The motor-pump unit is used to power flow of multi-phase fluid within the piping loop

The motor-pump unit is used to power flow of multi-phase fluid within the piping loop. A centrifugal pump with maximum flow rate of 0.0167 m3/s and a 2.2 kW three-phase induction motor with 4 poles are used within the piping system. The piping is made of PVC with a 50 mm diameter and 5 mm cross-sectional thickness. Each existing support pillar for the piping is made of a hollow steel column with a dimension of 0.5 m (height) x 50 mm (width) x 25 mm (length) x 3 mm (cross-sectional thickness).
Evaluate the natural frequencies of the motor-pump unit and express their corresponding mode shapes in terms of ?/?, considering the vertical displacement of the center of gravity (C.G.) and angular rotation about the C.G. of the unit. Provide your references on the data used for motor and pump and state your assumptions clearly.


Assume Motor,
M= 30kg
385mm(length)x215mheigth)x205mm(width)
E=200GPa


Assume Pump,
M=47kg
320mm(length)x505mheigth)x270mm(width)
E=200GPa