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Subject: Mechanical Vibrations Examiner: Dr. Farouk Omar Class: 4 Year Time: 3 Hrs

This document contains a mechanical vibrations final exam for 4th year students with 6 questions. The exam is from Wasit University's College of Engineering Mechanical Engineering Department. Question 1 has two parts about finding the spring constant and damping coefficient of an electric motor's foundation from its free vibration response graph, and deriving the natural frequencies of a clamped-free rod. Question 2 involves deriving the equation of motion and finding the frequency range of vibration for a mass-spring-damper system. Question 3 is about finding the support stiffness and damping that satisfy design criteria for a rigid rotor's transmitted force. Question 4 involves deriving the equations of motion and natural frequencies/mode shapes for a simplified airplane landing gear model.

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Farouk Hamdoon
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109 views2 pages

Subject: Mechanical Vibrations Examiner: Dr. Farouk Omar Class: 4 Year Time: 3 Hrs

This document contains a mechanical vibrations final exam for 4th year students with 6 questions. The exam is from Wasit University's College of Engineering Mechanical Engineering Department. Question 1 has two parts about finding the spring constant and damping coefficient of an electric motor's foundation from its free vibration response graph, and deriving the natural frequencies of a clamped-free rod. Question 2 involves deriving the equation of motion and finding the frequency range of vibration for a mass-spring-damper system. Question 3 is about finding the support stiffness and damping that satisfy design criteria for a rigid rotor's transmitted force. Question 4 involves deriving the equations of motion and natural frequencies/mode shapes for a simplified airplane landing gear model.

Uploaded by

Farouk Hamdoon
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Wasit University Subject: Mechanical Vibrations

College Of Engineering Examiner: Dr. Farouk Omar


Mechanical Engineering Dept. Class: 4th year
1st Attempt, Final Exam Time: 3 hrs

2018 - 2019

Note: Attempt five questions only. Each question carries 10 marks.

Q1) Answer the following:

A) The free-vibration response of an electric motor of weight 500 N mounted on a


viscous damped foundation is shown in Figure (1). Find the spring constant
and damping coefficient of the foundation.

B) Derive a formula for the natural frequencies of a clamped-free rod and find the
required length of the rod such that the second natural frequency is 1878 Hz.
Take E = 2 X 1011 N/m2 and ρ = 7800 kg/m3.

Q2) Consider the system shown in Figure (2) which is excited from its base by a
sinusoidal displacement y (t) = Y sin (ωt), where Y is the amplitude of the base or
support excitation, and ω is the excitation frequency.
a) Derive the equation of motion.
b) Find the frequency range at which the mass is vibrating with an amplitude of at
least 0.05 m when Y= 0.2 m. Take m= 1 kg, k1= 1000 N/m, k2 = 200 N/m, c2= 5
N.s/m.

Q3) The rigid rotor of a turbine, having a total mass (m=30 kg), is known to have
imbalance that produces undesirable transmitted force to the foundation. The
application requires that the transmitted force is (0.75) of the impressed force (i.e. FT
= 0.75 FO) when the turbine is operating at ω = 500 rad/sec. in addition, the
transmission can't exceed (Tr = 1.25) at resonance. Find the support stiffness (k) and
damping (c) that satisfies these design criteria.

Q4) A simplified model of the main landing gear system of a small airplane is shown
in Figure (3). With m1 = 100 kg, m2 = 5000kg, k1 = 104 N/m, and k2 =106 N/m:
a. Find the equations of motion of the system.
b. Find the natural frequencies and the mode shapes of the system.

Q5) Derive the equations of motion of the system shown in Figure (4) using Newton's
second law.

Q6) Derive the equations of motion of the system shown in Figure (5) using
Lagrange's equations.

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‫‪Figure 1‬‬ ‫‪Figure 2‬‬

‫‪Figure 3‬‬

‫‪X3‬‬

‫‪Figure 5‬‬

‫‪Figure 4‬‬

‫أتمنى لكم التوفيق‬

‫رئيس القسم‬ ‫مدرس المادة‬


‫ا‪.‬م‪.‬د‪ .‬هادي عبيد بشر‬ ‫م‪.‬د‪ .‬فاروق عمر حمدون‬

‫‪2‬‬

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