# Homework Help: Mechanical Vibration Problem?

1. Mar 7, 2014

### toolpusher123

Hi, I'm currently studying Mechanical Eng & have a class next semester 'Eng Analysis', which involves a large section on vibration. I've been trying to work my way through S.S.Rao, Mech Vibrations, 2nd edition. There's one specific problem; Project 5.51/Chapter 5/page 292.
The problem concerns; two step cone pulleys connected by a belt. All relevent variables are given i.e. input/output shaft rpm, driven puley rpms, distance between centres,polar moments of inertia etc.
I understand that this is a 2 Degrees of Freedom problem, & I should draw a free body diagram ( 2 pulleys connected by 2 springs). It's theinitial 'Equations of Motion' that I can't derive, & without these I can't really start the problem. I've attached a screen shot containing a clear example of the problem.
Any help thats offered would be greatfully received.

#### Attached Files:

• ###### 2 Degrees of Freedom.JPG
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Last edited by a moderator: Mar 7, 2014
2. Mar 7, 2014

### Staff: Mentor

What does the textbook say about this kind of problem? What equations does the text use when describing this kind of problem?

3. Mar 7, 2014

### AlephZero

From the question:
??? Either I don't understand the question, or there is a typo somewhere. Those numbers don't seem to be consistent with each other.

4. Mar 8, 2014

### toolpusher123

Same problem, updated rpm's & diameters...

Hi, sorry here's the question with updated variables i.e. input shaft speed, output pulley speeds.
Young's modulus for the belt: j1= 1x10^10 N/m^2, Drive step cone mass moment of inertia: j2=0.35 kg.m^2, Driven step cone mass moment of inertia: 0.6 kg.m^2, Distance between centres: c=2.8m, belt width: 19mm

1st step: Free Body Diagram. this is essentially the 2 masses connected by 2 springs.
2nd step: Using Newton's 2nd law (∑F=ma), write Eq's of motion.
3rd: Assume simple harmonics. x=X sin (ωt+ø), x'=ωX cos (ωt+ø)
4th: determine natural frequencies...
I think it's 'Rayleigh's energy method', I should use to find the KE of the step cones & PE of the springs.
It's the initial Eq's of motion that I can't derive.

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5. Mar 8, 2014

N=300rpm
No1=650rpm
No2=450rpm
No3=250rpm
No4=100rpm
d1=400mm
d2=300mm
d3=200mm
d4=100mm

6. Mar 8, 2014

### toolpusher123

..........

Last edited: Mar 8, 2014