ME 431 
ME 4600431: Mechanical Vibrations
What to Know 


Goal: 

What can we understand about the behavior of
mechanical systems in terms of the parameters such as mass,
damping, and stiffness? Specifically, how do the structure and
parameters of a mechanical system affect its dynamical
behavior? 


Requirements: 

This class requires the following knowledge:
 Dynamics (basic concepts of kinematics and kinetics)
 Linear Algebra (vectors, dot products, cross products, etc.)
 Differential Equations



Results: 

Put it all together. Use dynamics to model a
physical system and differential equations to find the resulting
behavior.
In general, to solve any linear differential equation we assume
a solution and then "make it fit". This results in a
characteristic equation, whose solution determines characteristics
of the system, such as frequency of oscillation and decay
rate.
When this class is over, you should understand the following concepts:
 Degreeoffreedom
 Single degreeoffreedom systems
 ModelingMomentum balance
 Free vibrationassumed solution
 Forced vibration
 Multi degreeoffreedom systems: the behavior of an
ndof system is determined by n 1dof
equations. Compare a singlemode solution with general
behavior.
 ModelingLagrange's equations
 Free vibration
 Forced vibration



Outcomes: 

This course is expected to address the following
highlighted ABET outcomes:
 Apply energy,
momentum, continuity, state and constitutive
equations
 Design and perform laboratory
experiments for thermal, fluid and mechanical systems to
gather data and test theories.
 Design thermal, fluid,
mechanical and control systems
 Participate effectively
in samediscipline and crossdisciplinary groups
 Identify, formulate,
and solve thermal, fluid, and mechanical engineering problems
by applying first principles, including openended
problems
 Develop practical
solutions for mechanical engineering problems under
professional and ethical constraints
 Communicate effectively
with written, oral, and visual means
 Recognize the fact that
solutions may sometimes require nonengineering
considerations such as art and impact on society.
 Be prepared for a lifetime of
continuing education.
 Recognize environmental
constraints and safety issues in engineering
 An ability to use
modern modeling and simulation techniques, and computing
tools
The complete list of ABET outcomes and objectives for the ME program
is also
available. 


Professor: 

Dr. Dane Quinn (quinn@uakron.edu)
ASEC313b
3309726302 
Lectures: 

4600:431002 M,W,F 9:55am10:45am; Whitby 210. 
Office Hours: 

tbd 
Text: 

B. Balachandran and E. B. Magrab
Vibrations;
ThomsonEngineering, 2004.
ISBN: 0534395104 


Communication Center File No. 394 
TA: 

Jason Miller (jason31@uakron.edu)
ASEC
Office Hours: tba 
