Mechanical Vibration mini project

Project description
The following figure shows an industrial mixer and the driving system (motor-shafts-gears) used to rotate the two mixing blades. (the shear modulus of elasticity for

the steel in all the shafts G=12*10^(6) Psi)

1. Use lagrange’s theorem to find the equations of motion

Determine the Kinetic Energy (T) of the system and deduce the mass matrix [ I ].

Determine the Potential Energy (V) of the system and deduce the stiffness matrix [ Kt ]

Determine the natural frequencies and the principal modes of vibration of the system by using any specific software (include the name of the software and the printout

of your program) (matlab is preferable)

Note: I will attach the figure when the order opens.

1 Mechanical Vibrations
Fall 2014
The following figure shows an industrial mixer and its driving system (motor~ r , ~ ‘ – I
IL“. ht r MAS ‘. 1453-4“? A ’95;
shafts-gears) used to rotate the two mixing blades. l 5 a”. M 6 1‘ ‘ ’*‘**”fi;
a} d%6+:C.-Lj 2»- JL- 51-3“ HA J M C k‘F‘tS 1< G ‘5 a? , V’ r
1. Use Lagrange’s theorem to find the equations of motion of the above- P“ é:
mentioned system. (fué/ mags,
2. Deduce the mass matrix [ l ]. y
3. Deduce the stiffness matrix [ Kt] ” v
4. Determine the natural frequencies and the principal modes of vibration of the system by using any
specific software (include the name of the software and the printout of your program)
V-“”-“‘-

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