Advanced Dynamics Assignment-

Question 1 -

Modify a wheelchair into 2 DoF system to enable patient feels less shaking (vibration impact) when moving over a playground rough surface.

Steps: 

• Modify the structure into a 2D spring and mass vibration model.
• Search from the product catalogues to get actual values of elastic stiffness for the wheels or spring stiffness in you 2 DoF model.
• Illustrate the modal forms of vibration.
• If to install a vibration absorber, determine the optimal operating frequency when the wheelchair is used to carry M* kgf weight of patient.
• The operating frequency has to be >20% between the 2 natural frequencies.
• Justify your design to convince the hospital on how the wheelchair is comfortable when carrying a patient.

* is a design variable where different values will be given to each student.

Question 2 -

The design of beams for constructing mega crane by considering the transverse vibration under the vertical load as shown in figure Q2.

Steps: 

• Select 2 types of beam from the product catalogues for making the hanging beams AB and CD (Consider different cross sectional beams, such as I beam or rectangular beam) for lifting the load M * with given the length L*.
• Determine the fundamental frequency of transverse vibration (consider the beam weight itself as well) for the 2 design cases.
• Justify your recommendation to choose which design for mega crane construction in terms of cost-effectiveness, safety factor and others.

* is a design variable where different values will be given to each student.

Question 3 -

The design of a stepped drive shaft to drive centrifugal pump with pulley B and pulley C by considering the critical whirling frequencies in Figure Q3.

Steps:

• Determine suitable diameter D₁ and D₂ for the two shaft lengths L₁*and L₂* for each pulley to absorb 113 Nm. The shaft is made of steel and let the safety factor be SF = 2 for yield by the maximum shear-stress criterion.
• The motor is capable to deliver power P = 6000 kW, determine the maximum frequency range f that can be operated.
• Suggest a possible design to hold the shaft with bearings to avoid whirling occurrence. Justify you design of choosing how many and what type of bearing (short or long bearings) to be used. You must choose the available products from the product catalogues and also try to minimise the cost.

* is a design variable where different values will be given to each student.