Mechanical Vibrations

ME 470: Mechanical Vibrations

Welcome to Mechanical Vibrations. This course develops your skills in vibration modeling and vibration analysis so you can predict vibration response and make design decisions that reduce unwanted motion in real mechanical systems.

Mechanical Vibrations is designed for mechanical and related engineering majors who have completed the core mathematics and introductory mechanics courses. You will use tools such as MATLAB and Mathematica to connect theory with computation, simulation, and engineering interpretation.

You will find files of the lecture slides and Mathematica code in the Box Folder and embedded slides and videos for each section in the “Course Content” tab.

Problem prompts are located in the slides at the top of each section. Be sure to refer to the prompt before watching the problem-solving video.

For Matlab resources, see https://sites.google.com/view/jmm-matlab/

Author

Joseph M. Mahoney, Ph.D.

Chair of Engineering and Associate Professor of Mechanical Engineering, Alvernia University (Reading, PA)

Joseph.Mahoney@alvernia.edu

https://sites.google.com/view/jmmahoney

https://www.linkedin.com/in/jmm694

https://www.youtube.com/@drjmm84

Course modules

The course content is organized into four main modules. Each module comprises several sections, each with its own learning goals, slides, videos, and practice problems.

Module 1: 1DOF systems

Build and analyze single-degree-of-freedom vibration models, including free vibration, forced vibration, damping, resonance, frequency response, and Fourier series foundations for periodic input.

Module 2: Multi-degree-of-freedom systems

Model 2DOF and general MDOF systems using matrices, compute natural frequencies and mode shapes, and apply modal analysis to predict response.

Module 3: Continuous systems

Introduce distributed-parameter vibration models and connect mode shapes and boundary conditions to practical approaches, including finite element analysis for axial and transverse vibrations.

Module 4: Nonlinear systems

Examine simple nonlinear vibration models and compare them to linear systems. Learn when linear approximations are valid and when nonlinear behavior dominates.

Each module page explains where to start, which sections to complete, and how the pieces fit together.

For Visitors and Educators

This site shares teaching materials related to mechanical vibrations and vibration engineering for undergraduate engineering students. Educators and self-learners are welcome to explore the modules and adapt ideas for their own courses.

Please respect copyright and fair use. If you would like to reuse substantial portions of these materials in your own teaching or publications, please contact the instructor to discuss appropriate attribution and permissions.