pqe vibr no solution07

8/9/2019 Pqe Vibr No Solution07

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COLLEGEOFENGINEERING

MECHANICALENGINEERING

Ph.D. Preliminary Qualifying Examination

Cover Page

VIBRATION Examination

anuary !"# !$$% &'on(ay)

"*$$ am + ,!*$$ noonRoom !,- Engineering Buil(ing

/ENERA0 IN1TR2CTION1*

Thi3 examination 4ontain3 five 5ro6lem3. 7ou are re8uire( to 3ele4t an( 3olve four ofthe five 5ro6lem3. Clearly in(i4ate the 5ro6lem3 you 9i3h to 6e gra(e(. If youattem5t 3olving all of them 9ithout in(i4ating 9hi4h four of your 4hoi4e# the 9or3tfour 5ro6lem3 9ill 6e 4on3i(ere(. Note that Pro6lem , i3 man(atory.

Do all your work on the provided sheets of paper. If you need extra sheets, please request

them from the proctor. When you are finished with the test, return the exam plus anyadditional sheets to the proctor.

For identification purposes, please fill out the following information in ink. Be sure toprint and sign your name. his cover page is for attendance purposes only, and will !eseparated from the rest of the exam !efore the exam is graded. Write your student num!eron all exam pages. Do "# write your name on any of the other exam pages !esides thecover page.

"ame $print in I"%&

'ignature $in I"%&

'tudent "um!er $in I"%&


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'e4hani4al Engineering Ph.D. Preliminary Qualifying ExaminationVi6ration + 'on(ay# anuary !"# !$$%

(ou are required to work four of the five pro!lems. )learly indicate which pro!lems you arechoosing. 'how all work on the exam sheets provided and write your student personalidentification $*ID& num!er on each sheet. Do not write your name on any sheet.

(our *ID num!er+

Que3tion :,

he figure shows a mass 1m hangs from a spring of stiffness k and is in the static

equili!rium position as shown. - second mass 2m at height h was dropped and sticks to

1m without re!ound+

!$;$i& draw the free !ody diagram of the two masses during thesu!sequent motion,


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(ou are required to work four of the five pro!lems. )learly indicate which pro!lems you arechoosing. 'how all work on the exam sheets provided and write your student personal

identification $*ID& num!er on each sheet. Do not write your name on any sheet.

(our *ID num!er+

Que3tion :!

-$;$i& Determine the kinetic energy of the system shown in the figure in terms of x .

=$;$ii& Determine the stiffness at 0m ,

=$;$iii& write the expression for the natural frequency.

x&

k

/k

om

/m

/r

/J

J

Rr


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(our *ID num!er+

Que3tion :=- weight attached to spring stiffness 0/0 "1m has a viscous damping device. When theweight is displaced and released, the period of vi!ration is .2 sec, and the ratio ofconsecutive amplitudes is 3./ to .4.=$;$i& Determine the damping ratio.

-$;$ii& 5nder a forcing excitation ( )/cos 6F t= , determine the steady state responseamplitude and=$;$iii& phase angle.


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(our *ID num!er+

Que3tion :-- counter7 rotating eccentric mass exciter shown in fig. 6 isused to determine the vi!ration characteristics of a structure ofmass 892.3 %g. -t a speed of :44 rpm, a stro!oscopeshows the eccentric masses to !e at the top at the instant thestructure is moving upward through its static equili!riumposition, and the corresponding amplitude is /.; mm. If theun!alance of each wheel of the exciter is 4.4:/ %g7m,determinea. he natural frequency of the structure !$;

6. the damping factor of the structure =$;4. the amplitude at /44 rpm, and !$;(. the angular position of the eccentrics at the instant the

structure is moving upward through its equili!rium positionat /44 rpm. !$;


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(our *ID num!er+

Que3tion :

For the system shown in Fig.:, 1W 9/44 l! and the a!sor!er weight 2W

904 l!. If 1W is excited !y a / l!7in un!alance rotating at 244 rpm,

!;$i& determine the proper value of the a!sor!er spring k .

!;$ii& What will !e the amplitude of 2W

pqe vibr no solution07

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