Notice: For the latest information and guidance on Purdue's response to COVID-19 please visit:

Mechanical Vibrations


Credit Hours:


Learning Objective:

Upon successful completion of this course, you will be able to understand basic and intermediate concepts necessary for the analysis of the dynamics of complex structures under various loading conditions. In particular, you will be able to:
  • Explain and correlate the structural properties of complex structures to the overall vibration characteristics in order to design systems having required dynamical properties.
  • Apply theoretical and numerical procedures to predict the dynamic response of discrete or continuous structural systems under the most diverse loading conditions.
  • Develop reduced order models to treat systems with a large number of DOF.
  • Understand and implement approximate methods for the numerical solution of distributed parameter systems.
  • Understand the main features of the dynamics of nonlinear lumped parameters systems.


The course will cover fundamental concepts on the vibration of mechanical systems including, but not limited to, review of systems with one degree for freedom, Lagrange's equations of motion for multiple degree of freedom systems, introduction to matrix methods, transfer functions for harmonic response, impulse response, and step response, convolution integrals for response to arbitrary inputs, principle frequencies and modes, applications to critical speeds, measuring instruments, isolation, torsional systems, introduction to nonlinear problems. Fall 2016 syllabus

Topics Covered:

Dynamics of Single Degree Of Freedom (SDOF) systems; Dynamics of Multiple Degree Of Freedom (MDOF) systems; Damping; Fundamentals of analytical dynamics; Numerical techniques for the response of dynamical systems; Dynamics of continuous systems; Analytical and approximate solutions of continuous systems; Intro to the dynamics of discrete nonlinear systems and perturbation techniques; Static and dynamic reduction.


Strength of materials; modeling and analysis of dynamical systems.

Applied / Theory:

30 / 70


Homework will be assigned following completion of major topics. The homework will require the use of a software like Matlab.




One midterm exam and a final exam.


Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
Required text --Course lecturebook: "Mechanical Vibrations: A lecturebook", Chuck Krousgrill and Jeff Rhoads. The course lecturebook is required and will be available for purchase at the University Bookstore (typically available two weeks before class).

Computer Requirements:

ProEd minimum computer requirements. Matlab is suggested (available via Software Remote, but students are free to use whatever they feel more comfortable with (Mathematica, Maple etc.).

ProEd Minimum Requirements: