Text Book:

1. S.S. Rao, Mechanical Vibration, 6th Edition, Prentice-Hall, 2018.

References:

1. W. T. Thomson and M. D. Dahleh, Theory of Vibration with Applications, 5th Edition, Prentice-Hall, 1998.
2. L. Meirovitch, Elements of Vibration Analysis, 2nd Edition, McGraw-Hill, 1986.
3. D. Inman, Engineering Vibration, 3rd Edition, Prentice-Hall, 2007.

Coordinator:

Dynamics and Control TAG

Prerequisites by Topics:

1. System Dynamics
2. Strength of Materials.
3. Linear Algebra: Matrices, Eigenvalues and Eigenvectors.
4. Ordinary Differential Equations.
5. Computer Programming Language, and Mathematics Software Packages (MATLAB, Mathematica,...)
6. Numerical Integration and Numerical Solution of Ordinary Differential Equations.

Learning Objectives[^1]:

1. Formulate the fundamentals of vibration (modeling and characterization) and identify possible causes of vibrations in machines and structures. (1)
2. Apply analytical and numerical methods in vibration analysis of discrete and continuous systems. (1)
3. Apply design principles in vibration control (balancing, isolation, vibration absorber). (1,2)
4. Explain the principle and describe the function of vibration measuring systems. (1)

Topics:

1. Fundamentals of Vibration (Review).
2. Free and Harmonically Excited Vibration of Single Degree-of-Freedom Systems (Review).
3. Vibration under General Forcing Conditions.
4. Multidegree-of-Freedom Systems.
5. Introduction to Continuous Systems.
6. Approximate Methods to Determine Natural Frequencies and Mode Shapes.
7. Vibration Control (balancing, isolation, whirling, absorber).
8. Vibration Measurement Equipment (vibration pickup, accelerometer).

[^1] Numbers in parentheses refer to the student outcomes.

Evaluation Methods

1. Exams.
2. Quizzes.
3. Homework.
4. Computer Assignments.
5. Project.

Learning Outcomes

Upon completion of this course, students will be able to:

Objective 1

1.1 perform analysis of mechanical components, recognize the mass, stiffness, and damping elements in a mechanical system.

1.2 identify the effects of damping, stiffness, inertia, and the change in geometry and dimensions on the dynamic behavior of mechanical systems.

1.3 explain the differences between the various types of excitation that cause the vibration of mechanical system, the difference between linear and nonlinear systems, and the difference between deterministic and random vibration.

Objective 2

2.1 solve the linearized governing equations and find the natural frequencies and mode shapes for multiple-degree of freedom systems.

2.2 derive the equations of motion of continuous systems and determine the natural frequencies.

2.3 model continuous systems as lumped parameter systems and use approximate methods to determine the first natural frequencies and mode shapes.

2.4 compute the steady state response of a mechanical system to a periodic excitation and the transient response to a general excitation.

2.5 use computational tools to determine numerically the natural frequencies of a mechanical system and compute the response of this system to any type of deterministic excitation.

Objective 3

3.1 apply design principles to achieve vibration control, depending on the vibration source (balancing of rotating or reciprocating components, active and passive vibration isolation, and vibration absorber).

Objective 4

4.1 identify the vibration measurement equipment needed in a specific situation, and how the equipment should be installed and utilized.

4.2 identify adequate vibration measuring instruments (vibrometer and accelerometer).

Course Classification