ME 566 Advanced Vibration and Structural Dynamics I
Fall 2013 Final Examination
Due Tuesday, December 10, 2013
1. Modal Analysis: A 2x2 system has the following mass and stiffness matrices:
M = ! 4 1
ME 566 Fall 2013
Homework # 1 Solutions
Problem 1
The bar is shown below in both equilibrium (left) and non-equilibrium (right) conditions. In general, both
y and can be nonzero simultaneously, so the
Mechanical and Structural Vibrations
Final Exam Solutions
12/13/2013
Problem 1: Modal Analysis
A 22 system has the following mass and stiness matrices:
4
1
1
M=
4
and
10
5
5
K=
10
Find the natural fre
ME 566
Advanced Vibration and Structural Dynamics I
Fall 2013 Midterm Examination
Open book / open notes
1. Consider an undamped single degree of freedom system,
2
!
q + ! nq =
Q (t )
m
Using any meth
ME 566 Fall 2013
Homework # 2 Solutions
1. An undamped system is subject to a triangular pulse, dened by:
10t kN
for 0 < t < 0.2 s
0
Q(t) =
for t > 0.2 s
The mass is 2kg and the natural frequency is 5
ME 566 - Fall 2013
Homework # 3 Solutions
Problem 1
An electronic instrument is isolated from the vibratory motion of the oor by a set of four springs collinearly
mounted with dampers (one spring/damp
ME 566 - Fall 2013
Midterm Exam Solutions
Problem 1
Consider an undamped single degree of freedom system,
2
q + n q =
Q(t)
m
Using any method you wish, derive the complete transient response q (t) to
Mechanical and Structural Vibrations Homework # 6
12/3/2013
Problem 1
Consider axial vibrations of a bar that is xed at both ends and has a lumped mass m attached at its center.
Using the Ritz method,
Mechanical and Structural Vibrations Homework # 5
11/19/2013
Problem 1
A two-degree of freedom system has matrix equations of motion
M
x1
x1
+C
x2
x2
x1
+K
=F
x2
where
M=
20
5
5
10
kg,
C=
and
4
1
1
8
ME 566 - Fall 2013
Homework # 4 Solutions
Problem 1
The mass and stiness matrices for a system are
M=
4
0
0
2
kg
and
K=
200
200
200
800
N/m
Determine the systems natural frequencies and corresponding