MAE 4730

Intermediate Dynamics and Vibrations

Course Description

Course information provided by the Courses of Study 2015-2016.

The course emphasizes the dynamics and vibrations of multi-degree-of-freedom systems including particles, rigid-objects and structures in 2 dimensions using three approaches: Newton-Euler, Lagrangian approach, both using minimal co- ordinates, and also a 'maximal coordinate' approach using differential algebraic equations (DAEs). The course emphasizes finding equations of motion, solving them analytically (if possible) and numerically; and graphical presentation of solutions. Vibrations topics include modal analysis of discrete systems, including analysis of damped systems using the matrix exponential. Special topics, such as vibration absorbers and vibration control, are introduced.

When Offered Fall.

Prerequisites/Corequisites Prerequisite: MATH 2940, MAE 3260 or equivalents, or permission of instructor.

• Given a description in sketches and/or simple words, for a variety of dynamical mechanical systems consisting of particles and rigid objects interacting with various standard connections (e.g., strings, springs, hinges, rolling, surface sliding) and forces (e.g., gravity, friction), the student should be able to find the governing differential equations, solve the simple cases by hand, solve the more complex cases with numerical integration (MATLAB), graphically represent the results, including animations, and check the reasonableness of the results using extreme cases and conservations laws (momentum, angular momentum and energy).
• Students will be proficient at writing Lagrange equations for simple conservative systems.
• Students will understand and be able to do analysis associated with vibrations of multi-degree-of-freedom and continuous systems.
• Students will understand means of controlling vibrations using absorbers and elementary feedback approaches.

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