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 $ and K = " 10 !5 %
#1 4&
$ !5 10 '
"
%
#
&
Find the na
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 amount of stretch in the springs depend on both y and
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 frequencies and mode shapes of the system, and normalize t
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 method you wish, derive the complete transient response q(t
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 50Hz (n = 100 rad/s). The system is initially at rest
in
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/damper combination at each corner), so that the entire appa
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 the input force Q(t) = t2 10t,
assuming zero initial co
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, calculate the rst two natural frequencies of the syste
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 mode shapes.
Solution: The generalized eigenvalue probl