Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 6th Sem 2161901 Dynamics Of Machinery Previous Question Paper

Seat No.: ________

Enrolment No.___________

**GUJARAT TECHNOLOGICAL UNIVERSITY**

**BE - SEMESTER? VI EXAMINATION ? SUMMER 2020**

**Subject Code: 2161901**

**Date:29/10/2020**

**Subject Name: Dynamics of Machinery**

**Time: 10:30 AM TO 01:00 PM**

**Total Marks: 70**

**Instructions:**

**1. Attempt all questions.**

**2. Make suitable assumptions wherever necessary.**

**3. Figures to the right indicate full marks.**

**MARKS**

**Q.1 (a)**Explain why the reciprocating masses are partially balanced.

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**(b)**Explain the terms static balancing and dynamic balancing. State

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the necessary conditions to achieve them.

**(c)**Four masses A, B, C and D carried by a rotating shaft are at radii

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110, 140, 210 and 160 mm respectively. The planes in which the

masses revolve are spaced 600 mm apart and the masses of B, C

and D are 16 kg, 10 kg and 8 kg respectively. Find the required

mass `A' and the relative angular positions of the four masses so

that shaft is in complete balance.

**Q.2 (a)**What is Hammer blow? Derive an expression for limiting speed

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required for hammer blow.

**(b)**Explain the balancing of several masses rotating in same plane by

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graphical method.

**(c)**For a twin V-engine the cylinder centerlines are set at 900. The

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mass of reciprocating parts per cylinder is 2 kg. Length of crank

is 100 mm and length of connecting rod is 400 mm. Determine the

primary and secondary unbalanced forces when the crank bisects

the lines of cylinder centerlines. The engine runs at 1000 rpm.

**OR**

**(c)**A four stroke five cylinder in-line engine has a firing order of 1-

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4-5-3-2-1. The centres lines of cylinders are spaced at equal

intervals of 15 cm, the reciprocating parts per cylinder have a

mass of 15 kg, the piston stroke is 10 cm and the connecting rods

are 17.5 cm long. The engine rotates at 600 rpm. Determine the

values of maximum primary and secondary unbalanced forces and

couples about the central plane.

**Q.3 (a)**What are the desirable and undesirable effects of vibration?

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**(b)**Define the terms: Natural frequency, Damping, Resonance, and

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Simple Harmonic Motion.

**(c)**A pendulum consists of a stiff weightless rod of length `l' carrying

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a mass `m' on its end as shown in Fig. Q.3(c). Two springs each

of stiffness `k' are attached to the rod at a distance `a' from the

upper end. Determine the frequency for small oscillation.

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**Fig. Q.3(c)**

**OR**

**Q.3 (a)**Find the equation for natural frequency of a spring mass vibrating

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system by using equilibrium method.

**(b)**Explain the terms `under-damping', `over-damping' and `critical

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damping'

**(c)**A vibrating system is defined by the following parameters: m = 3

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kg, k = 100 N/m, c = 3 N-sec/m. Determine (a) The damping

factor (b) the natural frequency of damped vibration (c)

logarithmic decrement (d) the ratio of two consecutive amplitudes

(e) the number of cycles after which the original amplitude is

reduced to 20%.

**Q.4 (a)**Draw and explain a plot of magnification factor versus frequency

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ratio curves

**(b)**Define and derive an expression for logarithmic decrement

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**(c)**A gun barrel of mass 500 kg has a recoil spring of stiffness 300

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KN/m. If the barrel recoils 1.2 meters on firing, determine, (a)

initial velocity of the barrel (b) Critical damping coefficient of the

dashpot which is engaged at the end of the recoil stroke (c) Time

required for the barrel to return to a position 50 mm from the

initial position.

**OR**

**Q.4 (a)**Differentiate between viscous damping and coulomb damping.

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**(b)**How does the force transmitted to the base change as the speed of

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the machine increases? Explain using an equation and the

corresponding graph.

**(c)**A mass of 50 kg is suspended by a spring of stiffness 12KN/m and

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acted on by a harmonic force of amplitude 40N. The viscous

damping coefficient is 100 N-s/m. Find

i.

Resonant amplitude ii. Peak amplitude

iii.

Peak frequency

iv. Resonant phase angle

v.

Peak phase angle

**Q.5 (a)**What is meant by critical speed of a shaft? Which are the factors

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affecting it?

**(b)**Derive an expression for length of torsionally equivalent shaft

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system

**(c)**Two rotors A and B are attached to the end of a shaft 50 cm long.

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Weight of the rotor A is 300 N and its radius of gyration is 30 cm

and the corresponding values of B are 500 N and 45 cm

respectively. The shaft is 7 cm in diameter for the first 25 cm, 12

cm for the next 10 cm and 10 cm diameter for the remaining of its

length. Modulus of rigidity for the shaft material is 8 ? 1011 N/m2.

Find: (i) the position of the node (ii) the frequency of torsional

vibration.

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**OR**

**Q.5 (a)**Discuss the Rayleigh's method to obtain the natural frequency of

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the beam.

**(b)**What is a continuous system? How does a continuous system

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differ from a discrete system in the nature of its equations of

motion?

**(c)**A rotor having a mass of 5 kg is mounted midway on a simply

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supported shaft of diameter 10 mm and length400 mm. Because

of manufacturing tolerances, the CG of the rotor is 0.02 mm away

from the geometric centre of the rotor. If the rotor rotates at 3000

rpm, find the amplitude of steady state vibrations and the dynamic

force transmitted to the bearings. Neglect the effect of damping.

Take E = 2 1011 N/m2.

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This post was last modified on 04 March 2021