Mechanical Vibrations MCT 4328/4311INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA END OF SEMESTER EXAMINATION SEMESTER II, 2012/2013 SESSION KULLIYYAH OF ENGINEERING Programme : MECHATRONICS ENGINEERING Level of Study : UG 4 Time : 2.30 pm – 5.30 pm Date : 25 May 2013 Duration : 3 Hrs Course Code : MCT 4328 / 4311 Section(s) : 1 Course Title : Vibration Analysis and Control This Question Paper Consists of 5 (Five) Printed Pages (Including Cover Page) With 5 (Five) Questions. INSTRUCTION(S) TO CANDIDATES Answer ALL questions SPECIAL REQUIREMENTS Vibration Data Book (supplied) KoE approved calculator allowed (non-programmable and non-graphical) Do NOT open until you are asked to do so by the invigilator ***** Any form of cheating or attempt to cheat is a serious offence which may lead to dismissal 1/5 The stiffness k1 = k2 = k correspond to the bending stiffness of the two wings. 2 can be used. b) It is required to design an electromechanical system to achieve a natural frequency of 1. direction of motion). Using the equations of motion derived in part (i). Determine the damping factor and the bandwidth of ( 6 marks ) the system. the masses of head. Give an interpretation of the results (e. The three masses indicate the masses of the two wings (m1 = m3 = m) and the fuselage (m2 = 5m). Derive the equations of motion (in matrix form) of the airplane using the three.g. which can be modelled as cantilever beam so that k1 = k2 = k = 3EI / l 3. a three- degree-of-freedom model.27 μm. Develop a sequence of three improved approximations for modelling the human body. [25 marks] For a simplified analysis of the vibration of an airplane in the vertical direction. ii. [20 marks] a) A study of the response of a human body subjected to vibration/shock is important in many applications. i. shown in Fig. (6 marks) degree-of-freedom model. Determine the damping ratio of the system when the static deflection of the ( 6 marks ) shaft is equal to 1. the natural frequencies and mode shapes of the airplane.000 Hz and a Q factor of 1200. spinal column. c) The Bode plot of shaft vibration of a turbine obtained during coast-down is shown in Fig. hips. and legs influence the response characteristics. find a. Mechanical Vibrations MCT 4328/4311 Q1. Fig. abdomen. (4 marks) 2/5 . and ( 8 marks ) legs and the elasticity / damping of neck. upper torso. In a standing posture. (15 marks) b. 1. 1 Q2. Assuming a deflection shape of ( ) find the natural frequency of transverse vibration of the beam using energy method. Fig. 3. [15 marks] A uniform simply supported beam of length 250 cm with a hollow rectangular section is shown in Fig. The material of the beam has a Young’s modulus of E = 205 GPa and a unit mass of γ = 7.83 g / cm3. 2 Q3. Mechanical Vibrations MCT 4328/4311 Fig. 3 3/5 . (7 marks) ii. [15 marks] The armature of a variable-speed electric motor. m = 150 kg. √ √ . [25 marks] a) What are the advantages and disadvantages of active vibration control? (4 marks) b) Briefly explain two types of smart materials used in vibration control.5. is close to the frequency of the disturbance. Find the magnitude of the response and the actuator force of the system in the steady state. The motor is mounted on an isolator having a stiffness of 10 kN/m and a dashpot having a damping ratio of 0. (10 marks) END OF PAPER 4/5 . 2) The damping ratio of the system is small with a value of √ . Find the speed range over which the amplitude of the fluctuating force transmitted (7 marks) to the foundation will be larger than the exciting force. Mechanical Vibrations MCT 4328/4311 Q4. of mass 200 kg. ii. it is proposed to use an active control system. i. the following observations can be made from the given data : 1) The natural frequency of the system. damping constant c = 4000 N- s/m. and stiffness k = 6 x 106 N/m is subjected to a rotating unbalance force given by f(t) = 100 sin (60π t).15. Because the values of k and c of the system cannot be altered. Find the speed range over which the transmitted force amplitude will be less than (8 marks) 10 percent of the exciting force amplitude. (4 marks) c) A single-degree-of-freedom of a mass. Design the control gains required to achieve the desired valued of ωn and ζ. i. is imbalance due to manufacturing errors. Q5. It is desired to change the natural frequency of the system to 100 rad/s and the damping ratio to 0. . Mechanical Vibrations MCT 4328/4311 Formula: 1) 2) ∫ ( ) ∫ [ ] 5/5 .
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