ME 431

## ME 4600-431: 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:

• Degree-of-freedom
• Single degree-of-freedom systems
1. Modeling-Momentum balance
2. Free vibration-assumed solution
3. Forced vibration
• Multi degree-of-freedom systems: the behavior of an n-dof system is determined by n 1-dof equations. Compare a single-mode solution with general behavior.
1. Modeling-Lagrange's equations
2. Free vibration
3. Forced vibration

Outcomes: This course is expected to address the following highlighted ABET outcomes:
1. Apply energy, momentum, continuity, state and constitutive equations
2. Design and perform laboratory experiments for thermal, fluid and mechanical systems to gather data and test theories.
3. Design thermal, fluid, mechanical and control systems
4. Participate effectively in same-discipline and cross-disciplinary groups
5. Identify, formulate, and solve thermal, fluid, and mechanical engineering problems by applying first principles, including open-ended problems
6. Develop practical solutions for mechanical engineering problems under professional and ethical constraints
7. Communicate effectively with written, oral, and visual means
8. Recognize the fact that solutions may sometimes require non-engineering considerations such as art and impact on society.
9. Be prepared for a lifetime of continuing education.
10. Recognize environmental constraints and safety issues in engineering
11. 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 ()
ASEC-313b
330-972-6302
Lectures: 4600:431-002 M,W,F 9:55am-10:45am; Whitby 210.
Office Hours: tbd
Text: B. Balachandran and E. B. Magrab
Vibrations;
Thomson-Engineering, 2004.
ISBN: 0534395104

Communication Center File No. 394
TA: Jason Miller ()
ASEC
Office Hours: tba