MEC421_KJM457_4

CONFIDENTIAL EM/JUN 2012/MEC421/KJM457

UNIVERSITI TEKNOLOGI MARA FINAL EXAMINATION

COURSE

COURSE CODE EXAMINATION TIME

DYNAMICS AND VIBRATIONS/VECTOR DYNAMICS AND VIBRATIONS MEC421/KJM457 JUNE 2012 3 HOURS

INSTRUCTIONS TO CANDIDATES

1. This question paper consists of five (5) questions. Answer ALL questions in the Answer Booklet. Start each answer on a new page. 2.

3. Do not bring any material into the examination room unless permission is given by the invigilator.

Please check to make sure that this examination pack consists of:

i) the Question Paper ii) an Answer Booklet - provided by the Faculty iii) a one - page Appendix 1

DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO This examination paper consists of 6 printed pages

Hak Cipta Universiti Teknologi MARA CONFIDENTIAL

CONFIDENTIAL 2 EM/JUN 2012/MEC421/KJM457

QUESTION 1

The hydraulic cylinder as shown in Figure Q1 produces a limited horizontal motion of point A. Given that vA =4m/s moves to the right at constant velocity. At the instant when

9 = 45, determine:

a) the angular velocity coABD of link ABD at this position, and

b) the velocity and acceleration of point D. (20 marks)

200m

Figure Q1



QUESTION 2

The assembly of spatial mechanism shown in Figure Q2 is rotating at constant angular velocity of Q = 2 rad/s and moving constantly with the velocity oiVcollar =\mls in the ditection shown. Simulteneously, arm AB and disc BC rotate constantly at ji = Iradls and q = Aradls respectively. At the instant when 6 = fi = tan"1 3/4, determine:

a) the total angular velocity and acceleration of disc BC, and b) the absolute velocity of point B. (Note that y2-z2 plane lies in the same plane with plane Z-y^

(20 marks)

Figure Q2



QUESTION 3

The assembly shown in Figure Q3, consisting of the solid sphere of mass m, and the uniform slender rod of length 2c and mass m, which revolves about the vertical z-axis with an angular velocity UJ. The rod is welded with the inclination B as shown to the horizontal rod with negligible mass. Determine:

i) the total angular momentum H0 of the sphere and inclined rod, and ii) the kinetic energy T of both sphere and inclined rod.

(20 marks)

Figure Q3



QUESTION 4

Figure Q4 shows a block with mass m linked to a stepped drum radius at r7. The motion of the block is influenced by a viscous damper with damping coefficient c. A spring stiffness k is attached to the outer part of the drum at radius r2.

a) Derive the equation of motion of the system from the first principle. b) If the amplitude of vibration of the system decays to half of its initial value in 5 complete

cycles with a period of 0.35 sec, determine the spring stiffness k and the viscous damping coefficient c.

(20 marks) [Given that total mass moment of inertia for the compound drum is 2.4 kg.m2, m = 5 kg, r1 = 200 mm and r2 = 400 mm.]

Figure Q4

) Hak Cipta Universiti Teknologi MARA CONFIDENTIAL


QUESTION 5

a) Shows that the mathematical model of a machine is represented by mass M, damper C, and stiffness K when subjected to an external force F cos cur, has the solution for the steady state amplitude which is given by the expression:

F/ xa = uL

[(co2n-o>2)2+(2axong)2]2

Specify all the units used in the expression. (8 marks)

b) A centrifugal pump of mass 500 kg is mounted on a flexible support which caused the support to deflect by 6 mm. The ratio of damping coefficient to the critical damping coefficient for the support found to be 0.15. If the pump running at 500 rev/min, an amplitude of vibration of 5 mm has been measured. Calculate the value of disturbing force created by the pump during its operation.

(12 marks)

END OF QUESTION PAPER


CONFIDENTIAL APPENDIX 1 EM/JUN 2012/MEC421/KJM457

Main Formulae for Dynamics

Kinematics

o R = Ru + OJAR

o R = Ru + 2COARU + aAR + G)A(COAR)

Moment of Inertia O * \J XX ytiy T" 1 7 W7 Z.1 yy tl yliy 2*1 yyllyUy 21 yyU yti y

Angular Momentum

o H_0 = RGAmvG + HG where HG = Hxi + Hyj + H2k

Hx

*y

H2

-

-

=

h^x - Ixy*y - / s f f l J

Iy

MEC421_KJM457_4

Documents

Transcript of MEC421_KJM457_4