Coursework - Engineering: structures and dynamics
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If you think you are strong in the field of aerospace structures and dynamics then this is for you,
it is a four question assignment.
(a) Explain what is meant by the term “neutral axis” and find the bending stresses at points A and B and also the position of the neutral axis.
(b) Explain the concept of principal axes and discuss their importance.
(c) Explain why it is important to consider the slenderness ratio of a strut. Illustrate your answer by sketching a graph of ‘critical buckling stresses’ against ‘slenderness ratio’.
(b) A structural steel with E = 210 GPa and yc = 300 MPa is to be used to manufacture struts. For what values of the slenderness ratio would compressive theory be valid? For what values of the slenderness ratio would Euler theory be valid? How could struts whose slenderness ratio lies outside these values be analysed?
Q2. An aircraft wing structure has the cross-section shown in Figure Q2. Assuming that one end is fully built-in, calculate the maximum shear stress, the torsional constant and the angular twist at the free end when the wing is subjected to a uniformly distributed torque of 30 kNm per metre length of the wing. Take G = 28.5 GPa.
The dynamic system shown in the figure Q3, consists of a uniform rigid bar of mass 40 kg hinged at point O. An engine of mass M=40 kg mounted at the other end, generating an excitation force of 600 N at a speed of 1200 rev/min. The suspension of the system consists of a spring of stiffness k = 6000 N/m and a damper with a damping coefficient of c = 60 Ns/m. The dimensions are as shown in the figure.
(a) Draw the free body diagram of the system clearly, hence show that the equation of motion for the system is:
(b) Calculate the damping ratio and the damped natural frequency of the system.
(c) Find the steady-state response (amplitude and phase) of the system and the amplitude of vibration of the engine
Q4- (a) With the aid of a sketch, clearly explain how the first five natural frequencies and mode shapes of a simple structure can be measured in a laboratory set-up, using the following equipment:
Shaker and amplifier
Dynamic strain gauge or accelerometer
Time / Frequency counter
(b) Calculate the first five natural frequencies in Hz and sketch the first five mode shapes of a cantilever beam using the following data:
Length = 1 m
Thickness = 10 mm
Density = 8700 kg/m3
Modulus of Elasticity = 200 GPa
Explain how Finite Elements Analysis may be used to carry out the above task.
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