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This coursework exercise involves two parts. Both parts should be completed and submitted as a pdf on the accompanying H7092 Coursework Solution Template available for 2022-23. Please refer to your own Assessment Deadlines & Exam Timetable in Sussex Direct for all submission details.

PART 1 – Dynamic Modelling
Figure 1 shows a 300 tonne earth-moving dumper truck. This vehicle has four huge wheels and a vertically sprung chassis. The chassis suspension system is designed to isolate the load from the effects of ground roughness as the vehicle rolls forward. Dampers are positioned in the system to absorb transmitted energy. Figure 2 shows an equivalent 2DOF system for modelling vertical motion. Two masses m1 and m2 are supported by vertical linear springs k1 and k2 . And two linear dampers, with respective coefficients c1 and c2, combine the effects of tyre and shock absorber damping. The vertical displacements of the two masses, are described by variables z1 and z2. Vertical input displacement arising from forward motion of the truck, is represented by variable y(t).

Construct a matrix equation to describe small amplitude coupled motion of the forced system in terms of variables z1 and z2, by first drawing appropriate free-body diagrams and then using Newtonian mechanics. Identify the excitation vector p(t) , and the matrices [m], [c], and [k], associated with mass,
damping, and stiffness.

PART 2 – Dynamic Analysis and Computation
This is designed to give you some experience of using orthogonality and superposition to predict the transient response of an aircraft wing. The exercise is sufficiently large to begin to resemble a real engineering application i.e. beyond the range of hand calculation. The wing is modelled as a linear 7- DOF system with proportional damping. Orthogonality properties of normal modes enable the system to be reduced to a set of forced SDOF oscillators – each (modal) equation can be solved separately. The response of the entire system can then be obtained by transforming back to physical coordinates. One parameter in the model (namely ‘d’) has been left unspecified. The value you should use, is the date of the month in which you were born. For example, if your birthday is 10th December 2000, your value of d =10. The coursework makes use of a matlab CODE folder (containing matlab m-files – these m-files are listed and attached). Please use the Template.doc, and coursenotes.doc. Template.doc is the pro- forma needed to present the solution. Coursenotes.doc gives 14 pages of theory. You will need to use Matlab to do the computation by completing owncode.m.

The problem
A crude finite element model of an aircraft wing structure involves 7 degrees of freedom, where the model is:
[??]??? + [??]??? + [??]?? = ?? (t) (1)

The vertical displacement vector z has units of length m. The mass and stiffness matrices are:
where the mass per unit length is m = 170 kg/m, and the length L = 40m (take g = 9.81 m/s2). The wing, is initially at rest and totally unloaded for t < 0. At t=0, the tip (node 7) is exposed to a downward step load of 11000N which remains in place for t > 0. The damping matrix [c] is proportional to the mass and stiffness matrices as follows: [c] = 0.6[m] + 0.002[k]. Uncouple equation (1) to obtain

single-degree-of-freedom modal equations with modal damping factors

?i and the undamped modal

natural frequencies

?ni

of the form ??? + 2??0????0??? + ??3 ?? = ??0(??). Solve each equation then

transform your solution back to physical coordinates z .

The form of required solution
You are required to complete the m-file owncode.m and use it to produce numerical and graphical output showing 2 seconds of vertical displacement response of: i) the wing centre (node 4) and ii) the wing tip (node 7) .

You should submit your completed Template document as a pdf by the deadline specified on Sussex Direct, by uploading to Canvas as instructed by the School Office. Please refer to your own Assessment Deadlines and Exam Timetable in Sussex Direct for all submission details.