ME 6442: Vibration of Mechanical Systems

Offered Every Spring


Credit Hours: 3-0-3
Prerequisites: ME 3015 and ME 3201
Catalog Description: Introduction to modeling and oscillatory response analysis for discrete and continuous mechanical and structural systems.
Textbooks: Jerry H. Ginsberg; Mechanical and Structural Vibrations: Theory and Applications, 1st Edition, John Wiley, 2001.
Instructors: Kenneth Cunefare, Aldo Ferri, and Jerry Ginsberg
Topics:
  • Equations of motion: Review of dynamics of planar motion, introduction to Lagrange's equations, linearization, lumped system parameters, inertial and stiffness coupling, numerical methods for differential equations of motion.
  • Linear vibration of a single degree of freedom systems with damping: free vibration, Coulomb friction, response to harmonic excitation, beating and resonant response, Fourier series solution for periodic excitation, transient response by superposition, convolution integrals, numerical methods, application of FFT algorithms.
  • Free motion of undamped multiple degree of freedom systems: General equations of motion, formulations using stiffness or flexibility matrix, eigenvalue problem for natural frequencies and modes, application of numerical methods, rigid body modes and repeated frequencies, orthogonality of modes.
  • Forced response of undamped multiple degree of freedom systems: modal analysis - principal coordinates and uncoupled equations, response to initial conditions, steady-state response to harmonic excitation, vibration absorbers, transient response.
  • Damping in multiple degree of freedom systems: modal analysis for proportional and light damping, frequency domain transfer functions, vibration absorbers, application of FFT's for transient response, damped modes in the state-space, modal analysis using damped modes.
  • Continuous systems by the Ritz method: Hamilton's principle for extensional and flexural deformation of bars, geometric and natural boundary conditions, elastic and inertial attachments, basis functions for Ritz series, discretized equations, natural frequencies and displacement mode shapes, orthogonality, forced response, time-dependent boundary conditions
  • Topics selected from: response of gyroscopic systems, dynamic stability of beams, pipes with ineternal fluid flow, and rotating shafts, random vibrations, basic concepts for finite element analysis, nonlinear vibration of single-degree-of freedom systems
Grading Scheme (%):

Homework

20

Project

20

Midterm

30

Final

50