ME 7442: Vibration of Continuous Systems

Offered Fall, Odd Years


Credit Hours: 3-0-3
Prerequisites: ME 6442 or equivalent, or with the consent of the instructor
Catalog Description: Equations of motion and oscillatory response of dynamic systems modeled as continuous media.
Textbooks: Jerry H. Ginsberg, Mechanical and Structural Vibrations: Theory and Applications, 1st Edition, John Wiley, 2001.
Instructors: A. A. Ferri, J. H. Ginsberg
Topics:

  • Free and forced response of bars: Separation of variables, eigensolutions, geometric, natural, and mixed boundary conditions, structural discontinuities and multi-spans bars, relation to assumed modes solution, orthogonality, modal synthesis, initial value problem, distributed and concentrated forces, Green's function, time-dependent boundary conditions, frequency domain formulation.
  • Approximate methods: Weighted residuals, collocation methods, finite difference approximation of partial differential equations of motion, deflection of beams under moving live loads.
  • Finite elements for bars: Interpolating functions, elemental properties, assembly of elements, connectivity, time-dependent boundary conditions.
  • Substructuring and component mode analysis: review of Lagrange's equations for constrained systems, constraint equations and reactions, application to assumed modes formulation, system equations for connected structural elements.
  • Timoshenko beam theory: partial differential equations accounting for shear deformation and rotatory inertia, natural frequencies and modes, validity of conventional bar theory, modification of Ritz method.
  • Vibration of plates: Equations of motion & boundary conditions by calculus of variations, interpretation, modes of free vibration in Cartesian & polar geometry, orthogonality, forced response by modal analysis, approximate solutions.
  • Selected topics including: Random vibrations, nonlinear vibration of beams, wave propagation in bars, Laplace and Fourier transform methods, transfer function formulation, concepts in dynamic stability, coupling of extension, torsion, and flexure in bars, vibration localization, constrained layer damping in bars, vibration of curved bars, dynamics of shells.
Grading Scheme (%):

Two projects

40 each

Homework

20