop a Simulink model of the three mass model with four degrees of freedom.  Add non-linearities and damping to the Simulink model to make it more reflective of the real situation.  Use the Simulink model to get an indication of the vehicle performance over the jump ramp. Reflection and discussion Reflect on the differences between the single, two and multiple degree of freedom models examined so far. Reflect on the assumptions upon which the model was originally based and the use of the model to simulate both ground contact and free flight behaviour at the jump. Identify any shortfalls of \RXU model.