CATALOG DATA:
Examines problems in the vibration of continuous linear elastic structures, including strings, rods, beams, membranes and plates; Hamilton's principle; solution by separation of variables, integral equation and transform methods; variational methods of approximation including the finite element method; computational methods; and elementary random vibrations.Topics:
- Mathematical background and description of vibrating systems: Classification of vibrations, mechanical vibrating systems, modeling of mechanical and structural systems, kinematics of multibody systems, Lagrange's equations of motion, state equations of vibrating systems, ordinary mechanical systems, general linear systems, transformation of linear systems, Eigenvalues and eigenvectors, fundamental matrix, general solution of dynamic systems, damping.
- Analysis of structures modeled as a single-degree-of-freedom system: Response to general dynamic loads, Fourier and Laplace transforms, and response in frequency domain, response spectra, seismic response.
- Analysis of multi-degree-of-freedom systems: Discrete systems, distribution systems, free and forced vibrations, mode displacement and acceleration techniques, reduction of dynamic matrices, dynamic analysis of structures employing finite element models, direct integration methods for dynamic response.
- Introduction to random vibration.
- Applications: Dynamic response of structures to environmental loads, e.g., wind, waves and earthquakes, requirements of building codes and design specifications.
ABET category content as estimated by faculty member who prepared the course description:
Engineering Science: 3 credits or 100%
Engineering Design: 0 creditsPrepared by: Professor Ahsan Kareem
Last Update: March 27, 1992
Direct comments, questions, and corrections to amedept@nd.edu