MEM423 Mechanics of Vibrations
Fall 2013
Home work #1;
Due 10/03/13
Objective: Review background material ; develop schematics
Problem 1:
Solve the following differential equation, ie. determine x(t), and plot x(t) over a reasonable
period of time (plot m

MEM423 Mechanics of Vibrations
Summer 2013
Home work #1;
Due 07/09/13
(ABET a-to-k allocation: 1(a), 2(a,k), 3(a,k)
Problem 1:
Solve the following differential equation, ie. determine x(t), and plot x(t) over a reasonable
period of time:
Problem 2:
Consid

MECHANICAL ENGINEERING AND MECHANICS
MEM 423 M ECHANICS OF VIBRATIONS
F ALL 2013-14
Designation:
Elective
Catalog Description:
Reviews Laplace transforms, linear algebra, and modeling of basic
mechanical systems; covers modeling and analysis of multi DOF

MEM 423: Mechanics of Vibrations
_ Mid-term Examination I take-home Team project relevance to a-k criteria: {a, b, e, g, k} Summer 2007-08 due: 08/16/08 11:59 PM submit electronic copies(pdf or word) to Halim, with cc to me _
Consider a bridge repr

MEM423 Mechanics of Vibrations
Fall 2013
Home work #1;
Due 10/03/13
Objective: Review background material ; develop schematics
Problem 1:
Solve the following differential equation, ie. determine x(t), and plot x(t) over a reasonable
period of time (plot m

MEM423 Mechanics of Vibrations
Summer 2013
Home work #3;
Due 07/25/2013
(ABET a-to-k allocation: (a,e);
Performance Indicators: (p1,p2,p5,p6)
Home work #4 (due 08/01/2013)
Problem 1:
Consider the 3-disc system from Home Work #3. Let J = 2 kg-m2 and k = 2

MEM 423 MECHANICS OF VIBRATIONS
TEAM C Lakir Patel Chris Esposito Erica Shwarz Sara Acklin
MEM 423 Mechanics of Vibrations Patel, Shwarz, Esposito, Acklin
Introduction: The study of Vibration analysis is crucial to science, due to the fact tha

MEM423 Mechanics of Vibrations
Summer 2013
Home work #2;
Due 07/25/2013
(ABET a-to-k allocation: (a,e);
Performance Indicators: (p1,p2,p5,p6)
Problem 1:
Consider the 3-disc system given below. The moment of inertia of each disc is denoted by
Ji. All rods

HWK Week 2 Class 1 (Tuesday, 4/5/16)
MEM 423 Spring 16, Dr. Antonios Kontsos
Refer to sections 2.6 and 2.9 from the textbook.
(Work #2.113 only, which corresponds to Figure 2.111 below.)

HWK10 Week 8 Class 2
MEM 423 SP16
Using the same approach shown in class, derive the equation that allows for the solution of the
natural frequencies and mode shapes to be determined (i.e. the frequency equation, whose roots
are used to determine the natu

MEM 423: Mechanics of Vibrations
(Coulumb Friction)
Dr. Ajmal Yousuff
Dept. MEM
Drexel University
A system with viscous damping
Consider a spring-mass system:
mx kx f ; x(0) x0 , x(0) 0
If f is due to viscous damping ( f x) ,we get
mx+kx=-cx
Note: the dam

MEM423:mechanicsofVibrations
Home work #1 (due 07/01/10)
from text, Edition IV
Problem: 2.62 . And
(i)
In case c, discuss the response of the system if a m < l p where
p and m are the natural frequencies of a traditional pendulum
and a spring-mass system

MEM423 Mechanics of Vibrations
Fall 2013-14
Midterm Exam 1: October 17, 2013
Open book and notes; you may use laptop but only for referring to text and notes usage of matlab is forbidden.
Problem 1 (15%):
An object weighing 1N (in a field of gravity of 1

MEM423 Mechanics of Vibrations
Fall 2013
Home work #3;
Due 10/31/2013
objectives: model development, analysis.
Problem 1:
Consider the 3-disc system given below. The moment of inertia of each disc is denoted by
Ji. All rods are mass-less with torsional el

MEM423 Mechanics of Vibrations
Summer 2013
Home work #3;
Due 07/25/2013
(ABET a-to-k allocation: (a,e);
Performance Indicators: (p1,p2,p5,p6)
Home work #4 (due 08/01/2013)
Problem 1:
Consider the 3-disc system from Home Work #3. Let J = 2 kg-m2 and k = 2

MEM 423: Mechanics of Vibrations
(simulation setup)
Dr. Ajmal Yousuff
Dept. MEM
Drexel University
State-space model
(1)
Define states as:
Yousuff
MEM423 Vibrations
2
simulation
Have a model
Analysis: (response to excitations)
x Ax Bu;
q
0
x ; A
q
M 1K

MEM423: Mechanics of Vibrations
(examples)
Dr. Ajmal Yousuff
Dept. MEM
Drexel University
Schematics of a hand
DOFs: cfw_x1, x2, x3, y3, 3.
cfw_x4, y4, are dependent.
is a reference, need not be horizontal.
yousuff
MEM423: Vibrations
5
Energy expression
I

Dr. Ajmal Yousuff
Dept. MEM
Drexel University
MEM 423: Mechanics of Vibrations
(Continuous Systems: lumped parameter approach)
Continuous Systems
Continuous systems are modeled by partial
differential equations (pde)
Y
w(x,y,t)
Lateral vibration:
x
dm
y

MEM 423: Mechanics of Vibrations
(Frequencies & mode shapes; Chapter 5)
Dr. Ajmal Yousuff
Dept. MEM
Drexel University
Overview
An example 5.1; 2 dof
Model
Solution
Frequencies
Mode shapes
Relation to eigenvalues & eigenvectors
Section 5.2 in text
Yousuff

MEM423: Mechanics of Vibrations
(Transformations & Lagranges Eqn.)
Dr. Ajmal Yousuff
Dept. MEM
Drexel University
Overview
Transformation of coordinates
Principal coordinates
Excitation of a specific mode
Modeling approach
DAlemberts Approach
Lagrang

MEM423 Mechanics of Vibrations
(1.10, 2.1-2.3, 2.6)
Dr. Ajmal Yousuff
Dept. Mech. Engg. & Mechanics
Drexel University
Vibrations (1-DOF)
Degrees of Freedom:
The (minimum # of) variables needed to describe the
dynamics of the system.
K1
K2
M1
mass
x1
You

MEM 423 Mechanics of Vibrations
Dr. Ajmal Yousuff
Dept. Mech. Engg. & Mechanics
Drexel University
Introduction - Personnel
Dr. Ajmal Yousuff
Associate Professor, Dept. MEM
Rm. AEL-171B, x 1868
[email protected]
Office hours: TR: 12:00-02:00 + ?
TA:
R

MEM423 Mechanics of Vibrations
Fall 2013
Home work #2;
Due 10/10/2013
objectives: model development, analysis.
Problem 1:
Problem 2.67 from text. And
(i)
In case c, discuss the response of the system if where p and m .
(ii) With the numerical values , plo

MEM423 Mechanics of Vibrations
Fall 2013
Home work #2;
Due 10/10/2013
objectives: model development, analysis.
Problem 1:
Problem 2.67 from text. And
(i)
In case c, discuss the response of the system if where p and m .
(ii) With the numerical values , plo

MEM423:MechanicsofVibrations
_
Mid-term Examination I
Summer 2009-2010
Allotted time: 1hr. 30 min.
_
Problem I: (50%)
The equations of motion, from class lectures,
In the special case these become
To determine the frequencies, find from :
Finad the modal