Lamped-parameter and finite difference models for a transversely vibrating beam
Consider continues and discrete mass-spring-rod models of a cantilever beam shown below.
E ( x ) ( x ) A( x ) I ( x )
2
1
n2
n 1
n
L
k2
k1
kn
L1
L0
0
m1
m0
m2
mn
mn 2
u1
m1
Ln
The system shown in the figure below consists of a disk of radius r , mass m1 and moment of
inertia I G which is rolled on the ground with no slip. A flexible pendulum of mass m 2 and
spring k , of free length L , is attached to the center of the disk as
Advanced Vibration
Ex. 5
Submit Wed. May 4, 2011
Write an appropriate Matlab program that calculates natural frequencies and mode-shape of a
transversely vibrating beam shown below and its discrete finite difference model. By using
the program calculate t
Advanced Vibration
Ex. 4
Submit Wed. April 27, 2011
1. Determine the spring k 2 which completely absorbs
the steady state motion of mass m1 . What is the
steady state amplitude of vibration for mass m2 ?
m2 = 1
k2
f = 2 sin 5t
m1 = 4
k1 = 10
10
2. Determi
Advanced Vibration
Ex. 3
Submit Wed. March 23, 2011
1. Consider the six d.o.f. shown below,
(a) Explain how you can find one natural frequency of the system by inspection.
(b) Determine the six natural frequencies and mode shape of the system by solving
t
Advanced Vibration
Ex. 2
Submit: Monday, February 28, 2011
1. Consider the system shown in Figure 1.
(a) Write the differential equation of motion for the system.
(b) Determine its poles and mode shapes analytically by using per-symmetry. Compare
your res
Advanced Vibration
Ex. 1
Submit Wed, Feb 2, 2011
Circle your final answers
1. The system shown in the figure below consists of a flexible pendulum of mass m1 and
spring k , of free length L , and a fixed length pendulum of length L and mass m2 , as
shown
After Notes
Lecture 2
Energy methods
2.a. Energy Method (Single Degree of Freedom System)
Another possible way to determine the dynamic of a system is by starting with the
same fundamental properties m, t, r, f, defining the velocity, kinetic energy and
p