Class Notes for Vibrational Analysis
(MEAM321)
Michael A. Carchidi
September 7, 2010
Chapter 1 - Introduction to Periodic Motion
The following notes were initially based around the text entitled: Theory of
Vibrations with Applications (5th Edition) by Wil

MEAM321 - Theory of Vibrations (Extra Practice Problems)
Fall Semester, 2011
M. Carchidi
Problem #1
Four blocks of masses m, 2m, 2m, and m, are connected to each other and
to two walls by 7 ideal springs having the stiness constants shown in the
gure belo

MEAM321 - Theory of Vibrations (Final Exam)
Fall Semester, 2011
M. Carchidi
Problem #1 (25 points)
The gure below shows the static deection shape of a uniform beam of mass
m and length L that is clamped at the left end (x = 0) and simply-supported
at the

MEAM321 Recitation
Jan. 27, 2015 (Tue)
Problem 1 (Last week) Assuming that the phase angle is zero, show that the response x(t) of
an underdamped single-degree-of-freedom system reaches a maximum value when
p
sin d t = 1 2
and show that the equations of t

MEAM321 Recitation 5
Feb. 17, 2015 (Tue)
Forced Vibration without Damping
If we make the damping term cx to be zero, therefore:
m
x + kx = P0 sin t
Assuming the solution has the form x = x0 sin t, substitude it into above equation and get:
x=
P0 /k
sin t

MEAM321 Recitation 6
Feb. 24, 2015 (Tue)
Response to Half-sine Pulse In the lecture, we have discussed pulses of Rise time and Rectangular pulse. Here is another common pulse of Half-sine as shown in Figure 1. The excitation
is:
t
for
t < t1 ;
F (t) = F0

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d extensive y in dome, ~- yum
ties, applhncz:
Sometimes such mom h?"
h
Small single-phase motors are use
washing machines, etc.
like refrigerators, varies considerably. in the rst construction (Fig. 2.4

MEAM321 - Theory of Vibrations (Homework #4)
Fall Semester, 2012
M. Carchidi
Problem #1 (20 points)
The gure below shows a mass m connected to an ideal spring of constant
k.
The Spring/Mass System
An external horizontal force F (t) = F0 sin5 ( t) is appli

MEAM321 - Vibrations (Homework #2)
Fall Semester, 2012
M. Carchidi
Problem #1 (20 points) - A Compound Pendulum
The gure below shows three uniform solid disks (each of mass m and radius
R) and three uniform rods (each also of mass m but length L = 3R) suc

MEAM321 - Theory of Vibrations (Practice Problems)
Fall Semester, 2010
M. Carchidi
Problem #1 (20 points)
Do Problem 5.11 and 5.12 on page 153 of the text Theory of Vibration with
Applications by William T. Thomson and Marie Dillion Dahleh.
Problem #2 (20

Class Notes for Vibrational Analysis
(MEAM321)
Michael A. Carchidi
December 3, 2010
Chapter 9 - Vibration of Continuous Systems
The following notes are based on the text entitled: Theory of Vibrations with
Applications (5th Edition) by William T. Thomson

Class Notes for Vibrational Analysis
(MEAM321)
Fall Semester, 2008
Michael A. Carchidi
December 3, 2010
Chapter 14 - Nonlinear Vibrations: One Degree-of-Freedom
The following notes are based on the text entitled: Theory of Vibrations with
Applications (5t

Class Notes for Vibrational Analysis
(MEAM321)
Michael A. Carchidi
October 8, 2010
Chapter 3 - Harmonically Excited Vibrations: One
Degree-Of-Freedom
The following notes were initially based around the text entitled: Theory of
Vibrations with Applications

Class Notes for Vibrational Analysis
(MEAM321)
Michael A. Carchidi
November 10, 2010
Chapter 6 - Properties of Systems With Two Or More
Degrees-Of-Freedom
The following notes are based on the text entitled: Theory of Vibrations with
Applications (5th Edit

Class Notes for Vibrational Analysis
(MEAM321)
Michael A. Carchidi
September 16, 2010
Chapter 2 - Free Vibrations: One Degree-of-Freedom
The following notes were initially based around the text entitled: Theory of
Vibrations with Applications (5th Edition

Part a
syms t n q sigma
H = 8;
a = 2;
k = 9*10^9;
%a = pi*k*q*sigma/m;
tau = 4*sqrt(H/a);
w = 2*pi*n/tau;
%y(t) functions
y1 = H - a*t^2;
y2 = a*(t-tau/2)^2 - H;
y3 = H - a*(t-tau)^2;
%coefficients
%k kept symbolic in these calculations for aethetic reaso

MEAM321 - Theory of Vibrations (Homework #6)
Fall Semester, 2012
M. Carchidi
Problem #1 (25 points)
A block of mass mB is held at the top of a frictionless incline plane of
xed angle , length L, and mass mI that rests of a frictionless tabletop.
The incli

MEAM321 - Theory of Vibrations (Homework #4)
Fall Semester, 2011
M. Carchidi
Problem #1 (20 points)
A mass m is connected to an ideal spring of constant k and conne to
move only in the horizontal direction. Initially the mass is at rest at the
equilibrium

MEAM321 - Vibrations (Homework #3)
Fall Semester, 2012
M. Carchidi
Problem #1 (30 points) - Spring and Damper Networks
The gure for this problem shows a block of mass m = 6.2 kg connected to
a combination of 5 springs and 3 dampers.
k2
k5 , m5
k4
k1
k3
m

MEAM321 - Vibrations (Take-Home Section for Exam #1)
Fall Semester, 2012
M. Carchidi
Problem #1 (20 points) - Computing The Period of Periodic Motion
The gure below shows a uniform rigid rod of mass m and length L = R 2
that is free to slide without frict