Overview

Elements of analytical dynamics, free and forced response of single degree and multi-degree of freedom systems. Dynamic response using modal superposition method. Properties of stiffness and inertia matrices, orthogonality of modal vectors, eigenvalue problem, modal truncation, vibration isolation and suppression. Vibration of bars, shafts, and beams. Supporting laboratory work.

Included in Degrees & Certificates

• 122

Prerequisites

• MA2121
• ME2502
• ME2601
• Or by consent of instructor

Learning Outcomes

At the completion of the course students will be able to:

• Model simple systems: Understand the concept of degrees-of-freedom and determine the number of degrees-of-freedom required to model simple systems. Develop differential equation models of simple mechanical and structural systems using both Newton’s 2nd Law and Lagrange’s equations. Understand and explain damping models in vibration.
• Model multi-degree-of-freedom systems: Understand and explain the relationship between lumped/discrete parameter models, continuous/distributed parameter models, and how these models are used to represent real structures.
• Analyze models developed: Solve a single, and set of, 2nd order homogenous and nonhomogeneous differential equation(s), including the application of initial conditions.
• Understand and explain the concepts of free response, forced response, and frequency response, and their relationships to the homogeneous and particular solutions in the total solution of a vibration problem.
• Understand and explain the concepts of matrix methods in vibration analysis, including eigenvalues and eigenvectors, modal analysis, and orthogonality.
• Understand the use of basic experimental equipment and techniques, including the measurement of transient and frequency response, the use of accelerometers, load cells, shakers, and instrumentation. Understand and explain the use of the FFT in analyzing vibration test data.
• Understand and apply vibration theory: Identify the critical speed of rotating shafts, design vibration isolation, and calculate transmissibility. Understand and apply vibration theory to the solution of Navy and DoD-relevant problems.